{"id":806,"date":"2024-12-07T19:25:48","date_gmt":"2024-12-07T11:25:48","guid":{"rendered":"https:\/\/lolife.top\/?p=806"},"modified":"2024-12-07T21:41:25","modified_gmt":"2024-12-07T13:41:25","slug":"%e6%91%a9%e5%b0%94%e6%8a%95%e7%a5%a8%e6%b3%95","status":"publish","type":"post","link":"https:\/\/lolife.top\/?p=806","title":{"rendered":"\u6469\u5c14\u6295\u7968\u6cd5"},"content":{"rendered":"\n

\u6469\u5c14\u6295\u7968\u6cd5\u662f\u7528\u6765\u7b5b\u9009\u51fa\u5728\u957f\u5ea6\u4e3an\u6570\u7ec4\u4e2d\u51fa\u73b0\u5927\u4e8e[n\/2]\u6b21\u7684\u5143\u7d20\u6570\uff08[ ]\u53d6\u6574\u7b26\uff09\uff0c\u4fd7\u540d\uff1a\u5bfb\u627e\u6c34\u738b\u6570\u3002<\/p>\n\n\n\n

\u56e0\u4e3a\u975e\u6c34\u738b\u6570\u51fa\u73b0\u6b21\u6570\u4e00\u5b9a\u4f1a\u5c0f\u4e8e[n\/2],\u56e0\u6b64\u6c34\u738b\u6570\u6709\u4e14\u4ec5\u67091\u4e2a\u3002<\/p>\n\n\n\n

\u5bf9\u4e8e\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u7528\u54c8\u5e0c\u8868\u89e3\u51b3<\/p>\n\n\n\n

#include <bits\/stdc++.h>\nusing namespace std;\nvector<int> majorityElement(vector<int>& nums) {\n    int n = nums.size();\n    vector<int> ans;\n    map<int, int> cnt;\n    for (auto& v : nums) {\n        cnt[v]++;\n    }\n    for (auto& v : cnt) {\n        if (v.second > n \/ 2) {\n            ans.push_back(v.first);\n        }\n    }\n    return ans;\n}\nint main()\n{\n\tint n;\n\tcin>>n;\n\tvector<int> nums;\n\tfor (int i = 0; i < n; i++) {\n        int x;\n        cin>>x;\n        nums.push_back(x);\n    }\n    for(auto& v : majorityElement(nums)){\n        cout<<v<<\" \";\n    }\n}\n\n\n\n<\/code><\/pre>\n\n\n\n
\u65f6\u95f4\u590d\u6742\u5ea6\uff1aO<\/em>(n<\/em>)\uff0c\u5176\u4e2d n<\/em> \u4e3a\u6570\u7ec4\u7684\u957f\u5ea6\u3002<\/p>\n\n\n\n
\u7a7a\u95f4\u590d\u6742\u5ea6\uff1aO<\/em>(n<\/em>)\uff0c\u5176\u4e2d n<\/em> \u4e3a\u6570\u7ec4\u7684\u957f\u5ea6\uff0c\u4f7f\u7528\u54c8\u5e0c\u8868\u9700\u8981\u5f00\u8f9f\u989d\u5916\u7684\u7a7a\u95f4\u3002<\/p>\n\n\n\n
\u4f46\u6469\u5c14\u6295\u7968\u6cd5\u65f6\u95f4\u590d\u6742\u5ea6\uff1aO<\/em>(n<\/em>)\uff0c\u5176\u4e2d n<\/em> \u4e3a\u6570\u7ec4\u7684\u957f\u5ea6\u3002\u7a7a\u95f4\u590d\u6742\u5ea6\uff1aO<\/em>(1)\uff1b<\/p>\n\n\n\n
<\/p>\n\n\n\n
\u4e00\u3001\u539f\u7406<\/h2>\n\n\n\n
\u7b2c\u4e00\u79cd\u60c5\u51b5<\/strong><\/p>\n\n\n\n
