{"id":2632,"date":"2022-02-11T15:50:06","date_gmt":"2022-02-11T07:50:06","guid":{"rendered":"http:\/\/139.9.1.231\/?p=2632"},"modified":"2022-03-29T19:19:48","modified_gmt":"2022-03-29T11:19:48","slug":"divide-and-conquer","status":"publish","type":"post","link":"http:\/\/139.9.1.231\/index.php\/2022\/02\/11\/divide-and-conquer\/","title":{"rendered":"\u5206\u6cbb\u7b97\u6cd5"},"content":{"rendered":"\n

\u5206\u6cbb\u6cd5\u7684\u8bbe\u8ba1\u601d\u60f3\u662f\uff1a\u5c06\u4e00\u4e2a\u96be\u4ee5\u76f4\u63a5\u89e3\u51b3\u7684\u5927\u95ee\u9898\uff0c\u5206\u5272\u6210\u4e00\u4e9b\u89c4\u6a21\u8f83\u5c0f\u7684\u76f8\u540c\u95ee\u9898\uff0c\u4ee5\u4fbf\u5404\u4e2a\u51fb\u7834\uff0c\u5206\u800c\u6cbb\u4e4b\u3002<\/p>\n\n\n\n

   \u5206\u6cbb\u7b56\u7565\u662f\uff1a\u5bf9\u4e8e\u4e00\u4e2a\u89c4\u6a21\u4e3an\u7684\u95ee\u9898\uff0c\u82e5\u8be5\u95ee\u9898\u53ef\u4ee5\u5bb9\u6613\u5730\u89e3\u51b3\uff08\u6bd4\u5982\u8bf4\u89c4\u6a21n\u8f83\u5c0f\uff09\u5219\u76f4\u63a5\u89e3\u51b3\uff0c\u5426\u5219\u5c06\u5176\u5206\u89e3\u4e3ak\u4e2a\u89c4\u6a21\u8f83\u5c0f\u7684\u5b50\u95ee\u9898\uff0c\u8fd9\u4e9b\u5b50\u95ee\u9898\u4e92\u76f8\u72ec\u7acb\u4e14\u4e0e\u539f\u95ee\u9898\u5f62\u5f0f\u76f8\u540c\uff0c\u9012\u5f52\u5730\u89e3\u8fd9\u4e9b\u5b50\u95ee\u9898\uff0c\u7136\u540e\u5c06\u5404\u5b50\u95ee\u9898\u7684\u89e3\u5408\u5e76\u5f97\u5230\u539f\u95ee\u9898\u7684\u89e3\u3002\u8fd9\u79cd\u7b97\u6cd5\u8bbe\u8ba1\u7b56\u7565\u53eb\u505a\u5206\u6cbb\u6cd5\u3002<\/p>\n\n\n\n

   \u5982\u679c\u539f\u95ee\u9898\u53ef\u5206\u5272\u6210k\u4e2a\u5b50\u95ee\u9898\uff0c1<k\u2264n\uff0c\u4e14\u8fd9\u4e9b\u5b50\u95ee\u9898\u90fd\u53ef\u89e3\u5e76\u53ef\u5229\u7528\u8fd9\u4e9b\u5b50\u95ee\u9898\u7684\u89e3\u6c42\u51fa\u539f\u95ee\u9898\u7684\u89e3\uff0c\u90a3\u4e48\u8fd9\u79cd\u5206\u6cbb\u6cd5\u5c31\u662f\u53ef\u884c\u7684\u3002\u7531\u5206\u6cbb\u6cd5\u4ea7\u751f\u7684\u5b50\u95ee\u9898\u5f80\u5f80\u662f\u539f\u95ee\u9898\u7684\u8f83\u5c0f\u6a21\u5f0f\uff0c\u8fd9\u5c31\u4e3a\u4f7f\u7528\u9012\u5f52\u6280\u672f\u63d0\u4f9b\u4e86\u65b9\u4fbf\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u53cd\u590d\u5e94\u7528\u5206\u6cbb\u624b\u6bb5\uff0c\u53ef\u4ee5\u4f7f\u5b50\u95ee\u9898\u4e0e\u539f\u95ee\u9898\u7c7b\u578b\u4e00\u81f4\u800c\u5176\u89c4\u6a21\u5374\u4e0d\u65ad\u7f29\u5c0f\uff0c\u6700\u7ec8\u4f7f\u5b50\u95ee\u9898\u7f29\u5c0f\u5230\u5f88\u5bb9\u6613\u76f4\u63a5\u6c42\u51fa\u5176\u89e3\u3002\u8fd9\u81ea\u7136\u5bfc\u81f4\u9012\u5f52\u8fc7\u7a0b\u7684\u4ea7\u751f\u3002\u5206\u6cbb\u4e0e\u9012\u5f52\u50cf\u4e00\u5bf9\u5b6a\u751f\u5144\u5f1f\uff0c\u7ecf\u5e38\u540c\u65f6\u5e94\u7528\u5728\u7b97\u6cd5\u8bbe\u8ba1\u4e4b\u4e2d\uff0c\u5e76\u7531\u6b64\u4ea7\u751f\u8bb8\u591a\u9ad8\u6548\u7b97\u6cd5\u3002<\/p>\n\n\n\n

