{"id":1881,"date":"2019-10-17T18:56:31","date_gmt":"2019-10-17T10:56:31","guid":{"rendered":"http:\/\/www.sniper97.cn\/?p=1881"},"modified":"2019-10-17T18:56:31","modified_gmt":"2019-10-17T10:56:31","slug":"%e3%80%90%e7%ae%97%e6%b3%95%e5%88%86%e6%9e%90%e4%b8%8e%e8%ae%be%e8%ae%a1%e3%80%91%e5%88%86%e6%b2%bb%e7%ad%96%e7%95%a5","status":"publish","type":"post","link":"http:\/\/www.sniper97.cn\/index.php\/note\/introduction_to_algorithms\/1881\/","title":{"rendered":"\u3010\u7b97\u6cd5\u5bfc\u8bba\u3011\u5206\u6cbb\u7b56\u7565"},"content":{"rendered":"\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"266\" height=\"308\" src=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-78.png\" alt=\"\" class=\"wp-image-2037\" srcset=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-78.png 266w, http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-78-259x300.png 259w\" sizes=\"(max-width: 266px) 100vw, 266px\" \/><\/figure><\/div>\n\n\n<p>\u5728\u5206\u6cbb\u7b56\u7565\u4e2d\uff0c\u6211\u4eec\u9012\u5f52\u5730\u6c42\u89e3\u4e00\u4e2a\u95ee\u9898\uff0c\u5728\u6bcf\u5c42\u9012\u5f52\u4e2d\u4f7f\u7528\u5982\u4e0b\u4e09\u4e2a\u6b65\u9aa4\uff1a<\/p>\n\n\n<ul><li><strong>\u5206\u89e3<\/strong>\uff08Divide\uff09\u6b65\u9aa4\u5c06\u95ee\u9898\u5212\u5206\u4e3a\u4e00\u4e9b\u5b50\u95ee\u9898\uff0c\u5b50\u95ee\u9898\u7684\u5f62\u5f0f\u4e0e\u539f\u95ee\u9898\u4e00\u6837\uff0c\u53ea\u662f\u89c4\u6a21\u66f4\u5c0f\u3002<\/li><li><strong>\u89e3\u51b3<\/strong>\uff08Conquer\uff09\u6b65\u9aa4\u9012\u5f52\u5730\u6c42\u89e3\u51fa\u5b50\u95ee\u9898\uff0c\u5982\u679c\u95ee\u9898\u7684\u89c4\u6a21\u8db3\u591f\u5c0f\uff0c\u5219\u505c\u6b62\u9012\u5f52\uff0c\u76f4\u63a5\u6c42\u89e3\u3002<\/li><li><strong>\u5408\u5e76<\/strong>\uff08Combine\uff09\u6b65\u9aa4\u5c06\u5b50\u95ee\u9898\u7684\u89e3\u7ec4\u5408\u6210\u539f\u95ee\u9898\u7684\u89e3\u3002<\/li><\/ul>\n\n\n<p>\u5f53\u5b50\u95ee\u9898\u8db3\u591f\u5927\u65f6\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a<strong>\u9012\u5f52\u60c5\u51b5<\/strong>\uff0c\u5f53\u95ee\u9898\u8db3\u591f\u5c0f\u65f6\uff0c\u6211\u4eec\u79f0\u4e3a\u8fdb\u5165\u4e86<strong>\u57fa\u672c\u60c5\u51b5<\/strong>\u3002<\/p>\n\n\n<p><strong>\u9012\u5f52\u5f0f<\/strong>\u662f\u4e00\u4e2a\u7b49\u5f0f\u6216\u4e0d\u7b49\u5f0f\uff0c\u5b83\u901a\u8fc7\u66f4\u5c0f\u7684\u8f93\u5165\u4e0a\u7684\u51fd\u6570\u503c\u6765\u63cf\u8ff0\u4e00\u4e2a\u51fd\u6570\uff0c\u5982\u4e0b\u3002<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"334\" height=\"61\" src=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-25.png\" alt=\"\" class=\"wp-image-1882\" srcset=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-25.png 334w, http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-25-300x55.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/figure><\/div>\n\n\n<h2 class=\"wp-block-heading\">1.