\u5728\u6570\u7ec4\u4e2d\u6bcf\u6b21\u5220\u53bb\u4e24\u4e2a\u4e0d\u540c\u7684\u6570\uff0c\u90a3\u4e48\u5728\u6700\u540e\u5269\u4e0b\u7684\u6570\u53ef\u80fd\u662f\u6c34\u738b\u6570\uff0c\u90a3\u4e48\u6211\u4eec\u518d\u904d\u5386\u4e00\u6b21\u6570\u7ec4\uff0c\u68c0\u67e5\u8fd9\u4e2a\u6570\u51fa\u73b0\u6b21\u6570\u662f\u5426\u5927\u4e8e[n\/2]\u3002<\/p>\n\n\n\n
\u4f8b1<\/strong>\uff1a[1,2,3,4,5]  n=5<\/p>\n\n\n\n
\u7b2c\u4e00\u6b21\u5220\u96641\uff0c2->[3,4,5]<\/p>\n\n\n\n
\u7b2c\u4e8c\u6b21\u5220\u96643\uff0c4->[5]<\/p>\n\n\n\n
\u904d\u5386\u53d1\u73b0[5]\u53ea\u51fa\u73b0\u4e00\u6b21\uff0c\u6240\u4ee5[5]\u4e0d\u662f\u6c34\u738b\u6570\uff0c\u90a3\u4e48[1,2,3,4,5]\u6ca1\u6709\u6c34\u738b\u6570\u3002<\/p>\n\n\n\n
\u4f8b2<\/strong>\uff1a[2,2,3,2,4,2,2,6,2,3]  n=10<\/p>\n\n\n\n
\u7b2c\u4e00\u6b21\u52202\uff0c3->[2,2,4,2,2,6,2,3]<\/p>\n\n\n\n
\u7b2c\u4e8c\u6b21\u52202\uff0c4->[2,2,2,6,2,3]<\/p>\n\n\n\n
\u7b2c\u4e09\u6b21\u52202\uff0c6->[2,2,2,3]<\/p>\n\n\n\n
\u7b2c\u56db\u6b21\u52202\uff0c3->[2,2]\uff08\u65e0\u4e0d\u540c\u7684\u6570\uff09<\/p>\n\n\n\n
\u904d\u5386\u53d1\u73b0[2]\u51fa\u73b06\u6b21\uff0c\u6240\u4ee5[2]\u4e3a[2,2,3,2,4,2,2,6,2,3]\u7684\u6c34\u738b\u6570\u3002<\/p>\n\n\n\n
\u7b2c\u4e8c\u79cd\u60c5\u51b5<\/strong><\/p>\n\n\n\n
\u5728\u6570\u7ec4\u4e2d\u6bcf\u6b21\u5220\u9664\u4e24\u4e2a\u4e0d\u540c\u7684\u6570\uff0c\u6700\u540e\u6ca1\u6709\u5269\u4e0b\u7684\u6570\uff0c\u90a3\u4e48\u8fd9\u4e2a\u6570\u7ec4\u6ca1\u6709\u6c34\u738b\u6570\u3002<\/p>\n\n\n\n
\u4f8b<\/strong>\uff1a[1,2,3,4]  n=4<\/p>\n\n\n\n
\u7b2c\u4e00\u6b21\u52201\uff0c2->[3,4]<\/p>\n\n\n\n
\u7b2c\u4e8c\u6b21\u52203\uff0c4->[ ]<\/p>\n\n\n\n
\u6240\u4ee5[1,2,3,4]\u6ca1\u6709\u6c34\u738b\u6570\u3002<\/p>\n\n\n\n
\u4e8c\u3001\u4ee3\u7801\u5206\u6790<\/h2>\n\n\n\n
\u5bf9\u4e8e\u6570\u7ec4\uff0c\u5982\u4f55\u5b9e\u73b0\u4e00\u6b21\u5220\u9664\u4e24\u4e2a\u4e0d\u540c\u7684\u6570\u5462\uff1f<\/p>\n\n\n\n
\u6211\u4eec\u5f15\u5165\u5019\u9009\u6570cond\u4ee5\u53ca\u7968\u6570hp\uff0c\u5f53hp=0\u65f6\uff0c\u6211\u4eec\u8ba4\u4e3a\u6ca1\u6709\u5019\u9009\u6570<\/p>\n\n\n\n
(1)\u5982\u679c\u65e0\u5019\u9009\uff0c\u5f53\u524d\u6570\u6210\u4e3a\u5019\u9009\uff0c\u7968\u6570hp=1<\/p>\n\n\n\n
(2)\u5982\u679c\u6709\u5019\u9009<\/p>\n\n\n\n
    \u5f53\u524d\u6570  ==  \u5019\u9009\u6570\uff0c\u7968\u6570hp+1<\/p>\n\n\n\n
    \u5f53\u524d\u6570  !=   \u5019\u9009\u6570\uff0c\u7968\u6570hp-1<\/p>\n\n\n\n
