{"id":76385,"date":"2026-02-22T12:17:08","date_gmt":"2026-02-22T04:17:08","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/76385.html"},"modified":"2026-02-22T12:17:08","modified_gmt":"2026-02-22T04:17:08","slug":"%e7%ae%80%e5%8d%95%e5%88%a9%e7%94%a8%e6%a0%91%e7%8a%b6%e6%95%b0%e7%bb%84%e4%bc%98%e5%8c%96%e5%ae%9e%e4%be%8b","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/76385.html","title":{"rendered":"\u7b80\u5355\u5229\u7528\u6811\u72b6\u6570\u7ec4\u4f18\u5316\u5b9e\u4f8b"},"content":{"rendered":"

<\/h2>\n

\u7b80\u5355\u5229\u7528\u6811\u72b6\u6570\u7ec4\u4f18\u5316\u5b9e\u4f8b：\u4ece O(n\u00b2) \u5230 O(n log n)<\/h2>\n

\u4f8b\u9898\u94fe\u63a5:\u5de6\u4fa7\u4e25\u683c\u5c0f\u4e8e\u8ba1\u6570_\u725b\u5ba2\u9898\u9738_\u725b\u5ba2\u7f51<\/p>\n

\u95ee\u9898\u7b80\u8ff0:<\/h3>\n

\u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4 a，\u5bf9\u4e8e\u6bcf\u4e2a\u4f4d\u7f6e i，\u6c42\u524d\u9762\u6709\u591a\u5c11\u4e2a\u6570\u6bd4 a[i] \u5c0f\u3002<\/p>\n

\u793a\u4f8b：<\/p>\n

\u8f93\u5165：a = [5, 2, 4, 1, 3]
\n\u8f93\u51fa：0 0 1 0 2
\n\u89e3\u91ca：
\n– i=1, a[1]=5, \u524d\u9762\u65e0\u6570 \u2192 0
\n– i=2, a[2]=2, \u524d\u9762[5], \u65e0\u6bd42\u5c0f\u7684 \u2192 0
\n– i=3, a[3]=4, \u524d\u9762[5,2], \u6bd44\u5c0f\u7684\u6709[2] \u2192 1
\n– i=4, a[4]=1, \u524d\u9762[5,2,4], \u65e0\u6bd41\u5c0f\u7684 \u2192 0
\n– i=5, a[5]=3, \u524d\u9762[5,2,4,1], \u6bd43\u5c0f\u7684\u6709[2,1] \u2192 2 <\/p>\n

\n

\u65b9\u6cd5\u4e00：\u66b4\u529b\u89e3\u6cd5 O(n\u00b2)<\/h3>\n

\u6838\u5fc3\u601d\u8def<\/h4>\n

\u5bf9\u4e8e\u6bcf\u4e2a\u4f4d\u7f6e，\u904d\u5386\u524d\u9762\u6240\u6709\u5143\u7d20，\u9010\u4e2a\u6bd4\u8f83\u7edf\u8ba1\u3002<\/p>\n

\u4ee3\u7801\u5b9e\u73b0<\/h4>\n

#include <bits\/stdc++.h>
\nusing namespace std;
\ntypedef long long ll;<\/p>\n

int main() {
\n ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);<\/p>\n

int n;
\n cin >> n;
\n vector<int> a(n+1, 0), b(n+1, 0);<\/p>\n

for(int i = 1; i <= n; i++) {
\n cin >> a[i];
\n int temp = a[i];
\n \/\/ \u904d\u5386\u524d\u9762\u6240\u6709\u5143\u7d20
\n for(int j = 1; j < i; j++) {
\n if(temp > a[j]) \/\/ \u524d\u9762\u6709\u6bd4\u5f53\u524d\u5c0f\u7684
\n b[i]++;
\n }
\n }<\/p>\n

