{"id":293,"date":"2021-09-11T17:27:28","date_gmt":"2021-09-11T09:27:28","guid":{"rendered":"https:\/\/aisumura.net\/blog\/?p=293"},"modified":"2021-09-20T23:22:53","modified_gmt":"2021-09-20T15:22:53","slug":"leetcode1409-queries-on-a-permutation-with-key","status":"publish","type":"post","link":"https:\/\/aisumura.net\/blog\/2021\/09\/11\/leetcode1409-queries-on-a-permutation-with-key\/","title":{"rendered":"[LeetCode]1409. Queries on a Permutation With Key"},"content":{"rendered":"\n

\u672c\u4eba\u65bc\u8a72blog\u7684\u5168\u90e8\u6587\u7ae0\u8f49\u79fb\u81f3[LeetCode]1409 Queries on a Permutation With Key – KKWBlog (kkwtech.com)<\/a><\/a>\u8a72\u7db2\u57df\u4e0b\uff0c\u5176\u5f8c\u6b64\u8655\u4e0d\u9032\u884c\u66f4\u65b0\uff0c\u4e00\u5f8b\u65bc\u65b0\u7ad9\u9ede\u66f4\u65b0\u3002<\/p>\n\n\n\n

\u984c\u76ee\u4f86\u6e90<\/em><\/strong>:Queries on a Permutation With Key – LeetCode<\/a><\/p>\n\n\n\n

\u984c\u76ee\u91cd\u9ede:<\/em><\/strong>
\u7d66\u5b9a\u4e00\u6578\u5217queries\u53ca\u6b63\u6574\u6578m\uff0c\u5f9em\u88e1\u627e\u51faqueries[i]\u7684index\u4e26\u4e14\u5c07m\u7684queries[i]\u79fb\u52d5\u5230\u6700\u524d\u7aef\uff0c\u8f38\u51fares\u88cf\u982d\u5305\u542b\u6240\u6709\u7684queries[i]\u7684index<\/p>\n\n\n\n

\u89e3\u984c\u601d\u8def:<\/em><\/strong>
\u4f7f\u7528Indexed Binary Tree\u5c31\u80fd\u9054\u5230\u6642\u9593\u8907\u96dc\u5ea6O(n*log(m))\u7684\u89e3\u6cd5\uff0c\u7c21\u55ae\u8aaa\u5c31\u662f\u8a08\u7b97m\u9663\u5217\u4e2d\u7684\u67d0\u6578\u5b57\u4e4b\u524d\u7684\u6578\u5b57\u91cf\u548c\u5f97\u51fa\u67d0\u6578\u5b57\u7684index\uff0c\u53e6\u5916\u9084\u8981\u8003\u91cf\u5230\u79fb\u5230\u524d\u7aef\u9019\u500b\u52d5\u4f5c\uff0c\u56e0\u6b64\u9700\u8981\u4fdd\u7559\u984d\u5916\u7684\u7a7a\u9593\u5c07\u6578\u5b57\u79fb\u52d5\u5230\u524d\u7aef\u66f4\u65b0BIT\u3002

