{"id":75,"date":"2026-04-06T15:15:11","date_gmt":"2026-04-06T07:15:11","guid":{"rendered":"https:\/\/www.sjll.top\/index.php\/2026\/04\/06\/acwing-260-%e4%b9%b0%e7%a5%a8%ef%bc%9a%e6%a0%91%e7%8a%b6%e6%95%b0%e7%bb%84%e4%b8%8e%e4%ba%8c%e5%88%86%e6%9f%a5%e6%89%be%e7%9a%84%e5%ae%8c%e7%be%8e%e7%bb%93%e5%90%88\/"},"modified":"2026-04-06T15:15:11","modified_gmt":"2026-04-06T07:15:11","slug":"acwing-260-%e4%b9%b0%e7%a5%a8%ef%bc%9a%e6%a0%91%e7%8a%b6%e6%95%b0%e7%bb%84%e4%b8%8e%e4%ba%8c%e5%88%86%e6%9f%a5%e6%89%be%e7%9a%84%e5%ae%8c%e7%be%8e%e7%bb%93%e5%90%88","status":"publish","type":"post","link":"https:\/\/www.sjll.top\/?p=75","title":{"rendered":"AcWing 260. \u4e70\u7968\uff1a\u6811\u72b6\u6570\u7ec4\u4e0e\u4e8c\u5206\u67e5\u627e\u7684\u5b8c\u7f8e\u7ed3\u5408"},"content":{"rendered":"<h2>\u9898\u76ee\u63cf\u8ff0<\/h2>\n<p>\u6625\u8fd0\u671f\u95f4\uff0c\u706b\u8f66\u7ad9\u552e\u7968\u5904\u6392\u8d77\u4e86\u957f\u961f\u3002\u6709\u4e9b\u4eba\u8d81\u4e71\u63d2\u961f\uff0c\u73b0\u5728\u9700\u8981\u6839\u636e\u6bcf\u4e2a\u4eba\u8fdb\u5165\u961f\u5217\u65f6\u7684\u4f4d\u7f6e\u548c\u7f16\u53f7\uff0c\u786e\u5b9a\u6700\u7ec8\u7684\u961f\u5217\u987a\u5e8f\u3002<\/p>\n<h3>\u8f93\u5165\u683c\u5f0f<\/h3>\n<p>\u8f93\u5165\u53ef\u80fd\u5305\u542b\u591a\u7ec4\u6d4b\u8bd5\u7528\u4f8b\u3002\u6bcf\u7ec4\u6d4b\u8bd5\u7528\u4f8b\uff1a<\/p>\n<ul>\n<li>\u7b2c\u4e00\u884c\u5305\u542b\u6574\u6570 N\uff0c\u8868\u793a\u6392\u961f\u7684\u603b\u4eba\u6570<\/li>\n<li>\u63a5\u4e0b\u6765 N \u884c\uff0c\u6bcf\u884c\u4e24\u4e2a\u6574\u6570 Pi, Vi<\/li>\n<li>Pi \u8868\u793a\u7b2c i \u4e2a\u4eba\u8fdb\u5165\u961f\u5217\u65f6\uff0c\u4ed6\u524d\u9762\u7684\u4eba\u6570\uff080\u8868\u793a\u961f\u9996\uff09<\/li>\n<li>Vi \u8868\u793a\u8fd9\u4e2a\u4eba\u7684\u7f16\u53f7<\/li>\n<\/ul>\n<h3>\u8f93\u51fa\u683c\u5f0f<\/h3>\n<p>\u6bcf\u4e2a\u6d4b\u8bd5\u7528\u4f8b\uff0c\u8f93\u51fa\u4e00\u884c\u5305\u542b N \u4e2a\u6574\u6570\u7684\u6700\u7ec8\u961f\u5217\u987a\u5e8f\u3002<\/p>\n<h2>\u95ee\u9898\u5206\u6790<\/h2>\n<h3>\u6838\u5fc3\u96be\u70b9<\/h3>\n<p>\u5982\u679c\u6b63\u7740\u5904\u7406\uff0c\u6bcf\u6b21\u63d2\u5165\u64cd\u4f5c\u90fd\u4f1a\u5f71\u54cd\u540e\u9762\u6240\u6709\u4eba\u7684\u4f4d\u7f6e\uff0c\u5bfc\u81f4\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n\u00b2)\uff0c\u65e0\u6cd5\u6ee1\u8db3 