{"id":2497,"date":"2022-03-25T12:32:03","date_gmt":"2022-03-25T04:32:03","guid":{"rendered":"https:\/\/www.zeroheart.xyz\/wordpress\/?p=2497"},"modified":"2022-03-25T14:52:33","modified_gmt":"2022-03-25T06:52:33","slug":"dp%e7%ac%ac%e4%b8%89%e5%a4%a9","status":"publish","type":"post","link":"https:\/\/www.zeroheart.xyz\/wordpress\/?p=2497","title":{"rendered":"dp\u7b2c\u4e09\u5929"},"content":{"rendered":"\n

\u300c\u52a8\u6001\u89c4\u5212\u300d – \u5b66\u4e60\u8ba1\u5212 – \u529b\u6263\uff08LeetCode\uff09\u5168\u7403\u6781\u5ba2\u631a\u7231\u7684\u6280\u672f\u6210\u957f\u5e73\u53f0 (leetcode-cn.com)<\/a><\/p>\n\n\n\n

198. \u6253\u5bb6\u52ab\u820d<\/a><\/p>\n\n\n\n

\u8fd9\u4e00\u9898\uff0c\u516c\u5f0f\u4e0d\u96be\uff0c\u76f4\u63a5\u63a8\u5230\u51fa\u6765\u4e86\uff0c\u4f46\u662f\u521d\u59cb\u5316dp[0]\uff0cdp[1]\u7684\u65f6\u5019\uff0c\u4e00\u5f00\u59cb\u9519\u4e86\uff0c\u505a\u4e2a\u8bb0\u5f55<\/mark><\/p>\n\n\n\n

\/**\n 198. \u6253\u5bb6\u52ab\u820d\n \u4f60\u662f\u4e00\u4e2a\u4e13\u4e1a\u7684\u5c0f\u5077\uff0c\u8ba1\u5212\u5077\u7a83\u6cbf\u8857\u7684\u623f\u5c4b\u3002\u6bcf\u95f4\u623f\u5185\u90fd\u85cf\u6709\u4e00\u5b9a\u7684\u73b0\u91d1\uff0c\u5f71\u54cd\u4f60\u5077\u7a83\u7684\u552f\u4e00\u5236\u7ea6\u56e0\u7d20\u5c31\u662f\u76f8\u90bb\u7684\u623f\u5c4b\u88c5\u6709\u76f8\u4e92\u8fde\u901a\u7684\u9632\u76d7\u7cfb\u7edf\uff0c\u5982\u679c\u4e24\u95f4\u76f8\u90bb\u7684\u623f\u5c4b\u5728\u540c\u4e00\u665a\u4e0a\u88ab\u5c0f\u5077\u95ef\u5165\uff0c\u7cfb\u7edf\u4f1a\u81ea\u52a8\u62a5\u8b66\u3002\n\n \u7ed9\u5b9a\u4e00\u4e2a\u4ee3\u8868\u6bcf\u4e2a\u623f\u5c4b\u5b58\u653e\u91d1\u989d\u7684\u975e\u8d1f\u6574\u6570\u6570\u7ec4\uff0c\u8ba1\u7b97\u4f60 \u4e0d\u89e6\u52a8\u8b66\u62a5\u88c5\u7f6e\u7684\u60c5\u51b5\u4e0b \uff0c\u4e00\u591c\u4e4b\u5185\u80fd\u591f\u5077\u7a83\u5230\u7684\u6700\u9ad8\u91d1\u989d\u3002\n\n \u793a\u4f8b 1\uff1a\n\n \u8f93\u5165\uff1a[1,2,3,1]\n \u8f93\u51fa\uff1a4\n \u89e3\u91ca\uff1a\u5077\u7a83 1 \u53f7\u623f\u5c4b (\u91d1\u989d = 1) \uff0c\u7136\u540e\u5077\u7a83 3 \u53f7\u623f\u5c4b (\u91d1\u989d = 3)\u3002\n \u5077\u7a83\u5230\u7684\u6700\u9ad8\u91d1\u989d = 1 + 3 = 4 \u3002\n \u793a\u4f8b 2\uff1a\n\n \u8f93\u5165\uff1a[2,7,9,3,1]\n \u8f93\u51fa\uff1a12\n \u89e3\u91ca\uff1a\u5077\u7a83 1 \u53f7\u623f\u5c4b (\u91d1\u989d = 2), \u5077\u7a83 3 \u53f7\u623f\u5c4b (\u91d1\u989d = 9)\uff0c\u63a5\u7740\u5077\u7a83 5 \u53f7\u623f\u5c4b (\u91d1\u989d = 1)\u3002\n \u5077\u7a83\u5230\u7684\u6700\u9ad8\u91d1\u989d = 2 + 9 + 1 = 12 \u3002\n\n\n \u63d0\u793a\uff1a\n\n 1 <= nums.length <= 100\n 0 <= nums[i] <= 400\n\n * <\/em>@author <\/em><\/strong>zeroheart\n *\n *\/\n<\/em>public class Question198 {\n    public static int rob(int[] nums) {\n\n\n        if(nums.length == 0) return 0;\n        if(nums.length == 1) return nums[1];\n\n        \/\/ dp[i] \u5982\u679c\u662f\u7684\u6700\u5927\u91d1\u989d\uff0c\u90a3\u4e48dp[i] = Math.max(dp[i-1], dp[i-2]+nums[i])\n\n        int[] dp = new int[nums.length];\n\n        \/\/ \u4e00\u5f00\u59cb\u8fd9\u91cc\u521d\u59cb\u5316\u6709\u95ee\u9898\uff0c\u8fd4\u56de\u7684\u662fdp[nums.length];\n        \/\/  dp[0] = 0;\n        \/\/  dp[1] = nums[0];\n\n        dp[0] = nums[0];\n        dp[1] = Math.max<\/em>(nums[0],nums[1]);\n\n        for(int i = 2; i<nums.length; i++){\n            dp[i] = Math.max<\/em>(dp[i-1], dp[i-2]+nums[i]);\n        }\n        return dp[nums.length-1];\n    }\n\n    public static void main(String[] args) {\n\/\/        System.out.println(rob(new int[]{1,2,3,1}));\n        System.out<\/em>.println(rob<\/em>(new int[]{2,7,9,3,1}));\n    }\n}<\/pre>\n\n\n\n
213. \u6253\u5bb6\u52ab\u820d II<\/a><\/p>\n\n\n\n
\/**\n\n 213. \u6253\u5bb6\u52ab\u820d II\n \u4f60\u662f\u4e00\u4e2a\u4e13\u4e1a\u7684\u5c0f\u5077\uff0c\u8ba1\u5212\u5077\u7a83\u6cbf\u8857\u7684\u623f\u5c4b\uff0c\u6bcf\u95f4\u623f\u5185\u90fd\u85cf\u6709\u4e00\u5b9a\u7684\u73b0\u91d1\u3002\u8fd9\u4e2a\u5730\u65b9\u6240\u6709\u7684\u623f\u5c4b\u90fd \u56f4\u6210\u4e00\u5708 \uff0c\u8fd9\u610f\u5473\u7740\u7b2c\u4e00\u4e2a\u623f\u5c4b\u548c\u6700\u540e\u4e00\u4e2a\u623f\u5c4b\u662f\u7d27\u6328\u7740\u7684\u3002\u540c\u65f6\uff0c\u76f8\u90bb\u7684\u623f\u5c4b\u88c5\u6709\u76f8\u4e92\u8fde\u901a\u7684\u9632\u76d7\u7cfb\u7edf\uff0c\u5982\u679c\u4e24\u95f4\u76f8\u90bb\u7684\u623f\u5c4b\u5728\u540c\u4e00\u665a\u4e0a\u88ab\u5c0f\u5077\u95ef\u5165\uff0c\u7cfb\u7edf\u4f1a\u81ea\u52a8\u62a5\u8b66 \u3002\n\n \u7ed9\u5b9a\u4e00\u4e2a\u4ee3\u8868\u6bcf\u4e2a\u623f\u5c4b\u5b58\u653e\u91d1\u989d\u7684\u975e\u8d1f\u6574\u6570\u6570\u7ec4\uff0c\u8ba1\u7b97\u4f60 \u5728\u4e0d\u89e6\u52a8\u8b66\u62a5\u88c5\u7f6e\u7684\u60c5\u51b5\u4e0b \uff0c\u4eca\u665a\u80fd\u591f\u5077\u7a83\u5230\u7684\u6700\u9ad8\u91d1\u989d\u3002\n\n\n\n \u793a\u4f8b 1\uff1a\n\n \u8f93\u5165\uff1anums = [2,3,2]\n \u8f93\u51fa\uff1a3\n \u89e3\u91ca\uff1a\u4f60\u4e0d\u80fd\u5148\u5077\u7a83 1 \u53f7\u623f\u5c4b\uff08\u91d1\u989d = 2\uff09\uff0c\u7136\u540e\u5077\u7a83 3 \u53f7\u623f\u5c4b\uff08\u91d1\u989d = 2\uff09, \u56e0\u4e3a\u4ed6\u4eec\u662f\u76f8\u90bb\u7684\u3002\n \u793a\u4f8b 2\uff1a\n\n \u8f93\u5165\uff1anums = [1,2,3,1]\n \u8f93\u51fa\uff1a4\n \u89e3\u91ca\uff1a\u4f60\u53ef\u4ee5\u5148\u5077\u7a83 1 \u53f7\u623f\u5c4b\uff08\u91d1\u989d = 1\uff09\uff0c\u7136\u540e\u5077\u7a83 3 \u53f7\u623f\u5c4b\uff08\u91d1\u989d = 3\uff09\u3002\n \u5077\u7a83\u5230\u7684\u6700\u9ad8\u91d1\u989d = 1 + 3 = 4 \u3002\n \u793a\u4f8b 3\uff1a\n\n \u8f93\u5165\uff1anums = [1,2,3]\n \u8f93\u51fa\uff1a3\n\n\n \u63d0\u793a\uff1a\n\n 1 <= nums.length <= 100\n 0 <= nums[i] <= 1000\n\n\n * <\/em>@author <\/em><\/strong>zeroheart\n *\n *\/\n<\/em>public class Question213 {\n    public int rob(int[] nums) {\n        \/\/ \u548c\u7b2c\u4e00\u9898\u7684\u533a\u522b\u662f\u9996\u5c3e\u76f8\u8fde\u7684\n        \/\/ \u601d\u8def\u662f0 - n-1\u7b97\u4e00\u6b21\uff0c1 - n\u7b97\u4e00\u6b21\uff0c\u770b\u54ea\u4e2a\u66f4\u5927\u3002\u3002\u3002<\/mark>\n\n\n        int len = nums.length;\n        if(len == 0){\n            return 0;\n        }\n        if(len == 1){\n            return nums[0];\n        }\n        if(len == 2){\n            return Math.max<\/em>(nums[0],nums[1]);\n        }\n        if(len == 3){\n            return Math.max<\/em>(Math.max<\/em>(nums[0], nums[1]), nums[2]);\n        }\n\n        int[] dp1 = new int[len-1];\n        int[] dp2 = new int[len-1];\n\n        dp1[0] = nums[0];\n        dp1[1] = Math.max<\/em>(nums[0],nums[1]);\n        for(int