 \u5206\u6cbb\u6cd5\u6240\u80fd\u89e3\u51b3\u7684\u95ee\u9898\u4e00\u822c\u5177\u6709\u4ee5\u4e0b\u51e0\u4e2a\u7279\u5f81\uff1a<\/p>\n\n\n\n

    1) \u8be5\u95ee\u9898\u7684\u89c4\u6a21\u7f29\u5c0f\u5230\u4e00\u5b9a\u7684\u7a0b\u5ea6\u5c31\u53ef\u4ee5\u5bb9\u6613\u5730\u89e3\u51b3<\/p>\n\n\n\n

    2) \u8be5\u95ee\u9898\u53ef\u4ee5\u5206\u89e3\u4e3a\u82e5\u5e72\u4e2a\u89c4\u6a21\u8f83\u5c0f\u7684\u76f8\u540c\u95ee\u9898\uff0c\u5373\u8be5\u95ee\u9898\u5177\u6709\u6700\u4f18\u5b50\u7ed3\u6784\u6027\u8d28\u3002<\/p>\n\n\n\n

    3) \u5229\u7528\u8be5\u95ee\u9898\u5206\u89e3\u51fa\u7684\u5b50\u95ee\u9898\u7684\u89e3\u53ef\u4ee5\u5408\u5e76\u4e3a\u8be5\u95ee\u9898\u7684\u89e3\uff1b<\/p>\n\n\n\n

    4) \u8be5\u95ee\u9898\u6240\u5206\u89e3\u51fa\u7684\u5404\u4e2a\u5b50\u95ee\u9898\u662f\u76f8\u4e92\u72ec\u7acb\u7684\uff0c\u5373\u5b50\u95ee\u9898\u4e4b\u95f4\u4e0d\u5305\u542b\u516c\u5171\u7684\u5b50\u5b50\u95ee\u9898\u3002<\/p>\n\n\n\n

\u7b2c\u4e00\u6761\u7279\u5f81\u662f\u7edd\u5927\u591a\u6570\u95ee\u9898\u90fd\u53ef\u4ee5\u6ee1\u8db3\u7684\uff0c\u56e0\u4e3a\u95ee\u9898\u7684\u8ba1\u7b97\u590d\u6742\u6027\u4e00\u822c\u662f\u968f\u7740\u95ee\u9898\u89c4\u6a21\u7684\u589e\u52a0\u800c\u589e\u52a0\uff1b<\/p>\n\n\n\n

\u7b2c\u4e8c\u6761\u7279\u5f81\u662f\u5e94\u7528\u5206\u6cbb\u6cd5\u7684\u524d\u63d0<\/strong>\u5b83\u4e5f\u662f\u5927\u591a\u6570\u95ee\u9898\u53ef\u4ee5\u6ee1\u8db3\u7684\uff0c\u6b64\u7279\u5f81\u53cd\u6620\u4e86\u9012\u5f52\u601d\u60f3\u7684\u5e94\u7528\uff1b<\/p>\n\n\n\n

\u7b2c\u4e09\u6761\u7279\u5f81\u662f\u5173\u952e\uff0c\u80fd\u5426\u5229\u7528\u5206\u6cbb\u6cd5\u5b8c\u5168\u53d6\u51b3\u4e8e\u95ee\u9898\u662f\u5426\u5177\u6709\u7b2c\u4e09\u6761\u7279\u5f81<\/strong>\uff0c\u5982\u679c\u5177\u5907\u4e86\u7b2c\u4e00\u6761\u548c\u7b2c\u4e8c\u6761\u7279\u5f81\uff0c\u800c\u4e0d\u5177\u5907\u7b2c\u4e09\u6761\u7279\u5f81\uff0c\u5219\u53ef\u4ee5\u8003\u8651\u7528\u8d2a\u5fc3\u6cd5\u6216\u52a8\u6001\u89c4\u5212\u6cd5<\/strong>\u3002<\/p>\n\n\n\n