N \u2264 200000 \u7684\u6570\u636e\u89c4\u6a21\u3002<\/p>\n<h3>\u5173\u952e\u8f6c\u5316\uff1a\u9006\u5e8f\u5904\u7406<\/h3>\n<p>\u4ece\u6700\u540e\u4e00\u4e2a\u4eba\u5f00\u59cb\u5f80\u524d\u5904\u7406\uff1a<\/p>\n<ul>\n<li>\u6700\u540e\u4e00\u4e2a\u4eba\u7684\u4f4d\u7f6e\u662f\u786e\u5b9a\u7684\uff08\u56e0\u4e3a\u540e\u9762\u6ca1\u6709\u4eba\u4f1a\u5f71\u54cd\u4ed6\uff09<\/li>\n<li>\u5bf9\u4e8e\u7b2c i \u4e2a\u4eba\uff0c\u4ed6\u5e94\u8be5\u63d2\u5165\u5230\u5f53\u524d\u7a7a\u4f4d\u4e2d\u7684\u7b2c p[i]+1 \u4e2a\u4f4d\u7f6e<\/li>\n<li>\u4f7f\u7528\u6811\u72b6\u6570\u7ec4\u7ef4\u62a4\u7a7a\u4f4d\u4fe1\u606f\uff0c\u4e8c\u5206\u67e5\u627e\u786e\u5b9a\u63d2\u5165\u4f4d\u7f6e<\/li>\n<\/ul>\n<h2>\u7b97\u6cd5\u8be6\u89e3<\/h2>\n<h3>\u6811\u72b6\u6570\u7ec4\uff08Fenwick Tree\uff09<\/h3>\n<p>\u6811\u72b6\u6570\u7ec4\u662f\u4e00\u79cd\u9ad8\u6548\u7684\u6570\u636e\u7ed3\u6784\uff0c\u7528\u4e8e\u7ef4\u62a4\u6570\u7ec4\u524d\u7f00\u548c\u7684\u52a8\u6001\u67e5\u8be2\u548c\u66f4\u65b0\u3002\u5176\u6838\u5fc3\u4f18\u52bf\u5728\u4e8e\uff1a<\/p>\n<ul>\n<li><strong>\u5355\u70b9\u66f4\u65b0 O(log n)<\/strong>\uff1a\u4fee\u6539\u4e00\u4e2a\u5143\u7d20\u7684\u503c<\/li>\n<li><strong>\u533a\u95f4\u67e5\u8be2 O(log n)<\/strong>\uff1a\u67e5\u8be2\u524d\u7f00\u548c<\/li>\n<\/ul>\n<p>\u5728\u672c\u9898\u4e2d\uff0c\u6811\u72b6\u6570\u7ec4\u7528\u4e8e\u7ef4\u62a4\u6bcf\u4e2a\u4f4d\u7f6e\u662f\u5426\u4e3a\u7a7a\u4f4d\uff1a<\/p>\n<ul>\n<li>tr[i] \u8868\u793a\u524d i \u4e2a\u4f4d\u7f6e\u5171\u6709\u591a\u5c11\u4e2a\u7a7a\u4f4d<\/li>\n<li>\u521d\u59cb\u65f6\u6240\u6709\u4f4d\u7f6e\u90fd\u662f\u7a7a\u4f4d\uff08\u503c\u4e3a1\uff09<\/li>\n<li>\u5f53\u4e00\u4e2a\u4eba\u5360\u636e\u4f4d\u7f6e\u540e\uff0c\u8be5\u4f4d\u7f6e\u7684\u503c\u53d8\u4e3a0<\/li>\n<\/ul>\n<h3>\u4e8c\u5206\u67e5\u627e\u7b2c k \u4e2a\u7a7a\u4f4d<\/h3>\n<p>\u901a\u8fc7\u6811\u72b6\u6570\u7ec4\u7684 sum(mid) \u51fd\u6570\uff0c\u53ef\u4ee5\u5feb\u901f\u5f97\u5230\u524d mid \u4e2a\u4f4d\u7f6e\u6709\u591a\u5c11\u7a7a\u4f4d\u3002<\/p>\n<p>\u4e8c\u5206\u67e5\u627e\u7684\u6838\u5fc3\u601d\u60f3\uff1a\u627e\u5230\u6700\u5c0f\u7684\u4f4d\u7f6e x\uff0c\u4f7f\u5f97 sum(x) \u2265 k\uff0c\u8fd9\u4e2a x \u5c31\u662f\u7b2c k \u4e2a\u7a7a\u4f4d\u7684\u4f4d\u7f6e\u3002<\/p>\n<p>\u8fd9\u4f53\u73b0\u4e86\u300c\u53ef\u4e8c\u5206\u6027\u300d\uff1a\u968f\u7740\u4f4d\u7f6e\u53f3\u79fb\uff0c\u7a7a\u4f4d\u6570\u91cf\u5355\u8c03\u9012\u589e\u3002<\/p>\n<h2>\u5904\u7406\u8fc7\u7a0b\u793a\u4f8b<\/h2>\n<p>\u4ee5\u8f93\u5165\u6837\u4f8b\u4e3a\u4f8b\uff1a<\/p>\n<pre><code>\u8f93\u5165\uff1a\n4\n0 77   \/\/ \u7b2c1\u4e2a\u4eba\u63d2\u5230\u4f4d\u7f6e0\uff08\u961f\u9996\uff09\n1 51   \/\/ \u7b2c2\u4e2a\u4eba\u63d2\u5230\u4f4d\u7f6e1\uff08\u7b2c1\u4e2a\u4eba\u540e\u9762\uff09\n1 33   \/\/ \u7b2c3\u4e2a\u4eba\u63d2\u5230\u4f4d\u7f6e1\n2 69   \/\/ \u7b2c4\u4e2a\u4eba\u63d2\u5230\u4f4d\u7f6e2<\/code><\/pre>\n<p>\u5904\u7406\u8fc7\u7a0b\uff1a<\/p>\n<pre><code>\u521d\u59cb\u5316\uff1a[1,1,1,1]  \/\/ 1\u8868\u793a\u7a7a\u4f4d\n\n\u5904\u7406\u7b2c4\u4eba\uff1ap[4]=2\uff0c\u627e\u7b2c3\u4e2a\u7a7a\u4f4d \u2192 \u4f4d\u7f6e3 \u2192 [1,1,0,1]\n\u5904\u7406\u7b2c3\u4eba\uff1ap[3]=1\uff0c\u627e\u7b2c2\u4e2a\u7a7a\u4f4d \u2192 \u4f4d\u7f6e2 \u2192 [1,0,0,1]\n\u5904\u7406\u7b2c2\u4eba\uff1ap[2]=1\uff0c\u627e\u7b2c2\u4e2a\u7a7a\u4f4d \u2192 \u4f4d\u7f6e4 \u2192 [1,0,0,0]\n\u5904\u7406\u7b2c1\u4eba\uff1ap[1]=0\uff0c\u627e\u7b2c1\u4e2a\u7a7a\u4f4d \u2192 \u4f4d\u7f6e1 \u2192 [0,0,0,0]\n\n\u6700\u7ec8\u7ed3\u679c\uff1a[77,33,69,51]<\/code><\/pre>\n<h2>\u590d\u6742\u5ea6\u5206\u6790<\/h2>\n<table>\n<tr>\n<th>\u64cd\u4f5c<\/th>\n<th>\u65f6\u95f4\u590d\u6742\u5ea6<\/th>\n<th>\u7a7a\u95f4\u590d\u6742\u5ea6<\/th>\n<\/tr>\n<tr>\n<td>\u521d\u59cb\u5316\u6811\u72b6\u6570\u7ec4<\/td>\n<td>O(n log n)<\/td>\n<td rowspan=\"3\">O(n)<\/td>\n<\/tr>\n<tr>\n<td>\u6bcf\u4eba\u627e\u4f4d\u7f6e<\/td>\n<td>O(log\u00b2 n)<\/td>\n<\/tr>\n<tr>\n<td>\u603b\u590d\u6742\u5ea6<\/td>\n<td>O(n log\u00b2 n)<\/td>\n<\/tr>\n<\/table>\n<p>\u5bf9\u4e8e N = 200000\uff0cO(n log\u00b2 n) \u5b8c\u5168\u53ef\u4ee5\u63a5\u53d7\u3002<\/p>\n<h2>\u5b8c\u6574\u4ee3\u7801\u5b9e\u73b0<\/h2>\n<pre><code>#include &lt;iostream&gt;\n#include &lt;cstdio&gt;\n#include &lt;cstring&gt;\nusing namespace std;\n\nconst int N = 2e5 + 10;\n\nint n;                  \/\/ \u6392\u961f\u7684\u603b\u4eba\u6570\nint p[N], v[N];        \/\/ p[i]: \u4f4d\u7f6e, v[i]: \u7f16\u53f7\nint ans[N];            \/\/ \u6700\u7ec8\u961f\u5217\u987a\u5e8f\nint tr[N];             \/\/ \u6811\u72b6\u6570\u7ec4\n\n\/\/ lowbit \u51fd\u6570\uff1a\u8fd4\u56de x \u4e8c\u8fdb\u5236\u7684\u6700\u4f4e\u4f4d 1\nint lowbit(int x) {\n    return x & -x;\n}\n\n\/\/ \u6811\u72b6\u6570\u7ec4\u5355\u70b9\u66f4\u65b0\nvoid add(int x, int c) {\n    for (; x <= n; x += lowbit(x))\n        tr[x] += c;\n}\n\n\/\/ \u6811\u72b6\u6570\u7ec4\u524d\u7f00\u548c\u67e5\u8be2\nint sum(int x) {\n    int res = 0;\n    for (; x; x -= lowbit(x))\n        res += tr[x];\n    return res;\n}\n\n\/\/ \u4e8c\u5206\u67e5\u627e\u7b2c k \u4e2a\u7a7a\u4f4d\u7684\u4f4d\u7f6e\nint find(int k) {\n    int l = 1, r = n, pos;\n    while (l <= r) {\n        int mid = (l + r) >> 1;\n        if (sum(mid) >= k) {\n            pos = mid;\n            r = mid - 1;\n        } else {\n            l = mid + 1;\n        }\n    }\n    return pos;\n}\n\nint main() {\n    while (~scanf(\"%d\", &n)) {  \/\/ \u8bfb\u53d6\u591a\u7ec4\u6570\u636e\n        \/\/ \u8bfb\u5165\u6570\u636e\n        for (int i = 1; i <= n; i++)\n            scanf(\"%d%d\", &#038;p[i], &#038;v[i]);\n        \n        \/\/ \u521d\u59cb\u5316\u6811\u72b6\u6570\u7ec4\uff1a\u6240\u6709\u4f4d\u7f6e\u90fd\u662f\u7a7a\u4f4d\n        for (int i = 1; i <= n; i++)\n            add(i, 1);\n        \n        \/\/ \u9006\u5e8f\u5904\u7406\uff1a\u6700\u540e\u4e00\u4e2a\u4eba\u5148\u786e\u5b9a\u4f4d\u7f6e\n        for (int i = n; i >= 1; i--) {\n            int k = p[i] + 1;      \/\/ \u627e\u7b2c k \u4e2a\u7a7a\u4f4d\n            int pos = find(k);     \/\/ \u4e8c\u5206\u67e5\u627e\u4f4d\u7f6e\n            ans[pos] = v[i];      \/\/ \u653e\u7f6e\u7f16\u53f7\n            add(pos, -1);         \/\/ \u5360\u7528\u8be5\u4f4d\u7f6e\n        }\n        \n        \/\/ \u8f93\u51fa\u7ed3\u679c\n        for (int i = 1; i <= n; i++)\n            printf(\"%d \", ans[i]);\n        printf(\"\\n\");\n    }\n    return 0;\n}<\/code><\/pre>\n<h2>\u5173\u952e\u8981\u70b9\u603b\u7ed3<\/h2>\n<ol>\n<li><strong>\u9006\u5e8f\u5904\u7406<\/strong>\uff1a\u907f\u514d\u6b63\u5e8f\u5904\u7406\u65f6\u4f4d\u7f6e\u52a8\u6001\u53d8\u5316\u7684\u95ee\u9898<\/li>\n<li><strong>\u6811\u72b6\u6570\u7ec4<\/strong>\uff1a\u9ad8\u6548\u7ef4\u62a4\u7a7a\u4f4d\u4fe1\u606f\uff0c\u652f\u6301 O(log