\u4f8b1<\/strong>\uff1a[2,3,3,3,1,4,5,3,3,3,2]  n=11  [3]\u51fa\u73b06\u6b21<\/p>\n\n\n\n
1)\u65e0\u5019\u9009\u6570\uff0c\u5019\u9009sum=2\uff0c\u7968\u6570hp=1;<\/p>\n\n\n\n
2)\u6709\u5019\u9009\u6570\uff0c\u5f53\u524d\u6570[3] !=\u5019\u9009\u6570[2],hp-1->hp=0;<\/p>\n\n\n\n
3)\u65e0\u5019\u9009\u6570\uff0c\u5019\u9009sum=3\uff0c\u7968\u6570hp=1\uff1b<\/p>\n\n\n\n
4)\u6709\u5019\u9009\u6570\uff0c\u5f53\u524d\u6570[3]==\u5019\u9009\u6570[3],hp+1->hp=2;<\/p>\n\n\n\n
5)\u6709\u5019\u9009\u6570\uff0c\u5f53\u524d\u6570[1]!=\u5019\u9009\u6570[3],hp-1->hp=1;<\/p>\n\n\n\n
…….<\/p>\n\n\n\n
\u4ee5\u6b64\u7c7b\u63a8\uff0c\u76f4\u5230\u6570\u7ec4\u6700\u540e\u4e00\u4e2a\u6570\u6211\u4eec\u4f1a\u5f97\u5230\u5019\u9009\u6570cond=3\uff0c\u7968\u6570hp=1;<\/p>\n\n\n\n
\u4e4b\u540e\u6211\u4eec\u5148\u68c0\u67e5hp\u662f\u5426\u4e3a0\uff0c\u5982\u679c\u4e3a\u96f6\uff0c\u5219\u8bf4\u660e\u6ca1\u6709\u6c34\u738b\u6570\uff08\u539f\u7406\u7684\u60c5\u51b52\uff09\uff0c\u5982\u679c\u4e0d\u4e3a\u96f6\uff0c\u518d\u68c0\u67e5\u5019\u9009\u6570sum\u5728\u6570\u7ec4\u51fa\u73b0\u7684\u6b21\u6570\uff08\u539f\u7406\u7684\u60c5\u51b51\uff09<\/p>\n\n\n\n
\u4e09\u3001\u4ee3\u7801\u8868\u793a<\/h2>\n\n\n\n
#include <bits\/stdc++.h>\nusing namespace std;\nint majorityElement(vector<int>& nums) {\n    int cond = 0;\n    int hp = 0;\n    for (auto& num : nums) {\n        if(hp == 0){\/\/\u65e0\u5019\u9009\u6570\n            cond=num;\n            hp=1;\n        }\n        else if(num!=cond){\/\/\u5f53\u524d\u6570\u4e0e\u5019\u9009\u6570\u4e0d\u540c\n            hp--;\n        }\n        else {\/\/\u5f53\u524d\u6570\u4e0e\u5019\u9009\u6570\u76f8\u540c\n            hp++;\n        }\n    }\n    if(hp == 0){\n        return -1;\n    }\n    hp = 0;\n    for (auto& num : nums) {\/\/\u5224\u65ad\u5019\u9009\u6570\u662f\u5426\u4e3a\u6c34\u738b\u6570\n        if(num==cond){\n            hp++;\n        }\n    }\n    return hp > nums.size()\/2 ? cond : -1;\n}\nint main()\n{\n\tint n;\n\tcin>>n;\n\tvector<int> nums;\n\tfor (int i = 0; i < n; i++) {\n        int x;\n        cin>>x;\n        nums.push_back(x);\n    }\n    cout<<majorityElement(nums)<<endl;\n}\n\n<\/code><\/pre>\n\n\n\n
\u56db\u3001\u62d3\u5c55<\/h2>\n\n\n\n
\u6469\u5c14\u6295\u7968\u6cd5\u662f\u53ef\u4ee5\u901a\u8fc7\u591a\u7ebf\u7a0b\u6765\u7f29\u77ed\u65f6\u95f4\u7684<\/p>\n\n\n\n