\u7b2c\u56db\u6761\u7279\u5f81\u6d89\u53ca\u5230\u5206\u6cbb\u6cd5\u7684\u6548\u7387<\/strong>\uff0c\u5982\u679c\u5404\u5b50\u95ee\u9898\u662f\u4e0d\u72ec\u7acb\u7684\u5219\u5206\u6cbb\u6cd5\u8981\u505a\u8bb8\u591a\u4e0d\u5fc5\u8981\u7684\u5de5\u4f5c\uff0c\u91cd\u590d\u5730\u89e3\u516c\u5171\u7684\u5b50\u95ee\u9898\uff0c\u6b64\u65f6\u867d\u7136\u53ef\u7528\u5206\u6cbb\u6cd5\uff0c\u4f46\u4e00\u822c\u7528\u52a8\u6001\u89c4\u5212\u6cd5\u8f83\u597d<\/strong>\u3002<\/p>\n\n\n\n

\u5206\u6cbb\u6cd5\u5728\u6bcf\u4e00\u5c42\u9012\u5f52\u4e0a\u90fd\u6709\u4e09\u4e2a\u6b65\u9aa4\uff1a<\/p>\n\n\n\n

    step1 \u5206\u89e3\uff1a\u5c06\u539f\u95ee\u9898\u5206\u89e3\u4e3a\u82e5\u5e72\u4e2a\u89c4\u6a21\u8f83\u5c0f\uff0c\u76f8\u4e92\u72ec\u7acb\uff0c\u4e0e\u539f\u95ee\u9898\u5f62\u5f0f\u76f8\u540c\u7684\u5b50\u95ee\u9898\uff1b<\/p>\n\n\n\n

    step2 \u89e3\u51b3\uff1a\u82e5\u5b50\u95ee\u9898\u89c4\u6a21\u8f83\u5c0f\u800c\u5bb9\u6613\u88ab\u89e3\u51b3\u5219\u76f4\u63a5\u89e3\uff0c\u5426\u5219\u9012\u5f52\u5730\u89e3\u5404\u4e2a\u5b50\u95ee\u9898<\/p>\n\n\n\n

    step3 \u5408\u5e76\uff1a\u5c06\u5404\u4e2a\u5b50\u95ee\u9898\u7684\u89e3\u5408\u5e76\u4e3a\u539f\u95ee\u9898\u7684\u89e3\u3002<\/p>\n\n\n\n

\u53ef\u4f7f\u7528\u5206\u6cbb\u6cd5\u6c42\u89e3\u7684\u4e00\u4e9b\u7ecf\u5178\u95ee\u9898
<\/strong> \uff081\uff09\u4e8c\u5206\u641c\u7d22\uff082\uff09\u5927\u6574\u6570\u4e58\u6cd5 \uff083\uff09Strassen\u77e9\u9635\u4e58\u6cd5\uff084\uff09\u68cb\u76d8\u8986\u76d6\uff085\uff09\u5408\u5e76\u6392\u5e8f\uff086\uff09\u5feb\u901f\u6392\u5e8f\uff087\uff09\u7ebf\u6027\u65f6\u95f4\u9009\u62e9
\uff088\uff09\u6700\u63a5\u8fd1\u70b9\u5bf9\u95ee\u9898\uff089\uff09\u5faa\u73af\u8d5b\u65e5\u7a0b\u8868\uff0810\uff09\u6c49\u8bfa\u5854<\/strong><\/p>\n\n\n\n

<\/p>\n\n\n\n

\u4f8b\u5982\uff1a<\/p>\n\n\n\n

\u6c42\u6700\u5927\u8fde\u7eed\u548c\uff1a<\/p>\n\n\n\n

\u7ed9\u51fa\u4e00\u4e2a\u957f\u5ea6\u4e3an\u7684\u5e8f\u5217A1,A2,A3\u00b7\u00b7\u00b7\u00b7\u00b7An\uff0c\u6c42\u6700\u5927\u8fde\u7eed\u548c\u3002\u5982\u5e8f\u5217\uff086\uff0c-1 , 5, 4\uff0c-7), \u8be5\u5e8f\u5217\u4e2d\u7684\u6700\u5927\u548c\u662f6 +\uff08 – 1\uff09+ 5 + 4 = 14\u3002<\/p>\n\n\n\n