\u6b65\u9a5f\u5982\u4e0b:
let n = queries.size()
1.\u5ba3\u544a1\u9663\u5217pos\u5132\u5b58m\u9663\u5217\u5404\u6578\u65bcBIT\u4e2d\u7684\u6240\u5728index(\u70ba\u6c42\u65b9\u4fbf\u56e0\u6b64pos[0]\u4e0d\u653e\u503c)
2.\u5ba3\u544abit\u9577\u5ea6\u70ba m + \u4fdd\u7559\u7684\u79fb\u52d5\u7a7a\u9593(n) + 1 (queries\u7684\u9577\u5ea6\u4ee3\u8868\u6703\u5f9em\u627en\u6b21index\u540c\u6642\u79fb\u52d5n\u6b21\u81f3\u524d\u7aef)
3.BIT\u521d\u59cb\u5316\uff0c\u908f\u8f2f\u662f\u628a\u7576\u524d\u6578\u5b57\u7576\u4f5cdelta\u70ba1\u4e5f\u5c31\u662f\u8a72\u4f4d\u7f6e\u67091\u500b\u6578\u5b57\uff0c\u5176\u4ed6\u90e8\u5206\u5c31\u5982\u540cBIT\u88e1\u5275\u5efa\u4e00\u6a23\uff0c\u4e0d\u904e\u9019\u908a\u7684\u958b\u59cb\u4f4d\u7f6e\u662f\u5f9en + 1\u958b\u59cb\uff0c\u524d\u9762n\u500b\u5fc5\u9808\u4fdd\u7559\u7d66\u79fb\u52d5\u81f3\u524d\u7aef\u7684\u6578\u5b57\uff0c\u540c\u6642pos\u88e1\u653e\u5165\u8a72\u6578\u5b57\u65bcBIT\u5167\u7684\u6240\u5728\u4f4d\u7f6e\u3002
4.\u8d70\u8a2aqueries\u5229\u7528pos[i]\u627e\u51fa\u4f4d\u7f6e\uff0c\u91dd\u5c0d\u6bcf\u500b\u6578\u5b57\u5229\u7528BIT\u7684\u6027\u8cea\u5f80\u4e0a\u8d70\u8a2a\u76f4\u5230\u6839\u70ba\u6b62\uff0c\u5373\u53ef\u627e\u51fa\u524d\u65b9\u5171\u6709\u591a\u5c11\u500b\u6578\u5b57\u548c\u4e5f\u5c31\u662findex\uff0c\u540c\u6642\u5c07\u5728m\u4e2d\u7684queries[i]\u653e\u5230\u6700\u524d\u65b9\uff0c\u5229\u7528\u7b2c3\u6b65\u7684\u6982\u5ff5\u4e5f\u5c31\u662fdelta = 1\u4e26\u4e14\u4f4d\u7f6e\u70ban\u9032\u884cBIT\u66f4\u65b0\u5c31\u80fd\u9806\u5229\u79fb\u5230\u524d\u7aef\uff0c\u9019\u6642\u6839\u64dapos[i]\u627e\u51fa\u7684\u4f4d\u7f6e\u56e0\u70ba\u8a72\u4f4d\u7f6e\u5df2\u7d93\u6e1b\u5c111\u500b\u6578\u5b57\u6240\u4ee5\u4e5f\u8981update\u4e14delta = -1\uff0cn\u6b64\u6642\u8981-1\u4ee5\u78ba\u4fdd\u4e0b\u500b\u524d\u7aef\u70ba\u7a7a\uff0c\u66f4\u65b0pos[queries[i]]\u65bcm\u4e2d\u7684\u4f4d\u7f6e\u3002

\u91cd\u8907\u4ee5\u4e0a4\u6b65\u5373\u53ef\u5f97\u5230\u89e3<\/p>\n\n\n\n

\"example
Example : queries = [3,1,2,1] , m = 5<\/p>\n\n\n\n

class Solution {\npublic:\n    vector<int> processQueries(vector<int>& queries, int m) {\n        int n = queries.size();\n        vector <int> pos(m + 1);\n        vector <int> bit(m + n + 1);\n        vector<int> res;\n        for(int i = 1; i <= m; i++) {\n            pos[i] = i + n;\n            updateBIT(bit,i + n,1);\n        }\n        for(int q : queries) {\n            res.push_back(getSumBIT(bit,pos[q] - 1));\n            updateBIT(bit,pos[q],-1);\n            pos[q] = n;\n            updateBIT(bit,n--,1);\n        }\n        return res;\n    }\nprivate:\n    void updateBIT(vector <int> &bit,int index,int delta) {\n        while(index < bit.size()) {\n            bit[index] += delta;\n            index += index & -index;\n        }\n    }\n    int getSumBIT(vector <int> &bit,int index) {\n       int sum = 0;\n        while(index > 0) {\n            sum += bit[index];\n            index -= index & -index;\n        }\n        return sum;\n    }\n};<\/code><\/pre>\n\n\n\n
\u6642\u9593\u8907\u96dc\u5ea6:O(N*log(M))<\/pre><\/div>\n","protected":false},"excerpt":{"rendered":"
\u672c\u4eba\u65bc\u8a72blog\u7684\u5168\u90e8\u6587\u7ae0\u8f49\u79fb\u81f3[LeetCode]1409 Queries on a Permutation […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[27],"tags":[28],"_links":{"self":[{"href":"https:\/\/aisumura.net\/blog\/wp-json\/wp\/v2\/posts\/293"}],"collection":[{"href":"https:\/\/aisumura.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/aisumura.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/aisumura.net\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/aisumura.net\/blog\/wp-json\/wp\/v2\/comments?post=293"}],"version-history":[{"count":18,"href":"https:\/\/aisumura.net\/blog\/wp-json\/wp\/v2\/posts\/293\/revisions"}],"predecessor-version":[{"id":339,"href":"https:\/\/aisumura.net\/blog\/wp-json\/wp\/v2\/posts\/293\/revisions\/339"}],"wp:attachment":[{"href":"https:\/\/aisumura.net\/blog\/wp-json\/wp\/v2\/media?parent=293"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/aisumura.net\/blog\/wp-json\/wp\/v2\/categories?post=293"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/aisumura.net\/blog\/wp-json\/wp\/v2\/tags?post=293"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}