\u6bd4\u5982\u6709\u5de6\u53f3\u4e24\u4e2a\u7ebf\u7a0b\uff0c\u7136\u540e\u6bd4\u8f83\u5de6\u53f3\u7ebf\u7a0b\u7684hp,hp\u5927\u7684\u5019\u9009\u6570\u4e3a\u6c34\u738b\u6570\u3002<\/p>\n\n\n\n
A<\/strong>.\u5bfb\u627e\u5206\u5272\u70b9\uff0c\u4f7f\u5206\u5272\u70b9\u4e24\u8fb9\u7684\u6c34\u738b\u6570\u76f8\u540c\uff0c\u5982\u529b\u62632780<\/p>\n\n\n\n
#include <bits\/stdc++.h>\nusing namespace std;\nint majorityElement(vector<int>& nums) {\n    int cond = 0;\n    int hp = 0;\n    for (auto& num : nums) {\n        if(hp == 0){\/\/\u65e0\u5019\u9009\u6570\n            cond=num;\n            hp=1;\n        }\n        else if(num!=cond){\/\/\u5f53\u524d\u6570\u4e0e\u5019\u9009\u6570\u4e0d\u540c\n            hp--;\n        }\n        else {\/\/\u5f53\u524d\u6570\u4e0e\u5019\u9009\u6570\u76f8\u540c\n            hp++;\n        }\n    }\n    if(hp == 0){\n        return -1;\n    }\n    hp = 0;\n    for (auto& num : nums) {\/\/\u5224\u65ad\u5019\u9009\u6570\u662f\u5426\u4e3a\u6c34\u738b\u6570\n        if(num==cond){\n            hp++;\n        }\n    }\n    int n=nums.size();\n    int lc = 0;\/\/lc\u5de6\u4fa7\u6c34\u738b\u6570\u4e2a\u6570\n    int rc = hp;\/\/rc\u53f3\u4fa7\u6c34\u738b\u6570\u4e2a\u6570\n    for(int i=0;i<n-1;i++){\n        if(nums[i]==cond){\n            lc++;\n            rc--;\n        }\n        if(lc>(i+1)\/2&&rc>(n-i-1)\/2){\n            return i;\n        }\n    }\n    return -1;\n}\nint main()\n{\n\tint n;\n\tcin>>n;\n\tvector<int> nums;\n\tfor (int i = 0; i < n; i++) {\n        int x;\n        cin>>x;\n        nums.push_back(x);\n    }\n    cout<<majorityElement(nums)<<endl;\n}\n\n<\/code><\/pre>\n\n\n\n
B<\/strong>\u7b5b\u9009\u51fa\u5728\u957f\u5ea6\u4e3an\u6570\u7ec4\u4e2d\u51fa\u73b0\u5927\u4e8e[n\/k]\u6b21\u7684\u5143\u7d20\u6570\uff0c\u5982\u529b\u6263229<\/p>\n\n\n\n
\u8fd9\u4e2a\u65f6\u5019\u6211\u4eec\u5148\u5224\u65ad\u6700\u591a\u6709\u591a\u5c11\u4e2a\u6c34\u738b\u6570\uff0c\u5047\u8bbe\u6709k\u4e2a\u6c34\u738b\u6570\uff0c\u90a3\u4e48k*\u6c34\u738b\u6570\u51fa\u73b0\u6b21\u6570>n,\u77db\u76fe<\/p>\n\n\n\n
\u5047\u8bbe\u6709k-1\u4e2a\u6c34\u738b\u6570\uff0c(k-1)*\u6c34\u738b\u6570\u51fa\u73b0\u6b21\u6570>n-n\/k,\u5b58\u5728\u53ef\u80fd\u6027\uff1b<\/p>\n\n\n\n
\u90a3\u4e48\u6211\u4eec\u5efa\u7acb\u4e00\u4e2ak-1* 2\u7684\u4e8c\u7ef4\u6570\u7ec4<\/p>\n\n\n\n
(1)\u5019\u9009\u6570\u4e0d\u8db3k-1\u4e2a\uff0c<\/p>\n\n\n\n