\u601d\u8def\u5206\u6790\uff1a<\/p>\n\n\n\n

\u57fa\u672c\u601d\u8def\u662f\u4f7f\u7528\u679a\u4e3e\u6cd5\uff0c\u4e09\u91cd\u5d4c\u5957\u5faa\u73af\uff0c\u65f6\u95f4\u590d\u6742\u5ea6\u4e3an\u7684\u4e09\u6b21\u65b9<\/p>\n\n\n\n

\u6211\u4eec\u6765\u7528\u5206\u6cbb\u6cd5\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898<\/p>\n\n\n\n

1.\u5212\u5206\u95ee\u9898\uff1a\u5c06\u5e8f\u5217\u5206\u6210\u5143\u7d20\u4e2a\u6570\u5c3d\u53ef\u80fd\u76f8\u7b49\u7684\u4e24\u534a\u3002<\/p>\n\n\n\n

2.\u9012\u5f52\u6c42\u89e3\uff1a\u5206\u522b\u6c42\u51fa\u4f4d\u4e8e\u5de6\u534a\u548c\u53f3\u534a\u7684\u6700\u4f73\u5e8f\u5217\u3002<\/p>\n\n\n\n

3.\u5408\u5e76\u95ee\u9898\uff1a\u6c42\u51fa\u8d77\u70b9\u4f4d\u4e8e\u5de6\u534a\uff0c\u7ec8\u70b9\u4f4d\u4e8e\u53f3\u534a\u7684\u6700\u5927\u8fde\u7eed\u548c\u5e8f\u5217\uff0c\u548c\u5b50\u95ee\u9898\u6700\u4f18\u89e3\u6bd4\u8f83\u3002<\/p>\n\n\n\n

int maxsum(int l,int r){
if(l==r)return a[l];
int m=(l+r)\/2;
int Max=max(maxsum(l,m),maxsum(m+1,r));\/\/\uff08\u5206\u89e3\uff09\u60c5\u51b51\uff1a\u5b8c\u5168\u5728\u5de6\u533a\u95f4\uff0c\u6216\u8005\u5b8c\u5168\u5728\u53f3\u533a\u95f4<\/p>\n\n\n\n

