{"id":54,"date":"2026-04-30T15:02:49","date_gmt":"2026-04-30T07:02:49","guid":{"rendered":"http:\/\/49.232.244.149\/?p=54"},"modified":"2026-04-30T15:15:59","modified_gmt":"2026-04-30T07:15:59","slug":"%e7%ae%97%e6%b3%95%e6%80%9d%e6%83%b3","status":"publish","type":"post","link":"https:\/\/www.everfades.cn\/index.php\/2026\/04\/30\/%e7%ae%97%e6%b3%95%e6%80%9d%e6%83%b3\/","title":{"rendered":"\u7b97\u6cd5\u601d\u60f3"},"content":{"rendered":"\n

\u2014\u2014by Everfades<\/h4>\n\n\n\n

\uff08\u26a0\ufe0f\u5fc5\u8bfb\uff09\u672c\u7b14\u8bb0\u4e3b\u8981\u9488\u5bf9\u4e8e\u8f83\u4e3a\u6838\u5fc3\u7684\u516d\u5927\u7b97\u6cd5(\u4e3b\u89c2\u5411) \u679a\u4e3e\u3001\u8d2a\u5fc3\u3001\u5206\u6cbb\u3001\u56de\u6eaf\u3001\u641c\u7d22\u3001dp(\u52a8\u6001\u89c4\u5212)<\/strong> \u8fdb\u884c\u8bb0\u5f55\uff0c\u4e3b\u8981\u9762\u5411\u60f3\u8981\u53c2\u52a0\u7b97\u6cd5\u7ade\u8d5b\uff0c\u5177\u6709\u4e00\u5b9a\u7f16\u7a0b\u57fa\u7840\uff0c\u5e0c\u671b\u63d0\u5347\u7b97\u6cd5\u80fd\u529b\u7684\u540c\u5b66\uff0c\u8fd9\u91cc\u4f1a\u901a\u8fc7\u7b97\u6cd5\u8f85\u4ee5\u7ade\u8d5b\u771f\u9898\u8fdb\u884c\u8bb2\u89e3\u3002\u867d\u7136\u7b97\u6cd5\u6709\u5f88\u591a\u79cd\uff0c\u4f46\u662f\u57fa\u672c\u6240\u6709\u7684\u5176\u4ed6\u7b97\u6cd5\uff0c\u90fd\u662f\u53ef\u4ee5\u4ece\u4e0a\u8ff0\u7684\u516d\u5927\u7b97\u6cd5\u4e2d\u884d\u751f\u51fa\u6765\u7684\u3002<\/p>\n\n\n\n

\u9274\u4e8e\u7b14\u8005\u6c34\u5e73\u6709\u9650\uff0c\u90e8\u5206\u793a\u4f8b\u4ee5\u53ca\u4ee3\u7801\u53ef\u80fd\u5b58\u5728\u4e0d\u89c4\u8303\u7684\u4e66\u5199\uff0c\u751a\u81f3\u5b58\u5728\u7eb0\u6f0f\uff0c\u4e8e\u6b64\u8fd8\u671b\u89c1\u8c05\uff0c\u5982\u679c\u60a8\u6709\u5b9d\u8d35\u7684\u610f\u89c1\u6216\u5efa\u8bae\uff0c\u8bf7\u53d1\u90ae\u4ef6\u81f3:everfades1218@gmail.com<\/a>\u6216everfades@foxmail.com<\/a><\/p>\n\n\n\n

\u5e0c\u671b\u5927\u5bb6\u80fd\u4ece\u8fd9\u7bc7\u7b14\u8bb0\u4e2d\u53d6\u5f97\u4e00\u4e9b\u6536\u83b7\uff01<\/p>\n\n\n\n

\uff08\u26a0\u5728\u4f7f\u7528Typora\u9605\u8bfb\u524d\uff0c\u8bf7\u5c06\u6587\u4ef6\u2192\u504f\u597d\u8bbe\u7f6e\u2192Markdown\u2192\u5185\u8054\u516c\u5f0f \u52fe\u9009\u4e0a\uff0c\u4ee5\u514d\u663e\u793a\u51fa\u9519\uff01\uff09<\/p>\n\n\n\n

Part 1\uff1a\u679a\u4e3e<\/h2>\n\n\n\n

\ud83d\udcd5\u679a\u4e3e<\/h3>\n\n\n\n

\u5728\u8bb8\u591a\u6559\u7a0b\u4e2d\u4e2d\uff0c\u679a\u4e3e\u7b97\u6cd5\u7ecf\u5e38\u4f1a\u548c\u904d\u5386\uff0c\u66b4\u529b\uff0c\u751a\u81f3brute force\u7b97\u6cd5\u76f8\u6df7\u6dc6\uff0c\u5728\u63a5\u4e0b\u6765\u7684\u7b14\u8bb0\u4e2d\uff0c\u4f1a\u8be6\u7ec6\u7684\u5bf9\u679a\u4e3e\u7b97\u6cd5\u8fdb\u884c\u5256\u6790\uff0c\u63ed\u793a\u679a\u4e3e\u7b97\u6cd5\u7684\u6838\u5fc3\u6240\u5728\u3002<\/p>\n\n\n\n

\u9996\u5148\uff0c\u6211\u4eec\u4e0d\u59a8\u5bf9\u679a\u4e3e\u7b97\u6cd5\u4e0b\u4e2a\u5b9a\u4e49<\/p>\n\n\n\n

\n

\u679a\u4e3e\u7b97\u6cd5\u2193<\/p>\n\n\n\n

\u5728\u67d0\u4e2a\u5305\u542b\u53ef\u80fd\u7684\u89e3\u7684\u96c6\u5408<\/strong>\u4e2d\uff0c\u6309\u67d0\u4e2a\u987a\u5e8f<\/strong>\u4f9d\u6b21\u68c0\u9a8c\u5143\u7d20\uff0c\u5e76\u7528\u9898\u76ee\u6240\u7ed9\u7684\u7ea6\u675f\u6761\u4ef6<\/strong>\u8fdb\u884c\u6821\u9a8c\u6216\u8ba1\u7b97<\/strong><\/p>\n<\/blockquote>\n\n\n\n

\u8fd9\u4e48\u8bf4\u53ef\u80fd\u6709\u70b9\u62bd\u8c61\uff0c\u6211\u4eec\u53ef\u4ee5\u4e3e\u4e2a\u4f8b\u5b50\u6765\u8bf4\u660e\u4e00\u4e0b\uff1a\u7ed9\u5b9a\u4e00\u4e2a\u6570\u7ec4\uff0c\u5224\u65ad\u662f\u5426\u5b58\u5728\u5947\u6570<\/strong>\uff0c\u90a3\u4e48\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u96c6\u5408\u5c31\u662f\u7ed9\u5b9a\u7684\u6570\u7ec4<\/strong>\uff0c\u987a\u5e8f\u53ef\u4ee5\u662f\u6b63\u5411\u6216\u8005\u53cd\u5411\u90fd\u884c<\/strong>\uff0c\u6761\u4ef6\u5c31\u662f\u5143\u7d20\u662f\u5426\u4e3a\u5947\u6570<\/strong>\u3002<\/p>\n\n\n\n

\u5bf9\u4e8e\u8fd9\u79cd\u662f\u5426\u5b58\u5728<\/strong>\u7684\u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u79f0\u5176\u4e3a any of \u679a\u4e3e<\/strong>\uff0c\u6216\u8005 find if \u679a\u4e3e<\/strong>\uff0c\u76ee\u7684\u5728\u4e8e\u627e\u5230\u4e00\u4e2a\u7b26\u5408\u6761\u4ef6\u7684\u5143\u7d20\u3002\u5f53\u7136\u6211\u4eec\u4e5f\u53ef\u4ee5\u53d8\u5f62\u4e00\u4e0b\uff0c\u63a8\u5e7f\u51fa all of \u679a\u4e3e<\/strong>\uff0c none of \u679a\u4e3e<\/strong>\uff0c\u5728\u672c\u4f8b\u5b50\u4e2d\uff0c\u5373\u6240\u6709\u5143\u7d20\u90fd\u662f\u5947\u6570( all of )\uff0c\u6216\u6240\u6709\u5143\u7d20\u90fd\u4e0d\u662f\u5947\u6570( none of )\u3002\u5bf9\u4e8e\u8fd9\u4e09\u79cd\u679a\u4e3e\u6765\u8bf4\uff0c\u6734\u7d20\u7684\u5199\u6cd5\u9700\u8981\u8bbe\u7f6e\u4e00\u4e2a flag \u6765\u6807\u6ce8\u662f\u5426\u7b26\u5408\u9898\u610f\uff0c\u8fd9\u91cc\u5c31\u4e0d\u8fc7\u591a\u5c55\u5f00\u4e86\u3002\u6211\u4eec\u66f4\u591a\u4f1a\u4f7f\u7528STL\u5e93\u4e2d\u7684\u51fd\u6570\uff0c\u6bd4\u5982 any_of \uff0call_of \uff0cnone_of \uff0cfind_if \uff0c max_element \uff0c min_element \uff0c accumulate<\/strong> \u7b49\uff0c\u8fd9\u4e9b\u51fd\u6570\u90fd\u662f \u201c \u6cdb\u578b\u6a21\u677f\u51fd\u6570 \u201d<\/strong> \uff0c\u53ef\u4ee5\u7528\u4e8e\u4efb\u610f\u7c7b\u578b\u7684\u6570\u636e\uff0c\u4ee5\u4e0a\u7b97\u662f\u679a\u4e3e\u6700\u57fa\u7840\u7684\u6a21\u578b\u3002<\/p>\n\n\n\n

\u6211\u4eec\u518d\u6765\u770b\u4e2a\u8fdb\u9636\u4e00\u70b9\u7684\uff1a\u5728\u4e00\u4e2a\u6570\u7ec4\u4e2d\uff0c\u5224\u65ad\u662f\u5426\u5b58\u5728\u5b50\u6570\u7ec4\uff1f<\/p>\n\n\n\n

\n

\u539f \u6570 \u7ec4\uff1a E V E R F A D E S<\/p>\n\n\n\n

\u76ee\u6807\u6570\u7ec4\uff1a E V A<\/p>\n<\/blockquote>\n\n\n\n

\u5b50\u6570\u7ec4\u7684\u610f\u601d\u662f\uff0c\u4ece\u539f\u6570\u7ec4\u4e2d \u6309\u987a\u5e8f\u53d6\u51fa<\/strong> \u82e5\u5e72\u4e2a\u5143\u7d20\uff0c\u7ec4\u6210\u4e00\u4e2a\u65b0\u6570\u7ec4\u7b49\u4e8e\u76ee\u6807\u6570\u7ec4\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u5957\u7528\u57fa\u7840\u7684\u6a21\u578b\uff0c\u76f8\u4fe1\u6709\u806a\u660e\u7684\u540c\u5b66\u5df2\u7ecf\u660e\u767d\u89e3\u6cd5\u4e86\uff0c\u6211\u4eec\u53ef\u4ee5\u7528 find<\/strong> if<\/strong> \u7684\u6a21\u578b\u53bb\u5224\u65ad\u7b2c\u4e00\u4e2a\u5143\u7d20\uff0c\u67e5\u627e\u6210\u529f\u5219\u518d\u53bb\u5224\u65ad\u7b2c\u4e8c\u4e2a\u5143\u7d20\uff0c\u67e5\u627e\u6210\u529f\u5219\u518d\u53bb\u5224\u65ad\u7b2c\u4e09\u4e2a\u5143\u7d20……<\/p>\n\n\n\n