\u5f53\u524d\u6570==\u5176\u4e2d\u4e00\u4e2a\u5019\u9009\u6570\uff0chp+1\uff1b<\/p>\n\n\n\n
\u5f53\u524d\u6570!=\u4efb\u4f55\u4e00\u4e2a\u5019\u9009\u6570\uff0c\u5f53\u524d\u6570\u4e3a\u5019\u9009\u6570\uff0chp=1\uff1b<\/p>\n\n\n\n
(2)\u5019\u9009\u6570\u8fbe\u5230k-1\u4e2a<\/p>\n\n\n\n
\u5f53\u524d\u6570==\u5176\u4e2d\u4e00\u4e2a\u5019\u9009\u6570\uff0c\u8fd9\u8be5\u5019\u9009\u6570hp+1<\/p>\n\n\n\n
\u5f53\u524d\u6570!=\u4efb\u4f55\u4e00\u4e2a\u5019\u9009\u6570\uff0c\u6240\u6709\u5019\u9009\u6570hp-1(\u76f8\u5f53\u4e8e\u4e00\u4e0b\u5b50\u5220\u4e86k\u4e2a\u4e0d\u540c\u7684\u6570\uff09<\/p>\n\n\n\n
\u6700\u540e\u904d\u5386\u6bcf\u4e2a\u5019\u9009\u6570\u51fa\u73b0\u6b21\u6570\uff0c\u5224\u65ad\u662f\u5426\u7b26\u5408\u6761\u4ef6<\/p>\n\n\n\n
\u4f8b\uff1a[3,5,2,3,4,2,5,3,7,7,6] k=4   <\u5019\u9009\u6570\uff0c\u7968\u6570><\/p>\n\n\n\n
1)\u5019\u9009\u6570<k-1,\u5019\u9009\u96c6[<3,1>]<\/p>\n\n\n\n
2)\u5019\u9009\u6570<k-1,\u5019\u9009\u96c6[<3,1>,<5,1>]<\/p>\n\n\n\n
3)\u5019\u9009\u6570<k-1,\u5019\u9009\u96c6[<3,1>,<5,1>,<2,1>]<\/p>\n\n\n\n
4)\u5019\u9009\u6570==k-1,\u5f53\u524d\u6570==\u5019\u9009\u6570[3]->\u5019\u9009\u96c6[<3,2>,<5,1>,<2,1>]<\/p>\n\n\n\n
5)\u5019\u9009\u6570==k-1,\u5f53\u524d\u6570[4]!=\u5019\u9009\u6570[3]->\u5019\u9009\u96c6[<3,1>,<5,0>,<2,0>](\u6ce8\u610fhp=0\u65f6\u5019\u9009\u6570<\/p>\n\n\n\n
6\uff09\u5019\u9009\u6570<k-1\uff0c\u5019\u9009\u96c6[<3,1>,<2,1>]<\/p>\n\n\n\n
…….<\/p>\n\n\n\n
#include <bits\/stdc++.h>\nusing namespace std;\nvoid update(vector<vector<int>>& count, int k, int num) {\n    for (int i = 0; i < k; i++) {\n        if (count[i][0] == num && count[i][1] > 0) {\/\/\u5f53\u524d\u6570\u7b49\u4e8e\u5019\u9009\u6570\n            count[i][1]++;\n            return;\n        }\n    }\n    for (int i = 0; i < k; i++) {\n        if (count[i][1] == 0) {\/\/\u5019\u9009\u6570<k-1\n            count[i][0] = num;\n            count[i][1]++;\n            return;\n        }\n    }\n    for (int i = 0; i < k; i++) {\n        if (count[i][1] > 0) {\/\/\u5f53\u524d\u6570\u4e0d\u7b49\u4e8e\u4efb\u4f55\u5019\u9009\u6570\uff0c\u5019\u9009\u6570\u7968\u6570-1\n            count[i][1]--;\n        }\n    }\n}\nvector<int> majorityElement(vector<int>& nums,int k) {\n    vector<vector<int>> count(--k, vector<int>(2, 0));\n    for(auto& num : nums) {\n        update(count, k, num);\n    }\n    vector<int> ans;\n    for (auto& c : count) {\n        