\u6700\u5927\u5b50\u6570\u7ec4\u95ee\u9898<\/h2>\n\n\n<p>\u83b7\u53d6\u4e00\u4e2a\u6570\u7ec4\u4e2d\u6700\u5927\u5b50\u5e8f\u5217\u7684\u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u7528<strong>\u66b4\u529b\u6c42\u89e3\u6cd5<\/strong>\uff0c\u8fd9\u6837\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662fn^2\u3002<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"527\" height=\"93\" src=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-61.png\" alt=\"\" class=\"wp-image-1975\" srcset=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-61.png 527w, http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-61-300x53.png 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><\/figure><\/div>\n\n\n<p>\u90a3\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528\u522b\u7684\u65b9\u6cd5\uff0c\u53d6\u5f53\u524d\u6570\u7ec4\u7684\u4e00\u4e2a\u4e2d\u95f4\u503c\uff0c\u90a3\u4e48\u6700\u5927\u5b50\u6570\u7ec4\u5c31\u6709\u4e14\u4ec5\u6709\u4e09\u79cd\u53ef\u80fd\uff0c\u5373\u8de8\u8d8a\u4e2d\u70b9\uff0c\u4e2d\u70b9\u4ee5\u5de6\u548c\u4e2d\u70b9\u4ee5\u53f3\u3002<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"790\" height=\"156\" src=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-62.png\" alt=\"\" class=\"wp-image-1976\" srcset=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-62.png 790w, http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-62-300x59.png 300w, http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-62-768x152.png 768w\" sizes=\"(max-width: 790px) 100vw, 790px\" \/><\/figure><\/div>\n\n\n<p>\u90a3\u4e48\u6211\u4eec\u5c31\u53ef\u4ee5\u5c06\u95ee\u9898\u8fdb\u4e00\u6b65\u7684\u5212\u5206\uff0c\u5728\u4e2d\u95f4\u70b9\u5de6\u53f3\u7684\u4e24\u79cd\u60c5\u51b5\u4e0b\uff0c\u6211\u4eec\u4f9d\u7136\u53ef\u4ee5\u8ba4\u4e3a\u662f\u8de8\u8d8a\u4e2d\u70b9\u7684\uff0c\u56e0\u4e3a\u6211\u4eec\u53ef\u4ee5\u622a\u53d6\u6570\u7ec4\u957f\u5ea6\u6765\u201c\u79fb\u52a8\u201d\u8fd9\u4e2a\u4e2d\u70b9\uff0c\u56e0\u6b64\u6211\u4eec\u53ea\u9700\u8981\u5728\u4e2d\u70b9\u5de6\u53f3\u5206\u522b\u8ba1\u7b97\u6700\u5927\u5b50\u6570\u7ec4\uff0c\u5408\u8d77\u6765\u5c31\u662f\u8de8\u8d8a\u5f53\u524d\u4e2d\u70b9\u7684\u6700\u5927\u5b50\u6570\u7ec4\uff0c\u7136\u540e\u4e8c\u5206\u5730\u79fb\u52a8\u4e2d\u70b9\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u8ba1\u7b97\u5176\u4ed6\u7684\u5f53\u524d\u6700\u5927\u5b50\u6570\u7ec4\uff0c\u5f53\u6211\u4eec\u4f7f\u7528\u4e8c\u5206\u904d\u5386\u5b8c\u6210\u6240\u6709\u7684\u201c\u4e2d\u70b9\u201d\u540e\u4fbf\u53ef\u4ee5\u627e\u5230\u6574\u4e2a\u6570\u7ec4\u957f\u5ea6\u4e0b\u7684\u6700\u5927\u5b50\u6570\u7ec4\u3002\u800c\u8fd9\u79cd\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u53ea\u6709n`lgn\u3002<\/p>\n\n\n<p>\u4ee3\u7801\u6c42\u89e3\u6700\u5927\u5b50\u6570\u7ec4\u4ee5\u53ca\u5b50\u6570\u7ec4\u548c\u3002<\/p>\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"568\" height=\"58\" src=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-63.png\" alt=\"\" class=\"wp-image-2009\" srcset=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-63.png 568w, http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-63-300x31.