\u90a3\u4e48\u8fd9\u91cc\u6709\u4e00\u4e2a\u95ee\u9898\uff0c\u5b58\u5728\u5b50\u6570\u7ec4\u7684\u7684\u5224\u65ad\u6761\u4ef6\uff0c\u6216\u8005\u8bf4\u8bbe\u7f6e\u7684 flag \u662f\u4ec0\u4e48\u5462\uff1f\u6211\u4eec\u76f4\u63a5\u6765\u770b\u6a21\u677f\u51fd\u6570<\/p>\n\n\n\n

template <typename T>
bool subMatch(constT &arr, const T &target) {
    size_t idx = 0;
    for (auto &elem : arr) {
        if (elem == target[idx]) {
            if (++idx ==target.size()) return true;
        }
    }
    return false;
}<\/pre>\n\n\n\n
\u4ece\u8fd9\u4e2a\u51fd\u6570\u6a21\u677f\u4e2d\uff0c\u6211\u4eec\u4e0d\u96be\u770b\u51fa\uff0c\u5728\u904d\u5386 arr \u4e2d\u7684\u5143\u7d20\u65f6\uff0c\u6bcf\u5f53 elem ==target[idx] \u7684\u8fd4\u56de\u503c\u4e3a true\uff0cidx\u7684\u503c\u90fd\u4f1a +1 \uff0c\u76f4\u5230 idx \u7684\u503c\u4e0e target.size \u76f8\u7b49\uff0c\u5373\u5b50\u6570\u7ec4\u7684\u5927\u5c0f\u4e0e\u6211\u4eec\u7684\u76ee\u6807\u6570\u7ec4\u7684\u5927\u5c0f\u76f8\u7b49\u65f6\uff0c\u518d return true \uff0c\u4ee3\u8868\u627e\u5230\u4e86\u8fd9\u6837\u4e00\u4e2a\u5b50\u6570\u7ec4\uff0c\u5426\u5219\u8fd4\u56de false\u3002<\/p>\n\n\n\n
\u518d\u6765\u8bf4\u5bf9\u4e8e\u679a\u4e3e\u7684\u4f18\u5316\uff0c\u6bd4\u5982\u56de\u6587\u4e32\u7684\u679a\u4e3e ( \u5173\u4e8e\u56de\u6587\u4e32\uff0c\u6709\u4e00\u4e2a\u7ecf\u5178\u7684\u7b11\u8bdd\uff0c(()) \u4e0d\u662f\u56de\u6587\u4e32\uff0c())( \u624d\u662f )<\/del><\/p>\n\n\n\n
int n = str.size();
for(int i = 0; i < n; i++){
    if(str[i] != str[n - i - 1]){
        return false;
    }
}<\/pre>\n\n\n\n
\u6839\u636e\u5b9a\u4e49\uff0c\u56de\u6587\u4e32\u7684\u6bcf\u4e2a\u5b57\u7b26\u5e94\u8be5\u548c\u5b83\u5bf9\u79f0\u4f4d\u7f6e\u7684\u5b57\u7b26\u76f8\u540c\uff0c\u56e0\u6b64\u6211\u4eec\u53ea\u9700\u8981\u679a\u4e3e\u524d\u4e00\u534a\u5c31\u53ef\u4ee5\u4e86\uff0c\u56e0\u4e3a\u540e\u4e00\u534a\u7684\u7ed3\u679c\u548c\u524d\u4e00\u534a\u4e00\u5b9a\u662f\u76f8\u540c\u7684<\/p>\n\n\n\n
int n = str.size();
for(int i = 0; i < n \/ 2; i++){
    if(str[i] != str[n - i - 1]){
        return false;
    }
}<\/pre>\n\n\n\n
\u6700\u540e\u518d\u6765\u8bf4\u4e00\u4e2a\u5e38\u89c1\u7684\u5199\u6cd5\u2014\u2014\u6309\u4f4d\u679a\u4e3e<\/strong>\uff1a\u679a\u4e3e\u4e00\u4e2a\u6574\u6570\u7684\u6bcf\u4e00\u4f4d\uff0c\u7136\u540e\u8fdb\u884c\u9898\u76ee\u8981\u6c42\u7684\u5224\u65ad\u3002\uff08 <\u2014 \u8fd9\u4e2a\u7528\u5230\u7684\u6bd4\u8f83\u591a \uff09<\/strong><\/p>\n\n\n\n
for( ; x; x \/= base){   \/\/base \u4ee3\u8868\u8fdb\u5236\u6570
    int digit = x % base;
    \/\/do something
}<\/pre>\n\n\n\n
\u5982\u679c\u6211\u4eec\u5c06\u679a\u4e3e\u51fa\u7684\u6bcf\u4e00\u4f4d\u5b58\u50a8\u5230\u6570\u7ec4\u4e2d\uff0c\u90a3\u5c31\u662f\u5c06\u6574\u6570\u8f6c\u5316\u6210\u5176\u4ed6\u8fdb\u5236<\/p>\n\n\n\n
vector<int> toDigits(int x, int base) {
    vector<int> digits;
    for( ; x; x \/= base){
        int digit = x % base;
        digit.push_back(digit); \/\/\u5728\u961f\u5217\u5c3e\u90e8\u63d2\u5165\uff0c\u800c\u4e0d\u662f\u50cf\u6570\u7ec4\u4e00\u6837\u5728\u5934\u90e8\u63d2\u5165\uff0c\u53ef\u4ee5\u5c11\u4e00\u6b65\u7ffb\u8f6c
    }
    return digits;
}<\/pre>\n\n\n\n
\u518d\u901a\u8fc7\u53e6\u4e00\u4e2a\u51fd\u6570\uff0c\u6211\u4eec\u8fd8\u80fd\u5c06\u6570\u7ec4\u8fd8\u539f\u56de\u539f\u6765\u7684\u6574\u6570<\/p>\n\n\n\n
int toDigit(vector<int> &digits, int base) {
    int x = 0;
    for(int i = digits.size() - 1; i >= 0; i--) {
        x = x * base +digits[i];    
    }
    return x;
}<\/pre>\n\n\n\n
\u6700\u540e\uff0c\u6211\u4eec\u5e94\u8be5\u4e3a\u679a\u4e3e\u7b97\u6cd5\u8ba8\u4e2a\u516c\u9053\uff0c\u5b83\u5e76\u4e0d\u7b49\u4ef7\u4e8e\u66b4\u529b\u7b97\u6cd5\uff0c\u56e0\u4e3a\u66b4\u529b\u8fd9\u4e2a\u8bcd\u662f\u76f8\u5bf9\u7684\uff0c\u6709\u4e9b\u9898\u5b83\u7684\u6b63\u786e\u89e3\u6cd5\u5c31\u662f\u679a\u4e3e\uff1b\u5b83\u4e5f\u4e0d\u7b49\u4ef7\u4e8e\u904d\u5386\u7b97\u6cd5\uff0c\u56e0\u4e3a\u904d\u5386\u7684\u610f\u601d\u662f\u6309\u67d0\u4e2a\u987a\u5e8f\u8bbf\u95ee\u6570\u636e\u7ed3\u6784\u4e2d\u7684\u6240\u6709\u5143\u7d20\uff0c\u800c\u679a\u4e3e\u7b97\u6cd5\u663e\u7136\u66f4\u4e3a\u6cdb\u5316\uff0c\u5b83\u53ef\u4ee5\u5bf9\u4efb\u610f\u96c6\u5408\u8fdb\u884c\u679a\u4e3e\u3002\u53e6\u5916\uff0c\u540e\u9762\u7684\u56de\u6eaf\u7b97\u6cd5\u672c\u8d28\u4e0a\u4e5f\u662f\u4e00\u79cd\u679a\u4e3e\uff0c\u56e0\u4e3a\u56de\u6eaf\u7b97\u6cd5\u7684\u6838\u5fc3\u5176\u5b9e\u4e5f\u662f\u679a\u4e3e\u6240\u6709\u89e3\u7684\u96c6\u5408\uff0c\u63a5\u4e0b\u6765\u6211\u4eec\u901a\u8fc710\u9053\u7ec3\u4e60\u9898\u6765\u5de9\u56fa\u4e00\u4e0b\u679a\u4e3e\u7b97\u6cd5\u3002<\/p>\n\n\n\n
\ud83d\udd8a\u679a\u4e3e\u7ec3\u4e60<\/h3>\n\n\n\n
Tips\uff1actrl + \u5355\u51fb\u84dd\u8272\u94fe\u63a5\u53ef\u76f4\u63a5\u8df3\u8f6c<\/em>\u81f3\u9898\u76ee<\/p>\n\n\n\n
-1.luogu P10424[\u84dd\u6865\u676f 2024 \u7701 B] \u597d\u6570\ud83d\udc4d<\/a><\/h4>\n\n\n\n
\u4e0d\u96be\u770b\u51fa\uff0c\u5728\u672c\u9898\u4e2d\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5bf91~N\u4e2d\u7684\u6bcf\u4e00\u4e2a\u6570\u5b57\u7684\u6bcf\u4e00\u4f4d\u8fdb\u884c\u6309\u4f4d\u679a\u4e3e\u5373\u53ef\uff0c\u6211\u4eec\u53ef\u4ee5\u8bbe\u7f6e\u4e00\u4e2a\u597d\u6570\u4e2a\u6570\u7684\u8ba1\u6570\u5668 goodCount\uff0c\u8bbe\u7f6e\u4e00\u4e2a bool \u7c7b\u578b\u7684 isGood\uff0c\u5982\u679c\u5728\u6309\u4f4d\u679a\u4e3e\u7684\u8fc7\u7a0b\u4e2d\u6709\u67d0\u4e00\u4f4d\u4e0d\u6ee1\u8db3\u6761\u4ef6\uff0c\u5219\u5c06 isGood \u8bbe\u7f6e\u4e3a false\uff0c\u5e76\u9000\u51fa\u540e\u7eed\u5faa\u73af\uff0c\u4e24\u4e2a\u5d4c\u5957\u5faa\u73af\u7ed3\u675f\u540e\uff0c\u6253\u5370 goodCount \u7684\u503c\uff0c\u5177\u4f53\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n\n\n\n
#include<bits\/stdc++.h>
using namespace std;
typedef long long ll;
int main(void) {
    ll n;
    cin >> n;
    ll goodCount = 0;   \/\/\u597d\u6570\u7684\u4e2a\u6570
    bool isGood = true; \/\/flag
    for(int i = 1; i <= n; i++) {
        isGood = true;
        ll index = 1;   \/\/\u7b2c\u4e00\u4f4d\u662f\u5947\u6570
        ll x = i;
        while(x) {
            ll digit = x % 10;  \/\/\u7528digit\u63d0\u53d6\u51fa\u6700\u4f4e\u4f4d
            if (index % 2 != digit % 2) {
                isGood = false;
                break;
            }
            index ++;
            x \/= 10;
        }
        if (isGood) {
            goodCount++;
        }
    }
    cout << goodCount << endl;
    return 0;
}<\/pre>\n\n\n\n
\"1\u679a\u4e3eP10424<\/div><\/figure>\n\n\n\n
-2.lanqiao[\u84dd\u6865\u676f 2023 \u7701 A]\u5e78\u8fd0\u6570\u2764<\/a><\/h4>\n\n\n\n
\u8fd9\u662f\u4e00\u9053\u7ed3\u679c\u586b\u7a7a\u9898\uff0c\u5728\u8bc4\u6d4b\u673a\u4e0a\uff0c\u6211\u4eec\u53ea\u9700\u8981 cout \u51fa\u9898\u76ee\u8981\u6c42\u7684\u7ed3\u679c\u5373\u53ef\uff0c\u8fd9\u5c31\u610f\u5473\u7740\u6211\u4eec\u53ef\u4ee5\u6682\u4e14\u5ffd\u7565\u8bc4\u6d4b\u673a\u9650\u5236\u7684\u65f6\u7a7a\u590d\u6742\u5ea6<\/strong>\uff0c\u53ea\u8981\u80fd\u6c42\u89e3\u51fa\u7b54\u6848\u5373\u53ef\u3002\u5bf9\u4e8e\u672c\u9898\u800c\u8a00\uff0c\u6211\u4eec\u53ef\u4ee5\u91c7\u7528\u6700\u6734\u7d20\u7684\u505a\u6cd5\uff0c\u76f4\u63a5\u4ece1\u679a\u4e3e\u52301e8\uff0c\u8bbe\u7f6e\u4e00\u4e2a\u5e78\u8fd0\u6570\u8ba1\u6570\u5668 luckyCount \uff0c\u8bbe\u7f6e\u4e00\u4e2a digitCount \u7528\u4e8e\u8ba1\u7b97\u4f4d\u6570\uff0c\u5e76\u8bbe\u7f6e\u5de6\u53f3\u4e24\u8fb9\u6c42\u548c\u7684\u6570leftNum\uff0crightNum\uff0c\u4ee5\u53ca\u4f4d\u6570\u7684\u4e2d\u503chalf\uff0c\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n\n\n\n
#include<bits\/stdc++.h>
using namespace std;
typedef long long ll;
int main(void){
    ll luckyCount = 0;
    for(ll i = 1; i <= 100000000; i++){
        ll digitCount = [](ll x){       \/\/\u4f7f\u7528lambda \u8868\u8fbe\u5f0f
            ll cnt = 0;
            for(; x; x \/= 10) cnt++;
            return cnt;
        }(i);
        
