{"id":123400,"date":"2026-11-07T06:41:05","date_gmt":"2026-11-06T22:41:05","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/123400.html"},"modified":"2026-11-07T06:41:05","modified_gmt":"2026-11-06T22:41:05","slug":"%e3%80%90%e7%ae%97%e6%b3%95%e6%8b%be%e5%85%89%e3%80%91%e5%88%86%e6%b2%bb%ef%bd%9c%e8%ae%a1%e7%ae%97%e5%8f%b3%e4%be%a7%e5%b0%8f%e4%ba%8e%e5%bd%93","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/123400.html","title":{"rendered":"\u200b\u200b\u200b\u200b\u200b\u200b\u3010\u7b97\u6cd5\u62fe\u5149\u3011\u5206\u6cbb\uff5c\u8ba1\u7b97\u53f3\u4fa7\u5c0f\u4e8e\u5f53\u524d\u5143\u7d20\u7684\u4e2a\u6570 + \u7ffb\u8f6c\u5bf9"},"content":{"rendered":"

\/* MD \/ \u5bcc\u6587\u672c\u4e2d\u7684 .toc\uff08\u542b\u535a\u5ba2\u56ed\u642c\u5bb6\u7b49\u5d4c\u5957\u7ed3\u6784\uff09\uff1b.toc-box \u5728\u4fa7\u680f\uff0c\u4e0d\u53d7\u5f71\u54cd *\/
\n #content_views .toc,
\n \/* \u7f16\u8f91\u5668\u5e38\u5728\u76ee\u5f55\u524d\u540e\u63d2\u5165\u7a7a p\uff08:empty \u4ecd\u5360 20px\uff09\uff0c\u4e00\u5e76\u53bb\u6389\u907f\u514d\u9876\u7a7a\u9699 *\/
\n #content_views.markdown_views > p:empty:has(+ .toc),
\n #content_views.markdown_views > .toc + p:empty,
\n \/* \u5bcc\u6587\u672c\u65e7\u7248\u76ee\u5f55\u6807\u8bb0 *\/
\n #content_views.htmledit_views #main-toc,
\n #content_views.htmledit_views #hr-toc,
\n #content_views.htmledit_views p[id*=\\”-toc\\”] {
\n display: none !important;
\n }
\n \/* \u76ee\u5f55\u53bb\u6389\u540e\uff0c\u7d27\u8ddf\u7684\u9996\u4e2a\u6807\u9898\u4e0d\u518d\u591a\u51fa\u4e00\u5757\u4e0a\u8fb9\u8ddd *\/
\n #content_views.markdown_views > .toc + h1,
\n #content_views.markdown_views > .toc + h2,
\n #content_views.markdown_views > .toc + h3,
\n #content_views.markdown_views > .toc + h4,
\n #content_views.markdown_views > .toc + p:empty + h1,
\n #content_views.markdown_views > .toc + p:empty + h2,
\n #content_views.markdown_views > .toc + p:empty + h3,
\n #content_views.markdown_views > .toc + p:empty + h4 {
\n margin-top: 0 !important;
\n }<\/p>\n

\"\"<\/p>\n

\u9898\u76ee 1：\u8ba1\u7b97\u53f3\u4fa7\u5c0f\u4e8e\u5f53\u524d\u5143\u7d20\u7684\u4e2a\u6570<\/h3>\n

\u9898\u76ee\u94fe\u63a5：315. \u8ba1\u7b97\u53f3\u4fa7\u5c0f\u4e8e\u5f53\u524d\u5143\u7d20\u7684\u4e2a\u6570 – \u529b\u6263（LeetCode）<\/p>\n

\u9898\u76ee\u5206\u6790<\/h4>\n

\u7ed9\u4f60\u4e00\u4e2a\u6574\u6570\u6570\u7ec4 nums，\u6309\u8981\u6c42\u8fd4\u56de\u4e00\u4e2a\u65b0\u6570\u7ec4 counts\u3002counts[i] \u8868\u793a\u5728 nums[i] \u7684\u53f3\u4fa7，\u6bd4 nums[i] \u5c0f\u7684\u5143\u7d20\u7684\u6570\u91cf\u3002 \u66b4\u529b\u505a\u6cd5\u53cc\u5c42\u5faa\u73af \\\\(O(n^2)\\\\)，\u5927\u6570\u636e\u76f4\u63a5\u8d85\u65f6\u3002\u53ef\u4ee5\u501f\u52a9\u5f52\u5e76\u6392\u5e8f\u5206\u6cbb\u601d\u60f3，\u5728\u5408\u5e76\u6709\u5e8f\u533a\u95f4\u7684\u65f6\u5019\u7edf\u8ba1\u7b54\u6848\u3002<\/p>\n

\u6ce8\u610f：\u6392\u5e8f\u4f1a\u6253\u4e71\u539f\u6570\u7ec4\u4e0b\u6807，\u6240\u4ee5\u4e0d\u80fd\u53ea\u5b58\u6570\u503c，\u8981\u4fdd\u5b58\u6570\u503c + \u539f\u59cb\u4e0b\u6807，\u4fdd\u8bc1\u7edf\u8ba1\u7ed3\u679c\u653e\u5230\u6b63\u786e\u4f4d\u7f6e\u3002<\/p>\n