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/figure>\n\n\n<p>\u4ee3\u7801\uff1a<\/p>\n\n\n<pre class=\"wp-block-code\"><code># -*- coding:utf-8 -*-\nclass FIndMaxSubarray:\n    def __init__(self, init_array):\n        self.init_array = init_array\n        pass\n    def find(self, start, end):\n        \"\"\"\n        \u9012\u5f52\u5bfb\u627e\u6700\u5927\u5b50\u6570\u7ec4\n        :return:\n        \"\"\"\n        # \u9012\u5f52\u7ed3\u675f\u6807\u8bb0\n        if start == end:\n            return [self.init_array[start]], self.init_array[start]\n        mid = int((start + end) \/ 2)\n        # \u5206\u522b\u5904\u7406\u5de6\u3001\u53f3\u3001\u4ee5\u53ca\u8de8\u8d8a\u91cd\u70b9\u7684\u60c5\u51b5\n        left_subarray, left_sum = self.find(start, mid)\n        right_subarray, right_sum = self.find(mid + 1, end)\n        cross_subarray, cross_sum = self.find_max_crossing_subarray(target_array=self.init_array[start:end+1])\n        # \u6bd4\u8f83\u4e09\u79cd\u7ed3\u679c\u5927\u5c0f\u5e76\u8fd4\u56de\n        if left_sum >= right_sum and left_sum >= cross_sum:\n            return left_subarray, left_sum\n        elif right_sum >= left_sum and right_sum >= cross_sum:\n            return right_subarray, right_sum\n        else:\n            return cross_subarray, cross_sum\n    def find_max_crossing_subarray(self, target_array):\n        \"\"\"\n        \u5bfb\u627e\u5f53\u524d\u5217\u8868\u4ee5\u4e2d\u70b9\u4e3a\u57fa\u51c6\u7684\u6700\u5927\u5b50\u5217\u8868\n        :param target_array:\n        :return:\n        \"\"\"\n        # \u5de6\u6700\u5927\u5b50\u6570\u7ec4\n        left_max_sub_array = []\n        # \u53f3\u6700\u5927\u5b50\u6570\u7ec4\n        right_max_sub_array = []\n        # \u4e2d\u95f4\u7d22\u5f15\n        mid_index = int(len(target_array) \/ 2)\n        # \u6700\u5927\u5b50\u6570\u7ec4\n        max_subarray = []\n        # \u4e2d\u95f4\u503c\n        mid_number = target_array[mid_index]\n        # \u4e34\u65f6\u5b58\u50a8\u7684\u6700\u5927\u503c\n        _sum = 0\n        # \u4e34\u65f6\u5b58\u50a8\u7684\u7d22\u5f15\u503c\n        _index = 0\n        # \u7528\u4e8e\u5b58\u653e\u4e34\u65f6\u548c\u7684\u53d8\u91cf\n        temp_sum = 0\n        # \u5bf9\u5de6\u4fa7\u6570\u5b57\u67e5\u627e\u6700\u5927\u5b50\u6570\u7ec4\n        for i in range(mid_index, 0, -1):\n            # \u8ba1\u7b97\u4e34\u65f6\u548c\n            temp_sum = temp_sum + target_array[i]\n            # \u5224\u65ad\u8be5\u4f4d\u53d6\u820d\n            if temp_sum > _sum:\n                _sum = temp_sum\n                _index = i\n        # \u622a\u53d6\u6570\u7ec4\n        left_max_sub_array = target_array[_index:mid_index]\n        # \u6570\u636e\u521d\u59cb\u5316\n        _sum = 0\n        _index = 0\n        temp_sum = 0\n        # \u5bf9\u53f3\u4fa7\u6570\u5b57\u67e5\u627e\u6700\u5927\u5b50\u6570\u7ec4\n        for i in range(mid_index, len(target_array)):\n            temp_sum = temp_sum + target_array[i]\n            if temp_sum > _sum:\n                _sum = temp_sum\n                _index = i\n        # \u622a\u53d6\u6570\u7ec4\n        right_max_sub_array = target_array[mid_index:_index + 1]\n        # \u5408\u5e76\u6570\u7ec4\n        max_subarray = left_max_sub_array + right_max_sub_array\n        # \u6c42\u548c\n        max_subarray_sum = sum(max_subarray)\n        return max_subarray, max_subarray_sum\nif __name__ == '__main__':\n    init_array = [13, -3, -25, 20, -3, -16, -23, 18, 20, -7, 12, -5, -22, 15, -4, 7]\n    max_sum, max_array = FIndMaxSubarray(init_array).find(0, len(init_array) - 1)\n    print(init_array)\n    print(max_array, '\\t', max_sum)\n    pass\n<\/code><\/pre>\n\n\n<h2 class=\"wp-block-heading\">2.