if (c[1] > 0) {\n            int num = c[0];\n            int sum=0;\n            for (auto& n : nums) {\n                if (n == num) {\n                    sum++;\n                }\n            }\n            if (sum > nums.size() \/ (k+1)) {\/\/\u5728\u5efa\u7acbcount\u65f6\u8fdb\u884c\u4e86--k\n                \n                ans.push_back(num);\n            }\n        }\n    }\n    return ans;\n    \n}\nint main()\n{\n\tint n,x;\n\tcin>>n;\n\tvector<int> nums;\n\tfor (int i = 0; i < n; i++) {\n        cin>>x;\n        nums.push_back(x);\n    }\n    for (auto& i : majorityElement(nums, 3)) {\n        cout << i << \" \";\n    }\n}\n\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
\u6469\u5c14\u6295\u7968\u6cd5\u662f\u7528\u6765\u7b5b\u9009\u51fa\u5728\u957f\u5ea6\u4e3an\u6570\u7ec4\u4e2d\u51fa\u73b0\u5927\u4e8e[n\/2]\u6b21\u7684\u5143\u7d20\u6570\uff08[ ]\u53d6\u6574\u7b26\uff09\uff0c\u4fd7\u540d\uff1a\u5bfb\u627e\u6c34\u738b\u6570\u3002 \u56e0\u4e3a\u975e […]<\/p>\n","protected":false},"author":2,"featured_media":813,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[20],"tags":[13,19],"class_list":["post-806","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-20","tag-c-c","tag-19"],"_links":{"self":[{"href":"https:\/\/lolife.top\/index.php?rest_route=\/wp\/v2\/posts\/806","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lolife.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lolife.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lolife.top\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/lolife.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=806"}],"version-history":[{"count":2,"href":"https:\/\/lolife.top\/index.php?rest_route=\/wp\/v2\/posts\/806\/revisions"}],"predecessor-version":[{"id":809,"href":"https:\/\/lolife.top\/index.php?rest_route=\/wp\/v2\/posts\/806\/revisions\/809"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/lolife.top\/index.php?rest_route=\/wp\/v2\/media\/813"}],"wp:attachment":[{"href":"https:\/\/lolife.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=806"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lolife.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=806"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lolife.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=806"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}