\u7b97\u6cd5\u539f\u7406<\/h4>\n

\u5206\u6cbb\u601d\u8def\u548c\u9006\u5e8f\u5bf9\u975e\u5e38\u76f8\u4f3c：<\/p>\n

  • \u5206\u89e3：\u5c06\u533a\u95f4\u5212\u5206\u4e3a\u5de6\u53f3\u4e24\u534a，\u9012\u5f52\u5904\u7406\u5de6\u533a\u95f4\u3001\u53f3\u533a\u95f4；<\/li>\n
  • \u9012\u5f52：\u5148\u7b97\u51fa\u5de6\u533a\u95f4\u5185\u90e8\u3001\u53f3\u533a\u95f4\u5185\u90e8\u6bcf\u4e2a\u5143\u7d20\u53f3\u4fa7\u66f4\u5c0f\u5143\u7d20\u6570\u91cf；<\/li>\n
  • \u5408\u5e76\u7edf\u8ba1\u8de8\u533a\u95f4\u8d21\u732e：\u5de6\u533a\u95f4\u5143\u7d20\u5728\u539f\u6570\u7ec4\u4e00\u5b9a\u5728\u53f3\u533a\u95f4\u5de6\u8fb9；\u53cc\u6307\u9488\u904d\u5386\u4e24\u4e2a\u6709\u5e8f\u533a\u95f4，\u5982\u679c\u5de6\u5143\u7d20 > \u53f3\u5143\u7d20，\u8bf4\u660e\u8fd9\u4e2a\u53f3\u5143\u7d20\u5bf9\u5de6\u533a\u95f4\u5f53\u524d\u53ca\u540e\u9762\u6240\u6709\u5143\u7d20\u90fd\u4ea7\u751f\u8d21\u732e；<\/li>\n
  • \u5408\u5e76\u6709\u5e8f\u6570\u7ec4，\u5411\u4e0a\u8fd4\u56de，\u6700\u540e\u8f93\u51fa\u7b54\u6848\u6570\u7ec4\u3002<\/li>\n

    \u4ee3\u7801\u7f16\u5199<\/h4>\n

    vector<int> countSmaller(vector<int>& nums) {
    \n int n = nums.size();
    \n vector<int> ans(n, 0);
    \n vector<pair<int,int>> arr(n);
    \n for(int i = 0; i < n; i++) arr[i] = {nums[i], i};
    \n vector<pair<int,int>> temp(n);
    \n mergeSort(arr, temp, ans, 0, n – 1);
    \n return ans;
    \n}<\/p>\n

    void mergeSort(vector<pair<int,int>>& arr, vector<pair<int,int>>& temp, vector<int>& ans, int l, int r) {
    \n if(l >= r) return;
    \n int mid = l + (r – l) \/ 2;
    \n mergeSort(arr, temp, ans, l, mid);
    \n mergeSort(arr, temp, ans, mid + 1, r);
    \n int i = l, j = mid + 1, k = l;
    \n while(i <= mid && j <= r) {
    \n if(arr[i].first <= arr[j].first) {
    \n temp[k++] = arr[i++];
    \n } else {
    \n \/\/ arr[i] > arr[j]，i~mid\u5168\u90e8\u90fd\u5927\u4e8earr[j]
    \n ans[arr[i].second] += r – j + 1;
    \n temp[k++] = arr[j++];
    \n }
    \n }
    \n while(i <= mid) temp[k++] = arr[i++];
    \n while(j <= r) temp[k++] = arr[j++];
    \n for(int p = l; p <= r; p++) arr[p] = temp[p];
    \n}<\/p>\n

    \n

    \u9898\u76ee 2：\u7ffb\u8f6c\u5bf9<\/h3>\n

    \u9898\u76ee\u94fe\u63a5：493. \u7ffb\u8f6c\u5bf9 – \u529b\u6263（LeetCode）<\/p>\n

    \u9898\u76ee\u5206\u6790<\/h4>\n

    \u7ed9\u5b9a\u4e00\u4e2a\u6570\u7ec4 nums，\u5982\u679c i < j \u4e14 nums[i] > 2 * nums[j]，\u79f0 (i,j) \u4e3a\u4e00\u7ec4\u7ffb\u8f6c\u5bf9\u3002\u6c42\u7ffb\u8f6c\u5bf9\u603b\u6570\u91cf\u3002 \u548c\u9006\u5e8f\u5bf9\u7684\u533a\u522b：\u5224\u65ad\u6761\u4ef6\u4e0d\u662f nums[i] > nums[j]，\u800c\u662f nums[i] > 2 * nums[j]\u3002 \u540c\u6837\u5f52\u5e76\u5206\u6cbb，\u4f46\u662f\u7edf\u8ba1\u7ffb\u8f6c\u5bf9\u548c\u5408\u5e76\u6709\u5e8f\u6570\u7ec4\u8981\u5206\u6210\u4e24\u8f6e\u5faa\u73af，\u4e0d\u80fd\u5728\u5408\u5e76\u7684\u65f6\u5019\u4e00\u8d77\u7edf\u8ba1，\u4e0d\u7136\u903b\u8f91\u4f1a\u51fa\u9519\u3002<\/p>\n