n) \u7684\u66f4\u65b0\u548c\u67e5\u8be2<\/li>\n<li><strong>\u4e8c\u5206\u67e5\u627e<\/strong>\uff1a\u5229\u7528\u5355\u8c03\u6027\u5feb\u901f\u5b9a\u4f4d\u7b2c k \u4e2a\u7a7a\u4f4d<\/li>\n<li><strong>\u7d22\u5f15\u8f6c\u6362<\/strong>\uff1a\u9898\u76ee\u4e2d p \u4ece 0 \u5f00\u59cb\u8ba1\u6570\uff0c\u5b9e\u9645\u627e\u7b2c p+1 \u4e2a\u7a7a\u4f4d<\/li>\n<\/ol>\n<h2>\u540c\u7c7b\u9898\u76ee\u62d3\u5c55<\/h2>\n<p>\u672c\u9898\u7684\u6838\u5fc3\u601d\u60f3\uff08\u9006\u5e8f + \u6811\u72b6\u6570\u7ec4 + \u4e8c\u5206\uff09\u53ef\u4ee5\u5e94\u7528\u4e8e\u4ee5\u4e0b\u573a\u666f\uff1a<\/p>\n<ul>\n<li>\u52a8\u6001\u63d2\u961f\u95ee\u9898<\/li>\n<li>\u5e8f\u5217\u4e2d\u7b2c k \u5927\u7684\u5143\u7d20\u67e5\u627e<\/li>\n<li>\u79bb\u7ebf\u5904\u7406\u6392\u5e8f\u95ee\u9898<\/li>\n<\/ul>\n<p>\u638c\u63e1\u8fd9\u4e00\u601d\u8def\u5bf9\u4e8e\u89e3\u51b3\u7b97\u6cd5\u7ade\u8d5b\u4e2d\u7684\u52a8\u6001\u5e8f\u5217\u95ee\u9898\u975e\u5e38\u6709\u5e2e\u52a9\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>AcWing 260. \u4e70\u7968\u662f\u4e00\u9053\u7ecf\u5178\u7684\u7b97\u6cd5\u9898\u76ee\uff0c\u8003\u5bdf\u6811\u72b6\u6570\u7ec4\u4e0e\u4e8c\u5206\u67e5\u627e\u7684\u7ed3\u5408\u5e94\u7528\u3002\u672c\u6587\u8be6\u7ec6\u8bb2\u89e3\u9006\u5e8f\u5904\u7406\u7684\u6838\u5fc3\u601d\u60f3\u3002<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"class_list":["post-75","post","type-post","status-publish","format-standard","hentry","category-3"],"_links":{"self":[{"href":"https:\/\/www.sjll.top\/index.php?rest_route=\/wp\/v2\/posts\/75","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.sjll.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.sjll.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.sjll.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.sjll.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=75"}],"version-history":[{"count":0,"href":"https:\/\/www.sjll.top\/index.php?rest_route=\/wp\/v2\/posts\/75\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.sjll.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=75"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.sjll.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=75"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.sjll.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=75"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}