for(int i = 1; i <= n; i++)
\n cout << b[i] << ' ';
\n} <\/p>\n

\u590d\u6742\u5ea6\u5206\u6790<\/h4>\n\n\u9879\u76ee\u590d\u6742\u5ea6\u8bf4\u660e<\/tr>\n\n\n\n\n
\u65f6\u95f4\u590d\u6742\u5ea6<\/td>\nO(n\u00b2)<\/td>\n\u53cc\u91cd\u5faa\u73af，\u5916\u5c42n\u6b21，\u5185\u5c42\u5e73\u5747n\/2\u6b21<\/td>\n<\/tr>\n
\u7a7a\u95f4\u590d\u6742\u5ea6<\/td>\nO(n)<\/td>\n\u5b58\u50a8\u6570\u7ec4a\u548c\u7b54\u6848b<\/td>\n<\/tr>\n
\u6700\u5927\u53ef\u5904\u7406\u89c4\u6a21<\/td>\nn \u2264 10\u2074<\/td>\n10\u2078\u6b21\u64cd\u4f5c\u7ea61\u79d2，n=10\u2074\u65f6\u521a\u597d10\u2078<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u74f6\u9888：\u6bcf\u6b21\u67e5\u8be2"\u524d\u9762\u6709\u591a\u5c11\u4e2a\u6bd4\u5b83\u5c0f"\u90fd\u8981\u904d\u5386\u4e00\u904d，\u505a\u4e86\u5927\u91cf\u91cd\u590d\u5de5\u4f5c\u3002<\/p>\n

\n

\u65b9\u6cd5\u4e8c：\u6811\u72b6\u6570\u7ec4\u4f18\u5316 O(n log n)<\/h3>\n

\u6838\u5fc3\u601d\u8def<\/h4>\n

\u5173\u952e\u89c2\u5bdf：\u6211\u4eec\u9700\u8981\u4e00\u4e2a\u6570\u636e\u7ed3\u6784，\u652f\u6301\u4e24\u79cd\u64cd\u4f5c：<\/p>\n

  • \n

    \u67e5\u8be2：\u5df2\u7ecf\u51fa\u73b0\u7684\u6570\u4e2d，\u6709\u591a\u5c11\u4e2a < x<\/p>\n<\/li>\n

  • \n

    \u63d2\u5165：\u628a\u5f53\u524d\u6570 x \u52a0\u5165\u96c6\u5408，\u4f9b\u540e\u7eed\u67e5\u8be2<\/p>\n<\/li>\n

    \u6811\u72b6\u6570\u7ec4（Fenwick Tree） \u6b63\u597d\u6ee1\u8db3：\u5355\u70b9\u4fee\u6539 + \u524d\u7f00\u67e5\u8be2\u90fd\u662f O(log n)\u3002<\/p>\n

    \u6280\u5de7\u2014\u2014\u79bb\u6563\u5316：\u5982\u679c\u6570\u503c\u5f88\u5927（\u598210\u2079），\u76f4\u63a5\u5f00\u6570\u7ec4\u4f1aMLE\u3002\u5148\u5c06\u6570\u503c\u6620\u5c04\u5230 [1, n] \u7684\u7d27\u51d1\u8303\u56f4\u3002<\/p>\n

    \u4ee3\u7801\u5b9e\u73b0<\/h4>\n

    #include <bits\/stdc++.h>
    \nusing namespace std;
    \ntypedef long long ll;<\/p>\n

    const int N = 2e5 + 10; \/\/ \u6839\u636e\u6570\u636e\u8303\u56f4\u8c03\u6574<\/p>\n

    int n;
    \nint c[N]; \/\/ \u6811\u72b6\u6570\u7ec4<\/p>\n

    \/\/ lowbit: \u63d0\u53d6\u4e8c\u8fdb\u5236\u6700\u4f4e\u4f4d\u76841
    \n\/\/ \u4f8b\u5982：6(110) \u2192 2(010), 8(1000) \u2192 8(1000)
    \nint lowbit(int x)
    \n{
    \nreturn x & (-x);
    \n}<\/p>\n

    \/\/ \u5728\u4f4d\u7f6ex\u589e\u52a0v，\u5e76\u66f4\u65b0\u6240\u6709\u7956\u5148\u8282\u70b9
    \nvoid add(int x, int v)
    \n{
    \nfor (int i = x; i <= n; i += lowbit(i))
    \nc[i] += v;
    \n}<\/p>\n

    \/\/ \u67e5\u8be2[1, x]\u7684\u524d\u7f00\u548c，\u5373\u6709\u591a\u5c11\u4e2a\u6570 \u2264 x
    \nint query(int x)
    \n{
    \nint res = 0;
    \nfor (int i = x; i > 0; i -= lowbit(i))
    \nres += c[i];
    \nreturn res;
    \n}<\/p>\n

    int main()
    \n{
    \nios::sync_with_stdio(0);
    \ncin.tie(0);
    \ncout.tie(0);<\/p>\n

    cin >> n;
    \nvector<int> a(n + 1), b(n + 1);
    \nvector<int> all; \/\/ \u7528\u4e8e\u79bb\u6563\u5316<\/p>\n

    \/\/ \u8bfb\u5165\u6570\u636e
    \nfor (int i = 1; i <= n; i++)
    \n{
    \ncin >> a[i];
    \nall.push_back(a[i]);
    \n}<\/p>\n