\/\/\uff08\u5408\u5e76\uff09\u60c5\u51b52\uff1a\u6a2a\u8de8\u5de6\u53f3\u4e24\u4e2a\u533a\u95f4\nint suml=a[m],t=0;\nfor(int i=m;i>=l;i--)\n    suml=max(suml,t+=a[i]);\nint sumr=a[m+1];t=0;\nfor(int i=m+1;i<=r;i++)\n    sumr=max(sumr,t+=a[i]);\n\nreturn max(Max,suml+sumr);\/\/\u53d6\u4e24\u79cd\u60c5\u51b5\u4e2d\u6700\u5927\u7684<\/code><\/pre>\n\n\n\n
}<\/p>\n\n\n\n
\u7ed9\u4f60\u4e00\u4e2a\u7531\u6570\u5b57\u548c\u8fd0\u7b97\u7b26\u7ec4\u6210\u7684\u5b57\u7b26\u4e32 expression<\/code> \uff0c\u6309\u4e0d\u540c\u4f18\u5148\u7ea7\u7ec4\u5408\u6570\u5b57\u548c\u8fd0\u7b97\u7b26\uff0c\u8ba1\u7b97\u5e76\u8fd4\u56de\u6240\u6709\u53ef\u80fd\u7ec4\u5408\u7684\u7ed3\u679c\u3002\u4f60\u53ef\u4ee5 \u6309\u4efb\u610f\u987a\u5e8f<\/strong> \u8fd4\u56de\u7b54\u6848\u3002<\/p>\n\n\n\n
\u8f93\u5165\uff1a<\/strong>expression = \"2-1-1\"\n\u8f93\u51fa\uff1a<\/strong>[0,2]\n\u89e3\u91ca\uff1a<\/strong>\n((2-1)-1) = 0 \n(2-(1-1)) = 2<\/code><\/pre>\n\n\n\n
\u89e3\u9898\u601d\u8def<\/h3>\n\n\n\n
\u5bf9\u4e8e\u4e00\u4e2a\u5f62\u5982 x op y<\/code>\uff08op<\/code> \u4e3a\u8fd0\u7b97\u7b26\uff0cx<\/code> \u548c y<\/code> \u4e3a\u6570\uff09 \u7684\u7b97\u5f0f\u800c\u8a00\uff0c\u5b83\u7684\u7ed3\u679c\u7ec4\u5408\u53d6\u51b3\u4e8e x<\/code> \u548c y<\/code> \u7684\u7ed3\u679c\u7ec4\u5408\u6570<\/strong>\uff0c\u800c x<\/code> \u548c y<\/code> \u53c8\u53ef\u4ee5\u5199\u6210\u5f62\u5982 x op y<\/code> \u7684\u7b97\u5f0f\u3002<\/p>\n\n\n\n
\u56e0\u6b64\uff0c\u8be5\u95ee\u9898\u7684\u5b50\u95ee\u9898\u5c31\u662f x op y<\/code> \u4e2d\u7684 x<\/code> \u548c y<\/code>\uff1a\u4ee5\u8fd0\u7b97\u7b26\u5206\u9694\u7684\u5de6\u53f3\u4e24\u4fa7\u7b97\u5f0f\u89e3<\/strong>\u3002<\/p>\n\n\n\n
\u7136\u540e\u6211\u4eec\u6765\u8fdb\u884c \u5206\u6cbb\u7b97\u6cd5\u4e09\u6b65\u8d70<\/strong>\uff1a<\/p>\n\n\n\n
  1. \u5206\u89e3\uff1a\u6309\u8fd0\u7b97\u7b26\u5206\u6210\u5de6\u53f3\u4e24\u90e8\u5206\uff0c\u5206\u522b\u6c42\u89e3<\/li>
  2. \u89e3\u51b3\uff1a\u5b9e\u73b0\u4e00\u4e2a\u9012\u5f52\u51fd\u6570\uff0c\u8f93\u5165\u7b97\u5f0f\uff0c\u8fd4\u56de\u7b97\u5f0f\u89e3<\/li>
  3. \u5408\u5e76\uff1a\u6839\u636e\u8fd0\u7b97\u7b26\u5408\u5e76\u5de6\u53f3\u4e24\u90e8\u5206\u7684\u89e3\uff0c\u5f97\u51fa\u6700\u7ec8\u89e3<\/li><\/ol>\n\n\n\n
    class Solution:\n    def diffWaysToCompute(self, input: str) -> List[int]:\n        # \u5982\u679c\u53ea\u6709\u6570\u5b57\uff0c\u76f4\u63a5\u8fd4\u56de\n        if input.isdigit():\n            return [int(input)]\n\n        res = []\n        for i, char in enumerate(input):\n            if char in ['+', '-', '*']:\n                # 1.\u5206\u89e3\uff1a\u9047\u5230\u8fd0\u7b97\u7b26\uff0c\u8ba1\u7b97\u5de6\u53f3\u4e24\u4fa7\u7684\u7ed3\u679c\u96c6\n                # 2.\u89e3\u51b3\uff1adiffWaysToCompute \u9012\u5f52\u51fd\u6570\u6c42\u51fa\u5b50\u95ee\u9898\u7684\u89e3\n                left = self.diffWaysToCompute(input[:i])\n                right = self.diffWaysToCompute(input[i+1:])\n                # 3.\u5408\u5e76\uff1a\u6839\u636e\u8fd0\u7b97\u7b26\u5408\u5e76\u5b50\u95ee\u9898\u7684\u89e3\n                for l in left:\n                    for r in right:\n                        if char == '+':\n                            res.append(l + r)\n                        elif char == '-':\n                            res.append(l - r)\n                        else:\n                            res.append(l * r)\n\n        return res<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
    \u5206\u6cbb\u6cd5\u7684\u8bbe\u8ba1\u601d\u60f3\u662f\uff1a\u5c06\u4e00\u4e2a\u96be\u4ee5\u76f4\u63a5\u89e3\u51b3\u7684\u5927\u95ee\u9898\uff0c\u5206\u5272\u6210\u4e00\u4e9b\u89c4\u6a21\u8f83\u5c0f\u7684\u76f8\u540c\u95ee\u9898\uff0c\u4ee5\u4fbf\u5404\u4e2a\u51fb\u7834\uff0c\u5206\u800c\u6cbb\u4e4b\u3002 &nb … \u7ee7\u7eed\u9605\u8bfb\u5206\u6cbb\u7b97\u6cd5<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[6],"tags":[],"_links":{"self":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/2632"}],"collection":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/comments?post=2632"}],"version-history":[{"count":10,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/2632\/revisions"}],"predecessor-version":[{"id":3192,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/posts\/2632\/revisions\/3192"}],"wp:attachment":[{"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/media?parent=2632"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/categories?post=2632"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/139.9.1.231\/index.php\/wp-json\/wp\/v2\/tags?post=2632"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}