        if(digitCount &1) continue;     \/\/digitCount &1 \u7684\u610f\u601d\u662f\uff0c\u82e5 digitCount \u662f\u5947\u6570\uff0c\u5176\u4e8c\u8fdb\u5236\u7684\u4e2a\u4f4d\u4e00\u5b9a\u4e3a1\uff0c\u90a3\u4e48 &1 \u7684\u7ed3\u679c\u4e3atrue
\u200b
        if([](ll x, ll digitCount){         \/\/\u4f7f\u7528lambda \u8868\u8fbe\u5f0f
            ll half = digitCount >> 1;
            ll leftNum = 0,rightNum = 0;
            for(ll i = 0; x; x \/= 10, i++){
                if(i < half) leftNum += x % 10;
                else rightNum += x % 10;
            }
            return leftNum == rightNum;
        }(i,digitCount))luckyCount++;
  }
  cout << luckyCount << endl;
  return 0;
}<\/pre>\n\n\n\n
\u6211\u4eec\u5148\u5728\u81ea\u5df1\u7684\u8ba1\u7b97\u673a\u4e0a run \u4e00\u4e0b\u4ee3\u7801\uff0c\u907f\u514dTLE<\/p>\n\n\n\n
\"2\u679a\u4e3e\u84dd\u68653491<\/div><\/figure>\n\n\n\n
\u8fd0\u884c\u7684\u7ed3\u679c\u4e3a 4430091\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5728\u8bc4\u6d4b\u673a\u4e0a\u6253\u5370\u7ed3\u679c\u5c31\u53ef\u4ee5\u4e86<\/p>\n\n\n\n
#include<bits\/stdc++.h>
using namespace std;
int main(void)
{   
  cout << 4430091 << endl;
  return 0;
}<\/pre>\n\n\n\n
\"3\u679a\u4e3e\u84dd\u68653491<\/div><\/figure>\n\n\n\n
\u26a0\ufe0f\u6ce8\u610f\uff1a\u672c\u9898\u6709\u4e00\u4e2a\u6bd4\u8f83\u5bb9\u6613\u88ab\u5ffd\u7565\u7684\u70b9\uff0c\u90a3\u5c31\u662f\u5728\u7b2c\u516d\u884c\u7684 for \u5faa\u73af\u4e2d\uff0c\u6709\u540c\u5b66\u53ef\u80fd\u4f1a\u5199\u6210<\/p>\n\n\n\n
for(ll i = 0; i < 100000000; i++);<\/pre>\n\n\n\n
\u4e4d\u4e00\u770b\u4f3c\u4e4e\u6ca1\u6709\u95ee\u9898\uff0c\u4e8c\u8005\u90fd\u662f\u5faa\u73af100000000\u6b21\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\uff0c\u5728 lambda \u8868\u8fbe\u5f0f\u4f20\u503c\u7684\u65f6\u5019\uff0ci = 0 \u4f1a\u88ab\u9519\u8bef\u7684\u4f20\u9012\u8fdb\u53bb\uff0c\u5b83\u4f1a\u987a\u5229\u901a\u8fc7 &1 \u7684\u5224\u65ad\uff0c\u6700\u540e\u5bfc\u81f4\u8f93\u51fa\u7684 luckyCount \u6bd4\u6b63\u786e\u7b54\u6848\u591a\u4e00\uff0c\u9519\u8bef\u7ed3\u679c\u5982\u4e0b\uff1a<\/p>\n\n\n\n
\"4\u679a\u4e3e\u84dd\u68653491<\/div><\/figure>\n\n\n\n
-3.lanqiao[\u84dd\u6865\u676f 2021 \u7701 B]\u5361\u7247\ud83c\udfb4<\/a><\/h4>\n\n\n\n
\u6211\u4eec\u77e5\u9053\uff0c\u5c0f\u84dd0~9\u7684\u5361\u7247\u6bcf\u5f20\u90fd\u67092021\u5f20\uff0c\u6211\u4eec\u53ef\u4ee5\u4ece 1 \u5f00\u59cb\u904d\u5386\uff0c\u5199\u4e00\u4e2a\u6b7b\u5faa\u73af\uff0c\u5bf9\u8fd9\u4e9b\u6570\u5b57\u7684\u6bcf\u4e00\u4f4d\u8fdb\u884c\u6309\u4f4d\u679a\u4e3e\uff0c\u5bf9\u679a\u4e3e\u5230\u7684\u6570\u5b57\uff0c\u5361\u7247\u6570\u91cf – 1\uff0c\u76f4\u5230\u67d0\u4e00\u4e2a\u6570\u5b57\u7684\u5361\u7247\u6570\u91cf\u4e3a 0 \uff0c\u4ee3\u8868\u65e0\u6cd5\u62fc\u6210\u8fd9\u4e2a\u6570\u5b57\uff0c\u90a3\u4e48\u6211\u4eec\u8f93\u51fa\u5b83\u7684\u524d\u4e00\u4f4d i – 1 \u5373\u53ef\u3002<\/p>\n\n\n\n
\u4e0b\u9762\u7ed9\u51fa\u4e86\u4e00\u79cd\u6734\u7d20\u7684\u505a\u6cd5\uff0c\u5728 cards[digit] == 0 \u65f6\uff0c\u6211\u4eecbreak\u51fa\u5f53\u524d\u5faa\u73af\uff0c\u4f46\u6211\u4eec\u53ea\u80fd\u8df3\u51fa\u7b2c\u4e00\u5c42\uff0c\u800c\u65e0\u6cd5\u8df3\u51fa\u7b2c\u4e8c\u5c42\u5faa\u73af\uff0c\u56e0\u6b64\u6211\u4eec\u9700\u8981\u8bbe\u7f6e\u4e00\u4e2a flag \u5e76\u521d\u59cb\u5316\u4e3a false\uff0c\u5f53 cards[digit] == 0 \u65f6\uff0c\u6211\u4eec\u4ee4 flag = true \uff0c\u5728\u5916\u5c42\u5faa\u73af\u4e2d\u5224\u65ad\uff0c\u5f53 flag == true \u7684\u65f6\u5019\uff0c\u8f93\u51fa i – 1 \u5e76\u518dbreak\u4e00\u6b21\uff0c\u8fd9\u6837\u5c31\u5b8c\u6210\u4e86\u8df3\u51fa\u5faa\u73af\uff0c\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n\n\n\n
#include<bits\/stdc++.h>
using namespace std;
int main(void){
    vector<int> cards(10,2021);
    for(int i = 1; ; i++){
        bool flag = false; 
        for(int j = i; j; j \/= 10){
            int digit = j % 10;
            if(cards[digit] == 0){
                flag = true;
                break;
            }
            cards[digit]--;
        }
        if(flag == true){
            cout << i - 1 << endl;
            break;
        }
    }
    return 0;
}<\/pre>\n\n\n\n
\u540c\u6837\u7684\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u91c7\u7528\u7b2c\u4e8c\u9898\u7684 lambda\uff0c\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n\n\n\n
#include<bits\/stdc++.h>
using namespace std;
int main(void){
    vector<int> cards(10,2021);
    for(int i = 1; ; i++){
        if([&](){
            for (int d = i; d; d \/= 10){
                int digit = d % 10;
                if (cards[digit] == 0) return true;
                cards[digit]--;   
            }
            return false;
        }()){
            cout << i - 1 << endl;
            break;
        }
    }
}<\/pre>\n\n\n\n
\"5\u679a\u4e3e\u84dd\u68651065\u5361\u7247\"\/<\/div><\/figure>\n\n\n\n
-4.lanqiao[\u84dd\u6865\u676f 2024 \u7701 B] \u5c0f\u7403\u53cd\u5f39 \u26bd<\/a><\/h4>\n\n\n\n