\u7528\u4ee3\u5165\u6cd5\u6c42\u89e3\u9012\u5f52\u5f0f<\/h2>\n\n\n<p>\u4f8b\u7ec3\u4e604.3-6\uff0c\u7c7b\u4f3c\u4e8e\u6570\u5b66\u5f52\u7eb3\u6cd5\uff0c\u9996\u5148\u5047\u8bbe\u4e00\u4e2a\u65f6\u95f4\u590d\u6742\u5ea6\uff0c\u7136\u540e\u4ee3\u5165\u9012\u5f52\u5f0f\u9a8c\u8bc1\u731c\u60f3\u662f\u5426\u6210\u7acb\u3002<\/p>\n\n\n<p>\u9700\u8981\u6ce8\u610f\uff0c\u6709\u7684\u65f6\u5019\u9700\u8981\u4f7f\u7528\u4e00\u4e9b\u5c0f\u6280\u5de7\uff0c\u5305\u62ec\u5408\u7406\u7684\u731c\u6d4b\uff0c\u5fae\u5999\u7684\u7ec6\u8282\u4ee5\u53ca<strong>\u6539\u53d8\u53d8\u91cf<\/strong>\uff08\u7c7b\u4f3c\u4e8e\u9ad8\u6570\u4e2d\u7684\u6362\u5143\uff0c\u4f8b4.3-9\uff09<\/p>\n\n\n<h2 class=\"wp-block-heading\">3.\u7528\u9012\u5f52\u6811\u65b9\u6cd5\u6c42\u89e3\u9012\u5f52\u5f0f<\/h2>\n\n\n<p>\u4f8b\u7ec3\u4e604.4-6\uff0c\u9996\u5148\u6839\u636e\u9012\u5f52\u5f0f\u753b\u51fa\u9012\u5f52\u6811\uff0c\u7136\u540e\u6839\u636e\u9012\u5f52\u6811\u5199\u51fa\u65f6\u95f4\u590d\u6742\u5ea6\u3002<\/p>\n\n\n<h2 class=\"wp-block-heading\">4.\u7528\u4e66\u65b9\u6cd5\u6c42\u89e3\u9012\u5f52\u5f0f<\/h2>\n\n\n<p>\u4f8b\u7ec3\u4e604.5.1\uff0c\u901a\u5f0f<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"228\" height=\"34\" src=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-75.png\" alt=\"\" class=\"wp-image-2031\"\/><\/figure><\/div>\n\n\n<p>\u5bf9\u4e8e\u8be5\u901a\u5f0f\u6709<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"45\" height=\"27\" src=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-76.png\" alt=\"\" class=\"wp-image-2032\"\/><\/figure><\/div>\n\n\n<p>\u7136\u540e\u5224\u65adf(n)\u548c\u4e0a\u5f0f\u7684\u5927\u5c0f\uff0c\u5219\u4f5c\u4e3aT(n)\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u3002<\/p>\n\n\n<h2 class=\"wp-block-heading\">\u7ec3\u4e604.3-6<\/h2>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" width=\"439\" height=\"23\" src=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-64.png\" alt=\"\" class=\"wp-image-2011\" srcset=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-64.png 439w, http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-64-300x16.png 300w\" sizes=\"(max-width: 439px) 100vw, 439px\" \/><\/figure><\/div>\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"569\" height=\"207\" src=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-65.png\" alt=\"\" class=\"wp-image-2012\" srcset=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-65.png 569w, http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-65-300x109.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/figure>\n\n\n<h2 class=\"wp-block-heading\">\u7ec3\u4e604.3-9<\/h2>\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"753\" height=\"62\" src=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-66.png\" alt=\"\" class=\"wp-image-2014\" srcset=\"http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-66.png 753w, http:\/\/www.sniper97.cn\/wp-content\/uploads\/2019\/10\/\u56fe\u7247-66-300x25.png 300w\" sizes=\"(max-width: 753px) 100vw, 753px\" \/><\/figure>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img loading=\"lazy\" decoding=\"async\" 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