    \/\/ \u79bb\u6563\u5316：\u6392\u5e8f + \u53bb\u91cd
    \nsort(all.begin(), all.end());
    \nall.erase(unique(all.begin(), all.end()), all.end());<\/p>\n

    \/\/ \u9010\u4e2a\u5904\u7406
    \nfor (int i = 1; i <= n; i++)
    \n{
    \n\/\/ \u627e\u5230a[i]\u5728all\u4e2d\u7684\u4f4d\u7f6e（1-based）
    \nint pos = lower_bound(all.begin(), all.end(), a[i]) – all.begin() + 1;<\/p>\n

    \/\/ \u67e5\u8be2：\u524d\u9762\u6709\u591a\u5c11\u4e2a\u6570 < a[i]（\u5373\u79bb\u6563\u5316\u503c\u5728[1, pos-1]\u8303\u56f4\u5185）
    \nb[i] = query(pos – 1);<\/p>\n

    \/\/ \u63d2\u5165：\u628a\u5f53\u524d\u6570\u52a0\u5165\u6811\u72b6\u6570\u7ec4
    \nadd(pos, 1);
    \n}<\/p>\n

    for (int i = 1; i <= n; i++)
    \ncout << b[i] << ' ';<\/p>\n

    return 0;
    \n} <\/p>\n

    \u4e24\u79cd\u65b9\u6cd5\u5bf9\u6bd4<\/h3>\n\n\u5bf9\u6bd4\u9879\u66b4\u529b O(n\u00b2)\u6811\u72b6\u6570\u7ec4 O(n log n)<\/tr>\n\n\n\n\n\n\n\n\n
    \u6838\u5fc3\u601d\u60f3<\/td>\n\u9010\u4e2a\u6bd4\u8f83<\/td>\n\u7528\u524d\u7f00\u548c\u5feb\u901f\u8ba1\u6570<\/td>\n<\/tr>\n
    \u5355\u6b21\u67e5\u8be2<\/td>\nO(n) \u904d\u5386<\/td>\nO(log n) \u4e8c\u5206\u8df3<\/td>\n<\/tr>\n
    \u5355\u6b21\u63d2\u5165<\/td>\n\u65e0\u9700\u63d2\u5165<\/td>\nO(log n) \u66f4\u65b0<\/td>\n<\/tr>\n
    \u603b\u65f6\u95f4<\/td>\nO(n\u00b2)<\/td>\nO(n log n)<\/td>\n<\/tr>\n
    \u53ef\u5904\u7406\u89c4\u6a21<\/td>\nn \u2264 10\u2074<\/td>\nn \u2264 10\u2076 ~ 10\u2077<\/td>\n<\/tr>\n
    \u989d\u5916\u7a7a\u95f4<\/td>\nO(n)<\/td>\nO(n)<\/td>\n<\/tr>\n
    \u4ee3\u7801\u91cf<\/td>\n\u5c11<\/td>\n\u8f83\u591a（\u9700\u5b9e\u73b0\u6811\u72b6\u6570\u7ec4）<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
    \n

    \u5173\u952e\u6b65\u9aa4\u56fe\u89e3<\/h3>\n

    \u4ee5 a = [5, 2, 4] \u4e3a\u4f8b：<\/p>\n

    \u79bb\u6563\u5316：5\u21923, 2\u21921, 4\u21922<\/p>\n

    \u6811\u72b6\u6570\u7ec4\u7ef4\u62a4\u7684\u662f"\u6bcf\u4e2a\u79bb\u6563\u5316\u503c\u51fa\u73b0\u4e86\u51e0\u6b21"<\/p>\n

    \u6b65\u9aa41: \u5904\u74065(pos=3)
    \n \u67e5\u8be2[1,2]\u7684\u548c = 0 \u2192 b[1]=0
    \n \u5728\u4f4d\u7f6e3\u52a01 \u2192 \u6570\u7ec4: [0,0,1,0]<\/p>\n

    \u6b65\u9aa42: \u5904\u74062(pos=1)
    \n \u67e5\u8be2[1,0]\u7684\u548c = 0 \u2192 b[2]=0
    \n \u5728\u4f4d\u7f6e1\u52a01 \u2192 \u6570\u7ec4: [1,0,1,0]<\/p>\n

    \u6b65\u9aa43: \u5904\u74064(pos=2)
    \n \u67e5\u8be2[1,1]\u7684\u548c = 1 \u2192 b[3]=1（\u524d\u9762\u67092）
    \n \u5728\u4f4d\u7f6e2\u52a01 \u2192 \u6570\u7ec4: [1,1,1,0] <\/p>\n