\u6309\u7167\u9898\u76ee\u6307\u5f15\u7684\u601d\u8def\uff0c\u6211\u4eec\u9700\u8981\u8ba1\u7b97\u5c0f\u7403\u53cd\u5c04\u7684\u70b9\u5e76\u53cd\u5c04\u901f\u5ea6\uff0c\u8fd9\u6837\u7684\u51e0\u4f55\u8fd0\u7b97\u6781\u5176\u590d\u6742\uff0c\u6d89\u53ca\u7684\u6761\u4ef6\u4e5f\u5341\u5206\u7684\u591a\uff0c\u6211\u4eec\u4e0d\u59a8\u8f6c\u6362\u4e00\u4e0b\u601d\u8def\ud83e\udd13\ud83d\udc46\uff0c\u6211\u4eec\u73b0\u5728\u9700\u8981\u8ba1\u7b97\u7684\u662f\u5c0f\u7403\u662f\u5426\u80fd\u5426\u5230\u8fbe \u201c\u539f\u70b9\u201d \uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u539f\u957f\u65b9\u5f62\u5411\u53f3\u7ffb\u8f6c\u590d\u5236\u4e00\u4efd\uff0c\u518d\u5411\u4e0b\u7ffb\u8f6c\u590d\u5236\u4e00\u4efd\uff0c\u8fd9\u6837\u6211\u4eec\u5c31\u83b7\u5f97\u4e86\u4e00\u4e2a\u957f\u4e3a 343720 * 2 \uff0c\u5bbd\u4e3a 233333 * 2 \u7684\u957f\u65b9\u5f62\uff0c\u5b83\u7684\u56db\u4e2a\u89d2\u90fd\u662f \u201c\u539f\u70b9\u201d \uff0c\u90a3\u4e48\u6211\u4eec\u4fbf\u53ef\u4ee5\u8ba9\u5c0f\u7403\u4e00\u76f4\u6cbf\u7740\u539f\u8def\u7ebf\u524d\u8fdb\uff0c\u5e76\u4e14\u4e0d\u65ad\u7684\u590d\u5236\u8fd9\u4e2a\u957f\u65b9\u5f62\uff0c\u76f4\u5230\u5c0f\u7403\u521a\u597d\u5230\u8fbe\u7b2c\u4e00\u4e2a\u539f\u70b9\u4e3a\u6b62\uff0c\u6700\u540e\u7528\u52fe\u80a1\u5b9a\u7406\u8ba1\u7b97\u51fa\u5c0f\u7403\u8fd0\u52a8\u7684\u8ddd\u79bb\u5373\u53ef\uff0c\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n\n\n\n
#include<bits\/stdc++.h>
using namespace std;
typedef long long ll;
int main(void){
    ll dx = 15,dy = 17;
    ll width = 343720 * 2, hight = 233333 * 2;      \/\/\u65b0\u957f\u65b9\u5f62\u7684\u957f\uff0c\u5bbd\uff0c\u4e3a\u539f\u957f\u5bbd\u7684\u4e8c\u500d
    for(int t = 1; ; t++){      \/\/\u65e0\u9650\u5faa\u73af      
\/\/\u8fd9\u91cct * dx % width == 0 \u4ee3\u8868\u5c0f\u7403\u89e6\u5230\u5e95\u8fb9\uff0ct * dy % hight == 0 \u4ee3\u8868\u5c0f\u7403\u89e6\u5230\u53f3\u8fb9\uff0c\u540c\u65f6\u6ee1\u8db3\u5219\u4ee3\u8868\u5230\u8fbe\u201c\u539f\u70b9\u201d
        if(t * dx % width == 0 && t * dy % hight == 0){
            \/\/ << fixed <<setprecision(2) \u4ee3\u8868\u8bbe\u7f6e\u8f93\u51fa\u5230\u5c0f\u6570\u70b9\u540e\u4e24\u4f4d\uff0chypot \u4e3a\u52fe\u80a1\u5b9a\u7406\u8ba1\u7b97\u51fd\u6570
            cout << fixed << setprecision(2) << hypot(t * dx, t * dy) << endl; 
            break;
        }
    }
    return 0;
}<\/pre>\n\n\n\n
\"6\u679a\u4e3e\u84dd\u686519732\u5c0f\u7403\u53cd\u5f39\"\/<\/div><\/figure>\n\n\n\n
-5.luogu P1149 [NOIP 2008 \u63d0\u9ad8\u7ec4] \u706b\u67f4\u68d2\u7b49\u5f0f\ud83d\udd25<\/a><\/h4>\n\n\n\n
NOIP 2008\u5e74\u7684\u63d0\u9ad8\u7ec4 ( \u8fd9\u771f\u662f\u63d0\u9ad8\u7ec4\u5417\uff1f)\uff0c\u8fd9\u9053\u9898\u7684\u8981\u6c42\u662f\uff0c\u5bf9\u4e8e\u4e00\u4e2a\u7ed9\u5b9a\u7684 n \uff0c\u6c42\u80fd\u62fc\u6210\u7b26\u5408\u9898\u610f\u7684\u7b49\u5f0f\u7684\u6570\u91cf\uff0c\u90a3\u4e48\u6211\u4eec\u4e0d\u96be\u60f3\u5230\u679a\u4e3e\u7b97\u6cd5\u3002\u9898\u5e72\u8fd8\u6709\uff0cA + B = C \u548c B + A = C \u89c6\u4e3a\u4e0d\u540c\u7684\u7b49\u5f0f\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u5bf9 A \u548c B \u90fd\u8fdb\u884c\u679a\u4e3e\uff0c\u8bbe\u7f6e\u4e00\u4e2a\u7528\u4e8e\u8ba1\u7b97\u6d88\u8017\u4e86\u591a\u5c11\u706b\u67f4\u68d2\u7684\u51fd\u6570 cnt() \uff0c\u6700\u540e\u5224\u65ad\u4e00\u4e0bif(cnt(A) + cnt(B) + cnt(C) + 4 == n) \u5373\u53ef\uff0c\u5982\u679c\u76f8\u7b49\u5219\u4ee4\u8ba1\u6570\u5668 ans++ \uff0c\u601d\u8def\u975e\u5e38\u6e05\u6670\u3002<\/p>\n\n\n\n
\u4f46\u662f\u672c\u9898\u7684\u5173\u952e\u70b9\u5728\u4e8e\u5982\u4f55\u786e\u5b9a\u679a\u4e3e\u7684\u8303\u56f4\uff0c\u89c2\u5bdf\u8f93\u5165\u683c\u5f0f\uff0c\u53d1\u73b0\u9898\u76ee\u6240\u7ed9\u51fa\u7684 n \u7684\u8303\u56f4\u4e3a 1 \u2264 n \u2264 24\uff0c\u5e76\u4e14\u6211\u4eec\u8fd8\u9700\u8981 4 \u6839\u706b\u67f4\u68cd\u6784\u6210 “+” \u548c “=” \uff0c\u6240\u4ee5\u5b9e\u9645\u6211\u4eec\u80fd\u7528\u6765\u6784\u6210\u6570\u5b57\u7684\u53ea\u670920\u6839\u706b\u67f4\u68d2\uff0c\u90a3\u4e48\u6211\u4eec\u4fbf\u9700\u8981\u627e\u5230\u4e00\u4e2a\u6700\u5927\u7684\u6570\u5b57\u4f5c\u4e3a\u679a\u4e3e\u4e0a\u754c\u3002\u9996\u5148\u6211\u4eec\u8981\u660e\u786e\u4e00\u70b9\uff0c\u90a3\u5c31\u662f\u6211\u4eec\u7684\u706b\u67f4\u68d2\uff0c\u4f7f\u7528\u7684\u4f18\u5148\u7ea7\u6c38\u8fdc\u662f\u589e\u52a0 “\u6570\u4f4d”\uff0c\u800c\u4e0d\u662f\u589e\u5927 “\u6570\u5b57”\uff0c\u5047\u8bbe\u6211\u4eec\u73b0\u5728\u6709 6 \u6839\u706b\u67f4\u68d2\u7528\u6765\u6784\u6210\u4e00\u4e2a\u6570\u5b57\uff0c\u90a3\u4e48\u663e\u7136 “111” \u5fc5\u7136\u662f\u6700\u5927\u7684\u89e3\uff0c\u6ca1\u6709\u5176\u4ed6\u60c5\u51b5\uff08\u5927\u5bb6\u53ef\u4ee5\u8bd5\u4e00\u4e0b\uff09\u3002\u4f46\u5047\u8bbe\u6211\u4eec\u6709 7 \u6839\u706b\u67f4\u68d2\uff0c\u6784\u6210 “111” \u4e4b\u540e\uff0c\u4f59\u4e0b\u7684\u4e00\u6839\u6ca1\u529e\u6cd5\u518d\u589e\u52a0 “\u6570\u4f4d” \uff0c\u90a3\u4e48\u6211\u4eec\u518d\u8003\u8651\u589e\u52a0 ” \u6570\u5b57 ” \uff0c\u6700\u5927\u6570\u4e3a “711”\uff0c\u8fd9\u91cc\u4e0d\u591a\u8bc1\u660e\u3002\u5bf9\u4e8e n == 24 \u800c\u8a00\uff0c\u6211\u4eec\u80fd\u627e\u5230\u7684A(B)\u6700\u5927\u7684\u7b49\u5f0f\u4e3a ” 711 + 1 = 712″\uff08\u6d88\u801723\u6839\u706b\u67f4\u68d2\uff09\uff0c\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u518d\u7a0d\u5fae\u589e\u52a0\u679a\u4e3e\u4e0a\u754c\u52301000\uff0c\u8fd9\u6837\u662f\u6bd4\u8f83\u5b89\u5168\u7684\uff0c\u4ee3\u7801\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n\n\n\n
#include<bits\/stdc++.h>
using namespace std;
int main(void){
    int n;
    cin >> n;
    int digits[] = {6, 2, 5, 5, 4, 5, 6, 3, 7, 6};  \/\/\u6bcf\u4e2a\u6570\u5b57\u6240\u9700\u8981\u7684\u706b\u67f4\u68d2\u6570
    