    \u7b97\u6cd5\u539f\u7406<\/h4>\n
  • \u5206\u89e3：\u533a\u95f4 [l, r] \u62c6\u6210 [l, mid] \u548c [mid+1, r]；<\/li>\n
  • \u9012\u5f52：\u5206\u522b\u6c42\u51fa\u5de6\u533a\u95f4\u7ffb\u8f6c\u5bf9\u3001\u53f3\u533a\u95f4\u7ffb\u8f6c\u5bf9；<\/li>\n
  • \u5355\u72ec\u53cc\u6307\u9488\u7edf\u8ba1\u8de8\u533a\u95f4\u7ffb\u8f6c\u5bf9：\u5de6\u3001\u53f3\u533a\u95f4\u5df2\u7ecf\u5404\u81ea\u6709\u5e8f，\u56fa\u5b9a i，\u627e\u5230\u6700\u5927\u7684 j \u6ee1\u8db3 nums[i] > 2 * nums[j]；<\/li>\n
  • \u518d\u6267\u884c\u5e38\u89c4\u5f52\u5e76\u5408\u5e76，\u5c06\u5f53\u524d\u533a\u95f4\u5408\u5e76\u4e3a\u6709\u5e8f\u6570\u7ec4，\u5411\u4e0a\u8fd4\u56de\u603b\u6570\u3002<\/li>\n

    \u4ee3\u7801\u7f16\u5199<\/h4>\n

    vector<int> temp;
    \nint reversePairs(vector<int>& nums) {
    \n temp.resize(nums.size());
    \n return mergeSort(nums, 0, nums.size() – 1);
    \n}<\/p>\n

    int mergeSort(vector<int>& nums, int l, int r) {
    \n if(l >= r) return 0;
    \n int mid = l + (r – l) \/ 2;
    \n int res = mergeSort(nums, l, mid) + mergeSort(nums, mid + 1, r);<\/p>\n

    \/\/ \u7b2c\u4e00\u6b65：\u5355\u72ec\u7edf\u8ba1\u7ffb\u8f6c\u5bf9
    \n int i = l, j = mid + 1;
    \n while(i <= mid) {
    \n while(j <= r && (long long)nums[i] > 2LL * nums[j]) {
    \n j++;
    \n }
    \n res += j – (mid + 1);
    \n i++;
    \n }<\/p>\n

    \/\/ \u7b2c\u4e8c\u6b65：\u5f52\u5e76\u5408\u5e76
    \n i = l, j = mid + 1;
    \n int k = l;
    \n while(i <= mid && j <= r) {
    \n if(nums[i] <= nums[j]) {
    \n temp[k++] = nums[i++];
    \n } else {
    \n temp[k++] = nums[j++];
    \n }
    \n }
    \n while(i <= mid) temp[k++] = nums[i++];
    \n while(j <= r) temp[k++] = nums[j++];
    \n for(int p = l; p <= r; p++) nums[p] = temp[p];
    \n return res;
    \n}<\/p>\n

    \n

    \u672c\u7bc7\u603b\u7ed3<\/h3>\n

    \u8fd9\u4e24\u9053\u9898\u90fd\u662f\u5f52\u5e76\u5206\u6cbb\u7684\u8fdb\u9636\u9898\u578b，\u548c\u9006\u5e8f\u5bf9\u4e00\u8109\u76f8\u627f：<\/p>\n

  • \u8ba1\u7b97\u53f3\u4fa7\u5c0f\u4e8e\u5f53\u524d\u5143\u7d20\u7684\u4e2a\u6570：\u96be\u70b9\u5728\u4e8e\u6392\u5e8f\u4f1a\u6253\u4e71\u4e0b\u6807，\u5fc5\u987b\u7ed1\u5b9a\u539f\u59cb\u4e0b\u6807，\u628a\u7edf\u8ba1\u503c\u56de\u586b\u5230\u6b63\u786e\u4f4d\u7f6e；<\/li>\n
  • \u7ffb\u8f6c\u5bf9：\u5224\u65ad\u6761\u4ef6\u53d8\u6210 nums[i] > 2*nums[j]，\u7edf\u8ba1\u548c\u5408\u5e76\u8981\u5206\u5f00\u4e24\u8f6e，\u5e76\u4e14\u4e00\u5b9a\u8981\u5f3a\u8f6c long long \u9632\u6b62\u6ea2\u51fa；<\/li>\n
  • \u5171\u6027：\u90fd\u5229\u7528\u300c\u5de6\u53f3\u5b50\u533a\u95f4\u5185\u90e8\u6709\u5e8f\u300d\u7684\u6027\u8d28，\u907f\u514d\u66b4\u529b\u679a\u4e3e，\u65f6\u95f4\u590d\u6742\u5ea6\u7a33\u5b9a \\\\(O(n\\\\log n)\\\\)\u3002<\/li>\n

    \"\"<\/p>\n","protected":false},"excerpt":{"rendered":"

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