    \n

    \u603b\u7ed3<\/h3>\n\n\u573a\u666f\u63a8\u8350\u65b9\u6cd5<\/tr>\n\n\n\n\n
    n \u2264 5000<\/td>\n\u66b4\u529b，\u7b80\u5355\u4e0d\u6613\u9519<\/td>\n<\/tr>\n
    n > 10\u2074 \u6216 \u591a\u7ec4\u6d4b\u8bd5<\/td>\n\u6811\u72b6\u6570\u7ec4，\u907f\u514dTLE<\/td>\n<\/tr>\n
    \u9700\u8981\u6c42\u9006\u5e8f\u5bf9\u3001\u533a\u95f4\u8ba1\u6570<\/td>\n\u6811\u72b6\u6570\u7ec4\u662f\u6807\u51c6\u5de5\u5177<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    \u6811\u72b6\u6570\u7ec4\u7684\u6838\u5fc3\u4ef7\u503c\u5728\u4e8e\u5c06"\u904d\u5386\u7edf\u8ba1"\u8f6c\u5316\u4e3a"\u524d\u7f00\u548c\u67e5\u8be2"，\u7528 O(log n) \u7684\u4ee3\u6570\u64cd\u4f5c\u66ff\u4ee3 O(n) \u7684\u7ebf\u6027\u626b\u63cf<\/p>\n

    \u7ed3\u8bed:<\/h2>\n

    \u5e0c\u671b\u672c\u7ae0\u80fd\u591f\u5e2e\u52a9\u5230\u60a8~,\u7801\u5b57\u4e0d\u6613,\u611f\u8c22\u60a8\u7684\u70b9\u8d5e\u6536\u85cfo(*￣\u25bd￣*)\u30d6<\/p>\n","protected":false},"excerpt":{"rendered":"

    \u7b80\u5355\u5229\u7528\u6811\u72b6\u6570\u7ec4\u4f18\u5316\u5b9e\u4f8b：\u4ece O(n\u00b2) \u5230 O(n log n)
    \n\u4f8b\u9898\u94fe\u63a5:\u5de6\u4fa7\u4e25\u683c\u5c0f\u4e8e\u8ba1\u6570_\u725b\u5ba2\u9898\u9738_\u725b\u5ba2\u7f51
    \n\u95ee\u9898\u7b80\u8ff0:
    \n\u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4 a，\u5bf9\u4e8e\u6bcf\u4e2a\u4f4d\u7f6e i，\u6c42\u524d\u9762\u6709\u591a\u5c11\u4e2a\u6570\u6bd4 a[i] \u5c0f\u3002
    \n\u793a\u4f8b：
    \n\u8f93\u5165：a [5, 2, 4, 1, 3]
    \n\u8f93\u51fa：0 0 1 0 2
    \n\u89e3\u91ca：
    \n– i1, a[1]5, \u524d\u9762\u65e0\u6570 \u2192 0
    \n– i2, a[2]2, \u524d\u9762<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[55,1813,427],"topic":[],"class_list":["post-76385","post","type-post","status-publish","format-standard","hentry","category-server","tag-c","tag-1813","tag-427"],"yoast_head":"\n\u7b80\u5355\u5229\u7528\u6811\u72b6\u6570\u7ec4\u4f18\u5316\u5b9e\u4f8b - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.wsisp.com\/helps\/76385.html\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u7b80\u5355\u5229\u7528\u6811\u72b6\u6570\u7ec4\u4f18\u5316\u5b9e\u4f8b - \u7f51\u7855\u4e92\u8054\u5e2e\u52a9\u4e2d\u5fc3\" \/>\n<meta property=\"og:description\" content=\"\u7b80\u5355\u5229\u7528\u6811\u72b6\u6570\u7ec4\u4f18\u5316\u5b9e\u4f8b：\u4ece O(n\u00b2) \u5230 O(n log n) \u4f8b\u9898\u94fe\u63a5:\u5de6\u4fa7\u4e25\u683c\u5c0f\u4e8e\u8ba1\u6570_\u725b\u5ba2\u9898\u9738_\u725b\u5ba2\u7f51 \u95ee\u9898\u7b80\u8ff0: \u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a n \u7684\u6570\u7ec4 a，\u5bf9\u4e8e\u6bcf\u4e2a\u4f4d\u7f6e i，\u6c42\u524d\u9762\u6709\u591a\u5c11\u4e2a\u6570\u6bd4 a[i] \u5c0f\u3002 \u793a\u4f8b： \u8f93\u5165：a [5, 2, 4, 1, 3] \u8f93\u51fa：0 0 1 0 2 \u89e3\u91ca： - 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