    auto cnt = [&](int x){      \/\/\u8ba1\u7b97\u6570\u5b57\u6240\u9700\u8981\u7684\u706b\u67f4\u68d2\u51fd\u6570
        if(x == 0)return digits[0];
        int num = 0;
        for(; x; x \/= 10){
            num += digits[x%10];
        }
        return num;
    };
    
    int ans = 0;
    for(int a = 0; a <= 1000; a++){         \/\/\u679a\u4e3e
        for (int b = 0; b <= 1000; b++){
            int c = a + b;
            if (cnt(a) + cnt(b) + cnt(c) + 4 == n) ans++;       \/\/\u7b26\u5408\u6761\u4ef6\u5219ans++
        }
    }
    cout << ans;
    return 0; 
}<\/pre>\n\n\n\n
\u5047\u8bbe\u679a\u4e3e\u8303\u56f4\u6ca1\u6709\u5224\u65ad\u597d\uff0c\u5bfc\u81f4TLE\u4e86\uff0c\u90a3\u5e94\u8be5\u600e\u4e48\u529e\u5462\ud83e\udd14\uff1f n \u7684\u8303\u56f4\u4e3a 1 \u2264 n \u2264 24 \uff0c\u8f93\u5165\u7684\u6570\u636e\u8303\u56f4\u6bd4\u8f83\u5c0f\uff0c\u90a3\u6211\u4eec\u5c31\u53ef\u4ee5\u5c06\u6240\u6709\u7684\u7b54\u6848\u5728\u81ea\u5df1\u7684\u8ba1\u7b97\u673a\u4e2d\u8fd0\u884c\u51fa\u6765\uff0c\u518d\u5c06\u7b54\u6848\u4fdd\u5b58\u5230\u4e00\u4e2a answer \u6570\u7ec4\u91cc\uff0c\u5bf9\u4e8e\u4e0d\u540c\u7684 n \u8f93\u5165\uff0c\u6211\u4eec\u76f4\u63a5\u8fd4\u56de answer[n] \u5373\u53ef\uff0c\u5bf9\u4e8e\u4e0d\u540c\u7684 n \uff0c\u7b54\u6848 run \u51fa\u6765\u7684\u8fc7\u7a0b\u5c31\u4e0d\u591a\u8d58\u8ff0\uff0c\u5177\u4f53\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n\n\n\n
#include<bits\/stdc++.h>
using namespace std;
int main(void){
    int n;
    cin >> n;
    int answer[] = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 8, 9, 6, 9, 29, 39, 38, 65, 88, 128};
    cout << answer[n] << endl;
    return 0;
}<\/pre>\n\n\n\n
\"7\u679a\u4e3eP1149NOIP<\/div><\/figure>\n\n\n\n
\u4e24\u79cd\u7b54\u6848\u5747\u987a\u5229AC\uff0c\u6211\u4eec\u521a\u624d\u6240\u63d0\u5230\u7684\u7b2c\u4e8c\u79cd\u5c06\u7b54\u6848\u4fdd\u5b58\u5230\u6570\u7ec4\u4e2d\u7684\u65b9\u6cd5\uff0c\u5c31\u53eb \u201c\u6253\u8868\u201d\ud83e\udd13\ud83d\udc46\uff0c\u8fd9\u79cd\u65b9\u6cd5\u4e00\u822c\u9002\u5408\u8f93\u5165\u6570\u636e\u8303\u56f4\u5c0f\uff0c\u4e14\u6bd4\u8f83\u5bb9\u6613 TLE \u7684\u9898\u76ee\u4e2d\u3002<\/p>\n\n\n\n
\ud83d\udcd5\u524d\u7f00\u548c-prefix<\/h3>\n\n\n\n
\u7ed9\u4f60\u4e00\u6bb5\u6570\u7ec4\uff0c\u8ba9\u4f60\u6c42\u4e00\u6bb5\u533a\u95f4 L \u5230 R \u7684\u548c\uff0c\u6211\u4eec\u53ea\u9700\u8981\u679a\u4e3e\u4ece L \u5230 R \u5373\u53ef<\/p>\n\n\n\n
int sum = 0;
for(int i = L; i <= R; i++){
    sum += arr[i];
}<\/pre>\n\n\n\n
\u4f46\u5982\u679c\u6709 M \u6b21\u67e5\u8be2\u5462\ud83e\udd14\uff1f<\/p>\n\n\n\n
int sum = 0;
while(M--){
    for(int i = L; i <= R; i++){
        sum += arr[i];
    }
}<\/pre>\n\n\n\n
\u6bcf\u6b21\u90fd\u67e5\u8be2\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u5c31\u53d8\u6210\u4e86\uff0c\u67e5\u8be2\u6b21\u6570 \u00d7 \u533a\u95f4\u957f\u5ea6\uff0c\u5373O(MN)\uff0c\u8fd9\u663e\u7136\u6548\u7387\u592a\u4f4e\u4e86\u274c\uff0c\u4e3a\u4e86\u66f4\u52a0\u9ad8\u6548\u7684\u5904\u7406\u67e5\u8be2\u8bf7\u6c42\uff0c\u6211\u4eec\u4fbf\u4f1a\u91c7\u7528\u4e00\u79cd\u540d\u4e3a ” \u524d\u7f00\u548c ” \u7684\u7b97\u6cd5\u3002<\/p>\n\n\n\n
vector<int> prefix(n);
for(int i= 0; i < n; i++){
    if(i)  prefix[i] = prefix[i - 1];
    prefix[i] += arr[i];
}<\/pre>\n\n\n\n
\u6211\u4eec\u4e5f\u53ef\u4ee5\u7528C++98\u4e2d\u5f15\u5165\u7684\u4e00\u4e2aSTL\u51fd\u6570 : partial_sum()\uff0c\u5b83\u4f4d\u4e8e numeric\u5e93\u4e2d\uff0c\u4e0b\u9762\u7684\u4ee3\u7801\u548c\u4e0a\u9762\u662f\u5b8c\u5168\u7b49\u4ef7\u7684\uff1a<\/p>\n\n\n\n
vector<int> prefix(n);
partial_sum(arr.begin(), arr.end(), prefix.begin());\/\/\u53c2\u6570\u5206\u522b\u4e3a\uff1a\u8d77\u59cb\uff0c\u7ec8\u6b62\uff0c\u76ee\u6807\u4f4d\u7f6e<\/pre>\n\n\n\n
\u5047\u5982\u6211\u4eec\u8981\u8fdb\u884c\u53cd\u5411\u904d\u5386\uff0c\u90a3\u4e48\u53ea\u9700\u8981\u5199\u6210 partial_sum(arr.rbegin(), arr.rend(), prefix.rbegin()); \uff0c\u7b80\u5355\u4fee\u6539\u4e00\u4e0b\u8fed\u4ee3\u5668\u5373\u53ef\u3002<\/p>\n\n\n\n
\u63a5\u4e0b\u6765\u8bf4\u67e5\u8be2\uff0c\u6bd4\u5982\u8981\u67e5\u8be2 L \u5230 R \u7684\u533a\u95f4\u548c\uff0csum(L, R) = prefix[ R ] – prefix[ L – 1 ]; \u5047\u8bbe L = 3\uff0cR = 6\uff0c\u90a3\u4e48prefix[ 3 ] = 1 + 2 + 3 , prefix[ 6 ] = 1 +2 + 3 + 4 + 5 + 6 , prefix[ 6 ] – prefix[ 2 ] = 3 + 4 + 5 + 6\u3002\u4f46\u5982\u679c L \u662f 0 \uff0c\u90a3\u4e48 L – 1\u5c31\u8d8a\u754c\u4e86\uff0c\u8fd9\u65f6\u6211\u4eec\u6709\u4e24\u79cd\u5904\u7406\u65b9\u6cd5\uff1a<\/p>\n\n\n\n
\u2460\uff1a\u7b2c\u4e00\u79cd\u662f\u5bf9 L == 0 \u7684\u60c5\u51b5\u8fdb\u884c\u7279\u5224\uff1aL ==0 \u65f6\uff0c\u76f4\u63a5\u8fd4\u56de prefix[ R ] \u5373\u53ef\u3002<\/p>\n\n\n\n
\u2461\uff1a\u7b2c\u4e8c\u79cd\u5219\u662f\u5728\u8ba1\u7b97 prefix \u65f6\uff0c\u4e0b\u6807\u4ece 1 \u5f00\u59cb\u8ba1\u6570\uff0c\u8fd9\u6837 L \u7684\u6700\u5c0f\u503c\u4e5f\u5c31\u662f 1 \uff0cL – 1 \u4e5f\u5c31\u4e0d\u4f1a\u8d8a\u754c\u4e86\u3002\u3002<\/p>\n\n\n\n
vector<int> arr(n + 1),prefix(n + 1);
for(int i = 1; i <= n; i++){
    cin >> arr[i];
}
partial_sum(arr.begin(), arr.end(), prefix.begin());<\/pre>\n\n\n\n
\u6211\u4eec\u4e5f\u53ef\u4ee5\u4f7f\u7528\u8303\u56f4\u5faa\u73af\uff0c\u4e24\u79cd\u5747\u53ef\uff0c\u770b\u4e2a\u4eba\u559c\u597d\u9009\u62e9\u5199\u6cd5\ud83d\udc4d\u3002<\/p>\n\n\n\n
vector<int> arr(n)\uff0cprefix(n + 1);
for(auto &x : arr) cin >> x;
partial_sum(arr.begin(), arr.end(), prefix.begin() + 1);<\/pre>\n\n\n\n
\u5f53\u7136\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u6309\u7167\u8fd9\u4e2a\u601d\u8def\uff0c\u5c06\u524d\u7f00\u548c\u63a8\u5e7f\u5230\u524d\u7f00\u79ef\u548c\u524d\u7f00\u5f02\u6216\uff1a<\/p>\n\n\n\n
\u524d\u7f00\u79ef\uff1amul(L,R) = prefix(R) \/ prefix(L - 1);<\/pre>\n\n\n\n
\uff08\u6ce8\uff1a\u5bf9\u4e8e int \u7c7b\u578b\u7684\u6570\u636e\uff0c2\u2076\u2074 \u5c31\u6ea2\u51fa\u4e86\uff0c\u56e0\u6b64\u6211\u4eec\u4e00\u822c\u4f1a\u5bf9\u524d\u7f00\u79ef\u7684\u7ed3\u679c\u8fdb\u884c\u53d6\u6a21\u8fd0\u7b97\uff0c\u4e00\u65e6\u53d6\u6a21\uff0c\u8fd8\u539f\u56de\u6765\u90a3\u5c31\u4e0d\u662f\u7b80\u5355\u7684\u9006\u8fd0\u7b97\u4e86\uff0c\u8fd9\u5c5e\u4e8e\u201c\u4e58\u6cd5\u9006\u5143\u201d\u7684\u8303\u7574\uff0c\u4f1a\u8fd0\u7528\u5230\u8d39\u9a6c\u5c0f\u5b9a\u7406\u548c\u5feb\u901f\u5e42\ud83d\ude28\uff0c\u5bf9\u4e8e\u7b97\u6cd5\u65b0\u624b\u6765\u8bf4\uff0c\u8fd9\u90e8\u5206\u6709\u4e00\u5b9a\u96be\u5ea6\uff0c\u5728\u6b64\u5c31\u4e0d\u8fdb\u884c\u5c55\u5f00\u4e86\uff0c\u611f\u5174\u8da3\u7684\u540c\u5b66\u53ef\u4ee5\u8bd5\u7740\u5c06\u8fd9\u51e0\u4e2a\u77e5\u8bc6\u70b9\u7ed3\u5408\u8d77\u6765\uff09<\/p>\n\n\n\n
\u524d\u7f00\u5f02\u6216\uff1axor(L,R) = prefix(R) ^ prefix(R - 1);<\/pre>\n\n\n\n
\u5f02\u6216\u7684\u8fd0\u7b97\u5982\u4e0b\uff1a<\/p>\n\n\n\n
\n
True ^ False = True
\u200b
False ^ True = True
\u200b
False ^ False = False
\u200b
True ^ True = False<\/pre>\n<\/blockquote>\n\n\n\n
\u5373\u76f8\u5f02\u4e3a\u771f\uff0c\u76f8\u540c\u4e3a\u5047\uff0c\u5176\u9006\u8fd0\u7b97\u540c\u6837\u4e3a\u5f02\u6216\uff0c\u5c11\u4e86\u5f88\u591a\u9ebb\u70e6\u3002<\/p>\n\n\n\n
\u6211\u4eec\u518d\u6765\u770b\u5f02\u6216\u8fd0\u7b97\u4e00\u4e2a\u6709\u8da3\u7684\u6027\u8d28\u3002<\/p>\n\n\n\n
\n
\u539f \u6570 \u7ec4\uff1a2 2 7 5 7 2 1 4 1 5<\/p>\n\n\n\n
\u2193 \u2193<\/p>\n\n\n\n
\u2193 \u2193<\/p>\n\n\n\n
\u524d\u7f00\u5f02\u6216\u6570\u7ec4\uff1a2 0 7<\/strong><\/em> 2 5 7<\/strong><\/em> 6 2 3 6<\/p>\n<\/blockquote>\n\n\n\n
\u5982\u679c\u524d\u7f00\u5f02\u6216\u6570\u7ec4\u4e2d\u7684\u4e24\u4e2a\u5143\u7d20\u76f8\u540c\uff0c\u5c31\u4ee3\u8868\u8fd9\u4e00\u6bb5\u5de6\u5f00\u53f3\u95ed\u533a\u95f4(5\uff0c7\uff0c2)\u7684\u5f02\u6216\u548c\u4e3a\u96f6\uff0c\u5176\u8bc1\u660e\u4e5f\u975e\u5e38\u7b80\u5355\uff1a<\/p>\n\n\n\n
\u6211\u4eec\u5047\u8bbe p[i] = p[j]\uff0c\u4e5f\u5c31\u662f a\u2081 \u2295 a\u2082 \u2295 a\u2083 \u2295 … \u2295 ai = a\u2081 \u2295 a\u2082 \u2295 a\u2083 \u2295 … \u2295 a\u1d62 \u2295 a\u1d62\u208a\u2081 \u2295 … \u2295 a\u2c7c\uff0c\u518d\u4e24\u8fb9\u540c\u65f6 \u2295 (a\u2081 \u2295 a\u2082 \u2295 a\u2083 \u2295 … \u2295 ai)\uff0c\u56e0\u4e3a\u5f02\u6216\u8fd0\u7b97\u7387\u662f\u76f8\u540c\u4e3a\u5047\uff0c\u6240\u4ee5 0 = a\u1d62\u208a\u2081 \u2295 … \u2295 a\u2c7c\u3002<\/p>\n\n\n\n
\u540c\u6837\u7684\uff0c\u5982\u679c\u524d\u7f00\u5f02\u6216\u6570\u7ec4\u4e2d\u6709\u591a\u4e2a\u6570\u5b57\u76f8\u540c\uff0c\u90a3\u4e48\u4efb\u9009\u4e24\u4e2a\u76f8\u540c\u7684\u6570\u5b57\u6240\u6784\u6210\u7684\u533a\u95f4\u5185\u5f02\u6216\u548c\u90fd\u4e3a 0\u3002<\/p>\n\n\n\n
\u5176\u5b9e\u8fd9\u4e9b\u4e0d\u662f\u7d2f\u52a0\u7684\u8fd0\u7b97\u540c\u6837\u53ef\u4ee5\u4f7f\u7528partial_sum\u6765\u7f16\u5199\uff1a<\/p>\n\n\n\n
partial_sum(arr.begin(), arr.end(), xorsum.begin,
[](int prev, int cur){
    return prev ^ cur
});<\/pre>\n\n\n\n
partial_sum\u7684\u7b2c\u56db\u4e2a\u53c2\u6570\u53ef\u4ee5\u63a5\u53d7\u4e00\u4e2a\u4e8c\u5143\u64cd\u4f5c\u51fd\u6570\uff0c\u7528\u4e8e\u8868\u793a\u5982\u4f55\u8fdb\u884c\u7edf\u8ba1\uff0c\u8fd9\u4e2a\u51fd\u6570\u7684\u7b2c\u4e00\u4e2a\u53c2\u6570\u662f\u5df2\u7ecf\u7edf\u8ba1\u7684\u7ed3\u679c\uff0c\u7b2c\u4e8c\u4e2a\u53c2\u6570\u662f\u5f53\u524d\u5143\u7d20\uff0c\u6240\u4ee5\u6211\u4eec\u53ea\u9700\u8981 return \u4e00\u4e2a prev ^ cur \u5373\u53ef\ud83d\ude0e\u3002<\/p>\n\n\n\n
\ud83d\ude0b\u4e0b\u9762\u6211\u4eec\u5c06 prefix \u6269\u5c55\u5230\u66f4\u9ad8\u7ef4\u5ea6\uff0c\u6211\u4eec\u53ef\u4ee5\u7528 prefix \u7684\u601d\u60f3\u6c42\u51fa\u4e00\u4e2a\u4e8c\u7ef4\u77e9\u9635\u4e2d\u4efb\u610f\u4e00\u4e2a\u5b50\u77e9\u9635\u7684\u548c\uff0c\u6211\u4eec\u4e4b\u9700\u8981\u5148\u5bf9\u884c\u548c\u5217\u5206\u522b\u6c42\u524d\u7f00\u548c\uff0c\u8fd9\u6837\u8fd9\u4e2a\u4e8c\u7ef4\u6570\u7ec4\u4e2d\u7684\u5143\u7d20\u5c31\u4ee3\u8868\u4e86\u5de6\u4e0a\u89d2\u5230\u5f53\u524d\u5143\u7d20\u4f4d\u7f6e\u7684\u6240\u6709\u5143\u7d20\u4e4b\u548c\u3002\u90a3\u4e48\u6c42\u67d0\u4e2a\u5b50\u77e9\u9635\u4e4b\u548c\uff0c\u5c31\u662f\u7528\u53f3\u4e0b\u89d2\u7684\u524d\u7f00\u548c\u51cf\u53bb\u5de6\u4e0b\u89d2\u7684\u524d\u7f00\u548c\uff0c\u518d\u51cf\u53bb\u53f3\u4e0a\u89d2\u7684\u524d\u7f00\u548c\uff0c\u518d\u52a0\u4e0a\u5de6\u4e0a\u89d2\u7684\u524d\u7f00\u548c\uff08\u5176\u5b9e\u770b\u56fe\u66f4\u76f4\u89c2\u4e00\u70b9\uff09\uff1a<\/p>\n\n\n\n
\"8prefix\u8bb2\u89e3\u90e8\u5206-\u4e8c\u7ef4prefix\u7406\u89e3\"\/<\/div><\/figure>\n\n\n\n
\u5176\u80cc\u540e\u6240\u8574\u542b\u7684\u5176\u5b9e\u662f\u6570\u5b66\u96c6\u5408\u5206\u652f\u4e2d\u7684\u5bb9\u65a5\u539f\u7406\uff0c\u5927\u5bb6\u9ad8\u4e2d\u5e94\u8be5\u90fd\u5b66\u8fc7\uff0c\u90a3\u4e48\u6839\u636e\u5b83\uff0c\u6211\u4eec\u4fbf\u53ef\u4ee5\u63a8\u5e7f\u5230\u4e09\u7ef4\u751a\u81f3\u66f4\u9ad8\u7ef4\u5ea6\u7684\u524d\u7f00\u548c\uff0c\u5728\u6b64\u5c31\u4e0d\u8fc7\u591a\u8d58\u8ff0\u4e86\uff0c\u611f\u5174\u8da3\u7684\u5404\u4f4d\u53ef\u4ee5\u81ea\u884c\u5199\u4e00\u6bb5\u4ee3\u7801\u5c1d\u8bd5\u4e00\u4e0b\u66f4\u9ad8\u7ef4\u7684\u524d\u7f00\u548c\u3002<\/p>\n\n\n\n
\ud83d\udd8a\u524d\u7f00\u548c-prefix\u7ec3\u4e60<\/h3>\n\n\n\n
-6.luogu P12206[\u84dd\u6865\u676f 2023\u56fdB] \u5f39\u73e0\u5806\u653e\ud83d\udd3a<\/a><\/h4>\n\n\n\n
\u672c\u9898\u662f\u4e00\u9053\u7b7e\u5230\u9898\uff0c\u8003\u5bdf\u7684\u91cd\u70b9\u5c31\u662f\u524d\u7f00\u548c\uff0c\u4ed4\u7ec6\u89c2\u5bdf\u8fd9\u4e2a\u91d1\u5b57\u5854\uff0c\u6211\u4eec\u4e0d\u96be\u53d1\u73b0\u5176\u89c4\u5f8b\uff1a\u5047\u8bbe\u6211\u4eec\u6709\u91d1\u5b57\u5854\u7684\u7b2c i \u5c42\uff0c\u90a3\u4e48\u8fd9\u4e00\u5c42\u7684\u603b\u5f39\u73e0\u6570\u5b9e\u9645\u4e0a\u7b49\u4e8e<\/p>\n\n\n\n
((1 + i) * i) \/ 2\uff0c\u662f\u4e00\u4e2a\u7b49\u5dee\u6570\u5217\u3002\u56e0\u4e3a\u662f\u4e00\u9053\u586b\u7a7a\u9898\uff0c\u6240\u4ee5\u601d\u8def\u4e5f\u5341\u5206\u7b80\u5355\uff0c\u6211\u4eec\u53ea\u9700\u8981\u8bbe\u7f6e\u4e00\u4e2a\u5f88\u5927\u7684\u6570 n \uff0c\u786e\u4fdd\u91d1\u5b57\u5854\u7edd\u5bf9\u4e0d\u53ef\u80fd\u5230\u8fbe\u7b2c n \u5c42\uff0c\u518d\u5bf9\u5f62\u5982<\/p>\n\n\n\n
1\uff0c2\uff0c3\uff0c4\uff0c5\uff0c6\uff0c7\uff0c8\uff0c9…\u7684\u6570\u7ec4\u505a\u4e24\u6b21\u524d\u7f00\u548c\u5373\u53ef\uff0c\u6700\u540e\u904d\u5386\u6570\u7ec4\uff0c\u5982\u679c\u6570\u7ec4\u5143\u7d20\u5927\u4e8etarget\uff0c\u8f93\u51fa\u5176\u524d\u4e00\u4e2a\u5143\u7d20\u7684\u4e0b\u6807\u5373\u53ef\uff0c\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n\n\n\n
#include<bits\/stdc++.h>
using namespace std;
int main(void){
    ios::sync_with_stdio(0),cin.tie(0),cout.tie(0);
    int n = 10000;              \/\/\u8bbe\u7f6e\u4e00\u4e2a\u5f88\u5927\u7684 n
    int target = 20230610;      \/\/\u76ee\u6807\u503c
    vector<int> a(n);           
    iota(a.begin(), a.end(), 0);    \/*iota\u662f\u4f4d\u4e8e<algorithm>\u4e2d\u7684\u51fd\u6570\uff0c\u5176\u4e09\u4e2a\u53c2\u6570\u5206\u522b\u4e3a\u3010\u8d77\u59cb\u4f4d\u7f6e\u3011\u3010\u7ec8\u6b62\u4f4d\u7f6e\u3011\u3010\u521d\u59cb\u503c\u3011\uff0ciota\u4f1a\u4ece\u521d\u59cb\u503c\u5f00\u59cb\uff0c\u6309\u7167\u6307\u5b9a\u7684\u6b65\u957f\uff08\u9ed8\u8ba4\u4e3a1\uff09\u9012\u589e\uff0c\u76f4\u5230\u8fbe\u5230\u6216\u8d85\u8fc7\u7ed3\u675f\u8fed\u4ee3\u5668*\/
    partial_sum(a.begin(), a.end(), a.begin()); 
    partial_sum(a.begin(), a.end(), a.begin());
    for(int i = 0; i <= n; i++){
        if(a[i] > target){
            cout << i - 1 << endl;      \/\/a[i] > target \u8bf4\u660e\u65e0\u6cd5\u642d\u6210\u8fd9\u4e00\u5c42\uff0c\u6240\u4ee5\u8f93\u51fa\u4e0a\u4e00\u5c42\u7684\u4e0b\u6807
            break;
        }
    }
    return 0;
}<\/pre>\n\n\n\n
-7.LeetCode 42.\u63a5\u96e8\u6c34\ud83d\udca7<\/a><\/h4>\n\n\n\n
\u6bd2\u7624\u9762\u8bd5\u9898\uff0c\u67d0\u4e2a\u5927\u5382(ByteDance)<\/del>\u6700\u559c\u6b22\u8003\u5bdf\u7684\u7b97\u6cd5\u9898\uff0c\u5176\u5728LeetCode\u4e0a\u4f5c\u4e3a\u7ea2\u9898\uff0c\u6b63\u786e\u7387\u5374\u5df2\u7ecf\u8fbe\u5230\u4e86\u60ca\u4eba\u768465.7%\uff0c\u8db3\u53ef\u89c1\u8fd9\u9053\u9898\u88ab\u591a\u5c11\u4eba\u5237\u8fc7\u3002<\/p>\n\n\n\n
\u90a3\u4e48\u6211\u4eec\u6765\u770b\u8fd9\u9053\u9898\uff0c\u4ee5LeetCode\u4e0a\u7684\u56fe\u7247\u4e3a\u4f8b\uff0c\u5982\u679c\u4e00\u4e2a\u4f4d\u7f6e\u53ef\u4ee5\u5bb9\u7eb3\u96e8\u6c34\uff0c\u90a3\u4e48\u5b83\u7684\u4e24\u4fa7\u5fc5\u987b\u8981\u6709\u9ad8\u4e8e\u5b83\u7684\u67f1\u5b50\uff0c\u8fd9\u4e2a\u4f4d\u7f6e\u5177\u4f53\u80fd\u5bb9\u7eb3\u591a\u5c11\u96e8\u6c34\uff0c\u53d6\u51b3\u4e8e\u5176\u5de6\u53f3\u4e24\u4fa7\u5404\u81ea\u6700\u9ad8\u7684\u67f1\u5b50\u53d6\u6700\u5c0f\u503c\u518d\u51cf\u53bb\u8fd9\u4e2a\u4f4d\u7f6e\u67f1\u5b50\u7684\u9ad8\u5ea6\uff0c\u5728\u56fe\u4e2d\uff0c\u9ed1\u8272\u7684\u90e8\u5206\u4e3a\u67f1\u5b50\uff0c\u84dd\u8272\u7684\u90e8\u5206\u4e3a\u96e8\u6c34\u3002<\/p>\n\n\n\n
\"9LeetCode\u63a5\u96e8\u6c34png\"\/<\/div><\/figure>\n\n\n\n
\u90a3\u4e48\u4f4d\u7f6e5\u7684\u96e8\u6c34\u91cf\u5c31\u7b49\u4e8emin(\u5de6\u8fb9\u67f1\u5b50\u7684\u6700\u5927\u503c\uff0c\u53f3\u8fb9\u67f1\u5b50\u7684\u6700\u5927\u503c)\uff0c\u5373min(\u4f4d\u7f6e3\uff0c\u4f4d\u7f6e7)=2<\/p>\n\n\n\n
\uff0c\u6240\u4ee55\u4f4d\u7f6e\u7684\u6c34\u91cf\u4e3a2 – 0 = 2\u3002\u601d\u8def\u5df2\u7ecf\u6e05\u6670\uff0c\u90a3\u4e48\u63a5\u4e0b\u6765\u8981\u89e3\u51b3\u7684\u5c31\u662f\u4efb\u610f\u4f4d\u7f6e\u5176\u5de6\u53f3\u4e24\u4fa7\u7684\u6700\u5927\u67f1\u5b50\u9ad8\u5ea6\uff0c\u6211\u4eec\u53ef\u4ee5\u5148\u4ece\u524d\u5411\u540e\u904d\u5386\uff0c\u627e\u51fa\u5de6\u4fa7\u5230\u8fd9\u4e2a\u4f4d\u7f6e\u7684\u6700\u9ad8\u67f1\u5b50<\/p>\n\n\n\n
\uff0c\u518d\u4ece\u540e\u5411\u524d\u904d\u5386\uff0c\u627e\u51fa\u53f3\u4fa7\u5230\u8fd9\u4e2a\u4f4d\u7f6e\u7684\u6700\u9ad8\u67f1\u5b50\u3002\u53d6min\u4e4b\u540e\u518d\u51cf\u53bb\u5f53\u524d\u4f4d\u7f6e\u7684\u67f1\u5b50\u9ad8\u5ea6\u5373\u53ef\u3002\u5176\u4ed6\u601d\u8def\u5341\u5206\u7b80\u5355\uff0c\u5c31\u4e0d\u591a\u8d58\u8ff0\u4e86\u3002\u5b9e\u73b0\u5982\u4e0b\uff1a<\/p>\n\n\n\n
class Solution {
public:
    int trap(vector<int>& height) {
        int n = height.size();
        int ans = 0;
        vector<int> leftMax(n), rightMax(n);    \/\/\u5f00\u4e24\u4e2avector
        leftMax[0] = height[0], rightMax[n - 1] = height[n - 1];    \/\/\u521d\u59cb\u5316\u8fb9\u754c\uff0c\u9632\u6b62\u8d8a\u754c\u3002\uff08\u8bb0\u5f97\u5904\u7406\u8fb9\u754c\u95ee\u9898\uff09
        for (int i = 1; i < n; i++) {
            leftMax[i] = max(leftMax[i - 1],height[i]);             \/\/\u4ece\u524d\u5f80\u540e\u904d\u5386
        }
        for(int i = n - 2; i >= 0; i--){
            rightMax[i] = max(rightMax[i + 1], height[i]);          \/\/\u4ece\u540e\u5f80\u524d\u904d\u5386
        }
        for(int i = 0; i < n; i++){
            ans += min(leftMax[i], rightMax[i]) - height[i];        \/\/ans\u8bb0\u5f55\u96e8\u6c34\u603b\u548c
        }
        return ans;
    }
};<\/pre>\n\n\n\n
\"10LeetCode\u63a5\u96e8\u6c34AC\"\/<\/div><\/figure>\n\n\n\n
\ud83d\udcd5\u5dee\u5206<\/h3>\n\n\n\n
\u26a0\u867d\u7136\u5355\u72ec\u62c6\u5206\u51fa\u6765\u4f5c\u4e3a\u4e00\u4e2a\u7b97\u6cd5\uff0c\u4f46\u5fc5\u987b\u5f3a\u8c03\u7684\u662f\uff0c”\u5dee\u5206”\u672c\u8d28\u4e0a\u662f”\u524d\u7f00\u548c”\u7684\u9006\u8fd0\u7b97<\/strong>\uff0c\u5176\u662f\u4e00\u79cd\u5feb\u901f\u5904\u7406\u533a\u95f4\u52a0\u51cf\u64cd\u4f5c\u7684\u7b97\u6cd5\uff0c\u90a3\u4e48\u5230\u5e95\u4ec0\u4e48\u662f\u5dee\u5206\u5462\uff1f<\/p>\n\n\n\n
\u524d<\/mtext>\u7f00<\/mtext>\u548c<\/mtext> <\/mtext>S<\/mi>i<\/mi><\/msub> <\/mtext>=<\/mo>{<\/mo>a<\/mi>i<\/mi><\/msub> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext>i<\/mi>=<\/mo>0<\/mn><\/mrow><\/mtd><\/mtr>a<\/mi>i<\/mi><\/msub>+<\/mo>s<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext>i<\/mi>><\/mo>0<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><\/mo><\/mrow><\/mrow>\u524d\u7f00\u548c\\ S_i\\ = \\begin{cases} a_i\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ i=0 \\\\ a_i+s_{i-1}\\ \\ \\ \\ \\ \\ i>0 \\end{cases}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n
\u5dee<\/mtext>\u5206<\/mtext> <\/mtext>d<\/mi>i<\/mi><\/msub> <\/mtext>=<\/mo>{<\/mo>a<\/mi>i<\/mi><\/msub> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext>i<\/mi>=<\/mo>0<\/mn><\/mrow><\/mtd><\/mtr>a<\/mi>i<\/mi><\/msub>\u2212<\/mo>a<\/mi>i<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext> <\/mtext>i<\/mi>><\/mo>0<\/mn><\/mrow><\/mtd><\/mtr><\/mtable><\/mo><\/mrow><\/mrow>\u5dee\u5206\\ d_i\\ = \\begin{cases} a_i\\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ i=0 \\\\ a_i-a_{i-1}\\ \\ \\ \\ \\ \\ i>0 \\end{cases}<\/annotation><\/semantics><\/math><\/div>\n\n\n\n
\u663e\u7136\uff0c\u5dee\u5206\u5c31\u662f\u5bf9\u67d0\u4e9b\u5143\u7d20\u51cf\u53bb\u524d\u4e00\u4e2a\u5143\u7d20\u7684\u503c\uff0c\u4e5f\u5c31\u662f\u8ba1\u7b97\u76f8\u90bb\u4e24\u4e2a\u6570\u7684\u5dee\uff0c\u56e0\u6b64\u53eb\u505a\u5dee\u5206\u3002\u5dee\u5206\u7684\u5199\u6cd5\u5982\u4e0b\uff1a<\/p>\n\n\n\n
for(int i = n - 1; i >= 0; i--){
    if(i == 0) d[i] = a[i];
    else d[i] = a[i] - a[i - 1];
}<\/pre>\n\n\n\n
\u5728C++\u6807\u51c6\u5e93\u4e2d\u4e5f\u6709\u4e00\u4e2a\u51fd\u6570<\/p>\n\n\n\n
adjacent_difference(a.begin(), a.end(), d.begin());<\/pre>\n\n\n\n
\u5176\u4f7f\u7528\u65b9\u6cd5\u548cpartial_sum\u7c7b\u4f3c\uff0c\u5728\u6b64\u5c31\u4e0d\u518d\u8d58\u8ff0\u4e86<\/p>\n\n\n\n
\u63a5\u4e0b\u6765\u6211\u4eec\u6765\u770b\u4e00\u4e2a\u63a8\u8bba\uff1a\u5bf9\u533a\u95f4 [l , r] \u533a\u95f4\u5185\u6bcf\u4e2a\u5143\u7d20\u90fd\u589e\u52a0 k\uff0c\u7b49\u4ef7\u4e8e\u5bf9\u5dee\u5206\u6570\u7ec4 l \u7684\u4f4d\u7f6e\u589e\u52a0 k \uff0cr + 1 \u7684\u4f4d\u7f6e\u51cf k\u3002\u63a5\u4e0b\u6765\u6211\u4eec\u4e3e\u4e00\u4e2a\u4f8b\u5b50\u6765\u770b\u770b\u8fd9\u4e2a\u63a8\u8bba\u6709\u4ec0\u4e48\u7528\u3002<\/p>\n\n\n\n
\u5047\u8bbe\u539f\u6570\u7ec4\u4e3a 1 2 3 4 5\uff0c\u6211\u4eec\u60f3\u5728 0 ~ 3 \u7684\u533a\u95f4\u90fd +2 \uff0c\u663e\u7136\u6734\u7d20\u7684\u505a\u6cd5\u662f\u679a\u4e3e0 ~ 3 \u4f4d\u7f6e\u7684\u6bcf\u4e00\u4e2a\u5143\u7d20\u90fd\u52a02\uff0c\u8fd9\u6837\u7ecf\u8fc7 m \u6b21\u67e5\u8be2\u540e\uff0c\u590d\u6742\u5ea6\u662fO(n * m),\u5728\u6570\u636e\u8303\u56f4\u8f83\u5927\u7684\u65f6\u5019\u663e\u7136\u592a\u6162\u4e86\uff0c1 2 3 4 5\u5bf9\u5e94\u7684\u5dee\u5206\u6570\u7ec4\u4e3a 1 1 1 1 1 -5\uff08\u4e3a\u4e86\u9632\u6b62\u8d8a\u754c\uff0c\u53ef\u4ee5\u591a\u5f00\u4e00\u4f4d\uff09,\u533a\u95f4\u4fee\u6539\u540e\u7684\u539f\u6570\u7ec4\u4e3a 3 4 5 6 5\uff0c\u5bf9\u5e94\u7684\u5dee\u5206\u6570\u7ec4\u4e3a 3 1 1 1 -1 -5, \u53ef\u4ee5\u53d1\u73b0\uff0c[0 , 3] \u533a\u95f4\u52a02\u7684\u64cd\u4f5c\uff0c\u5bf9\u5e94\u7684\u5c31\u662f\u5728\u5dee\u5206\u6570\u7ec4 0 \u7684\u4f4d\u7f6e\u52a0 2 \uff0c4 \u7684\u4f4d\u7f6e – 2\u3002\u8fd9\u610f\u5473\u7740\u6bcf\u6b21\u4fee\u6539\u6211\u4eec\u90fd\u53ea\u9700\u8981\u4ee5O(1)\u7684\u590d\u6742\u5ea6\u6539\u4e24\u4e2a\u4f4d\u7f6e\uff0c\u90a3\u4e48\u6211\u4eec\u5c31\u53ef\u4ee5\u5bf9\u539f\u6570\u7ec4\u5148\u8fdb\u884c\u4e00\u6b21\u5dee\u5206\uff0c\u518d\u8fdb\u884c\u4fee\u6539\uff0c\u6700\u540e\u8fdb\u884c\u524d\u7f00\u548c\u8fd8\u539f\u4e3a\u539f\u6570\u7ec4\uff0c\u590d\u6742\u5ea6\u7531O(n * m)\u964d\u4f4e\u5230\u4e86O(n + m)\uff0c\u53ef\u559c\u53ef\u8d3a\uff01\ud83e\udd70<\/p>\n\n\n\n
\u8ba9\u6211\u4eec\u7ee7\u7eed\u63a8\u5e7f\u5230\u4e8c\u4f4d\u5dee\u5206\u6570\u7ec4\uff0c\u5982\u679c\u6211\u4eec\u5bf9(x\u2081,y\u2081)\u5230(x\u2082,y\u2082)\u7684\u533a\u95f4\u90fd +k\uff0c\u5c31\u7b49\u4ef7\u4e8e\u5bf9\u5dee\u5206\u6570\u7ec4\u4e2d(x\u2081,y\u2081) +k\uff0c(x\u2082+1,y\u2082+1) +k\uff0c(x\u2081,y\u2082+1) -k\uff0c(x\u2082+1,y\u2081) -k\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u5c06\u539f\u672c\u9700\u8981n^2\u7684\u679a\u4e3e\u4fee\u6539\uff0c\u4f18\u5316\u5230\u4e86O(1)\u7684\u590d\u6742\u5ea6\uff0c\u53ef\u559c\u53ef\u8d3a\uff01\uff01\uff01\ud83e\udd70\ud83e\udd70\ud83e\udd70<\/p>\n\n\n\n
\ud83d\udd8a\u5dee\u5206\u7ec3\u4e60<\/h3>\n\n\n\n
-8.Potyczki Algorytmiczne 2020 KOL \u2764<\/strong>\ud83d\udc9b\ud83d\udc99<\/a>–<\/h4>\n\n\n\n
\n
\u539f\u9898\u94fe\u63a5: https:\/\/pan.baidu.com\/s\/1x7WcXFJATeGxC-wm_XmxVw?pwd=0721<\/a> \u63d0\u53d6\u7801: 0721<\/p>\n<\/blockquote>\n\n\n\n
-9.luogu P13879[\u84dd\u6865\u676f 2023\u7701JAVA A] \u68cb\u76d8\u26ab\u26aa\ufe0f<\/a><\/h4>\n\n\n\n
\u6316\u4e2a\u5751\u5728\u8fd9\u91cc\uff01<\/p>\n\n\n\n
-10.luogu P10903[\u84dd\u6865\u676f 2024\u7701C++ C]\u5546\u54c1\u5e93\u5b58\u7ba1\u7406\ud83d\udce6\ufe0f<\/a><\/h4>\n\n\n\n
\u6316\u4e2a\u5751\u5728\u8fd9\u91cc\uff01<\/p>\n\n\n\n
\ud83d\udcd5*\u5355\u8c03\u6027\u679a\u4e3e<\/h3>\n\n\n\n
\u6316\u4e2a\u5751\u5728\u8fd9\u91cc\uff01<\/p>\n\n\n\n
Part 2 : \u8d2a\u5fc3<\/h2>\n\n\n\n
\ud83d\udcd5\u8d2a\u5fc3<\/h3>\n\n\n\n
\u4f60\u6709\u65e0\u9650\u591a\u7684\u6570\u5b57 5 5 5 5 5 5 5 … ; 2 2 2 2 2 2 2… ; 1 1 1 1 1 1 1 … ;<\/p>\n\n\n\n
\u5982\u4f55\u9009\u62e9\u6700\u5c11\u7684\u6570\u5b57<\/strong>\uff0c\u8ba9\u9009\u62e9\u7684\u6570\u5b57\u4e4b\u548c n \u6070\u597d\u6ee1\u8db3 n == 27\uff1f\u6700\u7b26\u5408\u6211\u4eec\u76f4\u89c9\u7684\u7b56\u7565\u5c31\u662f\u5148\u8d2a\u5fc3\u62ff\u6700\u5927\u7684\u6570\u5b57\uff0c\u76f4\u5230\u63a5\u8fd1 n \u4f46\u4e0d\u8d85\u8fc7 n \uff0c\u7136\u540e\u5269\u4e0b\u7684\u518d\u7528\u540c\u6837\u7684\u65b9\u5f0f\u7528\u66f4\u5c0f\u7684\u6570\u5b57\u586b\u8865\u7a7a\u7f3a\uff0c\u4e5f\u5c31\u662f\u9700\u89815\u4e2a5\u548c1\u4e2a2\uff0c\u8fd9\u4e2a\u601d\u60f3\u5bf9\u4e8e\u8fd9\u7ec4\u6570\u5b57\u6765\u8bf4\u662f\u6b63\u786e\u7684\uff0c\u4f46\u662f\u5bf9\u4e8e\u8fd9\u4e2a\u6a21\u578b\u6765\u8bf4\u662f\u6d45\u663e\u7684\u3001\u9519\u8bef\u7684\u3002\u90a3\u4e48\u7a76\u7adf\u4ec0\u4e48\u662f\u8d2a\u5fc3\u5462\uff1f<\/p>\n\n\n\n
\u9996\u5148\u8ba9\u6211\u4eec\u5bf9\u8d2a\u5fc3\u4e0b\u4e00\u4e2a\u5b9a\u4e49\ud83d\udc47<\/p>\n\n\n\n
\n
\u4ece \u521d\u59cb\u72b6\u6001<\/strong> \u5230 \u76ee\u6807\u72b6\u6001<\/strong><\/p>\n\n\n\n
\u6c42\u4e00\u4e2a \u6700\u4f73\u65b9\u6848<\/strong><\/p>\n\n\n\n
\u6709\u591a\u4e2a \u72b6\u6001\u8f6c\u79fb<\/strong> \u65b9\u5f0f \uff08\u6539\u53d8\u5f53\u524d\u72b6\u6001\u7684\u65b9\u5f0f\uff09<\/p>\n\n\n\n
\u4ec5\u6839\u636e<\/u><\/strong> \u5f53\u524d\u72b6\u6001<\/strong> \u6765\u5236\u5b9a\u7684 \u7b56\u7565<\/strong><\/p>\n\n\n\n
\u79f0\u4e4b\u4e3a \u8d2a\u5fc3<\/strong><\/p>\n<\/blockquote>\n\n\n\n
emm…\u6709\u70b9\u770b\u4e0d\u61c2\uff0c\u8fd9\u4e9b\u540d\u8bcd\u90fd\u662f\u4ec0\u4e48\u610f\u601d\uff1f\u90a3\u5c31\u8ba9\u6211\u4eec\u4ee5\u521a\u624d\u90a3\u4e2a\u95ee\u9898\u4e3a\u4f8b\u8fdb\u884c\u89e3\u91ca<\/p>\n\n\n\n
\n
\u72b6\u6001\uff1a\u5df2\u9009\u62e9\u6570\u5b57\u4e4b\u548c<\/p>\n\n\n\n
\u521d\u59cb\u72b6\u6001\uff1a0<\/p>\n\n\n\n
\u76ee\u6807\u72b6\u6001\uff1an<\/p>\n\n\n\n
\u6700\u4f18\u65b9\u6848\uff1a\u4e2a\u6570\u6700\u5c11<\/p>\n\n\n\n
\u72b6\u6001\u8f6c\u79fb\uff1a+1,+2,+5<\/p>\n\n\n\n
\u7b56\u7565\uff1a\u4ec5\u6839\u636e<\/strong>\u5f53\u524d\u7684\u548c\uff0c\u4f18\u5148\u9009\u6700\u5927\u7684\u6570<\/p>\n<\/blockquote>\n\n\n\n
\u8fd9\u4e9b\u6982\u5ff5\u90fd\u6e05\u695a\u4e4b\u540e\uff0c\u6211\u4eec\u4e0d\u59a8\u91cd\u65b0\u5ba1\u89c6\u6211\u4eec\u4e4b\u524d\u8d2a\u5fc3\u7684\u7b56\u7565\uff0c\u7b26\u5408\u6211\u4eec\u76f4\u89c9\u7684\u7b56\u7565\u5c31\u662f\u5148\u8d2a\u5fc3\u62ff\u6700\u5927\u7684\u6570\u5b57\uff0c\u4f46\u6211\u4eec\u5e94\u8be5\u5982\u4f55\u8bc1\u660e\u6211\u4eec\u7684\u7b56\u7565\u662f\u6b63\u786e\u7684\u5462\uff1f<\/p>\n\n\n\n
\u6211\u4eec\u6765\u5c1d\u8bd5\u7740\u8bc1\u660e\u4e00\u4e0b\uff1a\u56e0\u4e3a\u6211\u4eec\u662f\u62ff\u6700\u5927\u7684\u6570\u5b57\uff0c\u76f4\u5230\u63a5\u8fd1 n \u4f46\u4e0d\u8d85\u8fc7 n \uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u53cd\u8bc1\u6cd5\uff0c\u8bbe\u5f53\u524d\u72b6\u6001\u4e3ax\uff0cx+5\u2264n\uff0c\u6839\u636e\u6211\u4eec\u7684\u7b56\u7565\uff0c\u5e94\u8be5\u90095\u3002<\/p>\n\n\n\n
\u90a3\u4e48\u6211\u4eec\u5047\u8bbe\uff1a\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u6709\u6bd4\u90095\u66f4\u597d\u7684\u65b9\u6848\uff0c\u6bd4\u5982\u9009\u62e92\uff0c\u518d\u5047\u8bbe\u9009\u62e9\u4e862\u540e\uff0c\u540e\u7eed\u8fd8\u4f1a\u90095\uff0c\u7531\u4e8e\u9009\u62e9\u987a\u5e8f\u6ca1\u6709\u5173\u7cfb\uff0c\u6240\u4ee5\u5148\u90092\u518d\u90095\u548c\u5148\u90095\u518d\u90092\u662f\u7b49\u4ef7\u7684\uff0c\u56e0\u6b64\u8fd9\u4e2a\u5047\u8bbe\u4e0b\u90092\u5e76\u4e0d\u6bd4\u90095\u66f4\u597d\uff0c\u5047\u8bbe\u4e0d\u6210\u7acb\u274c<\/p>\n\n\n\n
\u6240\u4ee5\u6211\u4eec\u770b\u53e6\u5916\u7684\u60c5\u51b5\uff0c\u5728\u6211\u4eec\u9009\u4e862\u4e4b\u540e\uff0c\u5269\u4e0b\u7684\u72b6\u6001\u8f6c\u79fb\u53ea\u5269\u4e0b+2\u548c+1\uff0c\u56e0\u4e3ax + 5 \u2264 n\uff0c \u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\uff1a<\/p>\n\n\n\n