i = 2; i < len-1; i++){\n            dp1[i] = Math.max<\/em>(dp1[i-1],dp1[i-2]+nums[i]);\n        }\n\n\n        dp2[0] = nums[1];\n        dp2[1] = Math.max<\/em>(nums[1],nums[2]);\n        for(int i = 2; i < len-1; i++){\n            dp2[i] = Math.max<\/em>(dp2[i-1],dp2[i-2]+nums[i+1]<\/mark>);\n        }\n\n        return Math.max<\/em>(dp1[len-2], dp2[len-2]);\n\n    }\n}<\/pre>\n\n\n\n
\u9996\u5c3e\u6210\u73af\u7684\u65f6\u5019\uff0c\u9700\u8981\u6ce8\u610f\u7684\u662f\u53ef\u4ee5\u5206\u6210\u4e24\u6761\u94fe[0, n-1],[1, n]\u6765\u5904\u7406\uff0c\u7136\u540e\u5728\u6bd4\u8f83\u5927\u5c0f\u3002<\/mark><\/p>\n\n\n\n
740. \u5220\u9664\u5e76\u83b7\u5f97\u70b9\u6570<\/a><\/p>\n\n\n\n
\u8fd9\u9898\u662f\u6253\u5bb6\u52ab\u820d\u7684\u53d8\u79cd\u3002\u3002\u3002\u3002\u3002<\/p>\n\n\n\n
\/\/ nums = [2,2,3,3,3,4]\n\/\/ \u8fd9\u9898\u9700\u8981\u4e00\u4e2a\u8f6c\u5316\uff0c\u5b9a\u4e49\u6570\u7ec4arr[]\uff0c\u5b58\u653e\u6bcf\u4e2a\u70b9\u6570\u7684\u548c\uff0carr[0] = 0, arr[1] = 0, arr[2] = 4, arr[3] = 9, arr[4] = 4\n\/\/ \u7531\u4e8e\u53d6\u5230nums[i]\u4e4b\u540e\uff0c\u8981\u5220\u9664nums[i] + 1 \u548c nums[i] - 1\u7684\uff0c\u5728\u65b0\u7684\u6570\u7ec4\u91cc\u9762\uff0c\u76f8\u5f53\u4e8e\u4e0d\u80fd\u53d6\u76f8\u90bb\u7684\u503c\uff0c\u6253\u5bb6\u52ab\u820d\u3002\u3002\u3002\u3002\u3002<\/mark><\/pre>\n\n\n\n
\/**
<\/em>
<\/em> 740. \u5220\u9664\u5e76\u83b7\u5f97\u70b9\u6570
<\/em> \u7ed9\u4f60\u4e00\u4e2a\u6574\u6570\u6570\u7ec4 nums \uff0c\u4f60\u53ef\u4ee5\u5bf9\u5b83\u8fdb\u884c\u4e00\u4e9b\u64cd\u4f5c\u3002
<\/em>
<\/em> \u6bcf\u6b21\u64cd\u4f5c\u4e2d\uff0c\u9009\u62e9\u4efb\u610f\u4e00\u4e2a nums[i] \uff0c\u5220\u9664\u5b83\u5e76\u83b7\u5f97 nums[i] \u7684\u70b9\u6570\u3002\u4e4b\u540e\uff0c\u4f60\u5fc5\u987b\u5220\u9664 \u6240\u6709 \u7b49\u4e8e nums[i] - 1 \u548c nums[i] + 1 \u7684\u5143\u7d20\u3002
<\/em>
<\/em> \u5f00\u59cb\u4f60\u62e5\u6709 0 \u4e2a\u70b9\u6570\u3002\u8fd4\u56de\u4f60\u80fd\u901a\u8fc7\u8fd9\u4e9b\u64cd\u4f5c\u83b7\u5f97\u7684\u6700\u5927\u70b9\u6570\u3002
<\/em>
<\/em>
<\/em>
<\/em> \u793a\u4f8b 1\uff1a
<\/em>
<\/em> \u8f93\u5165\uff1anums = [3,4,2]
<\/em> \u8f93\u51fa\uff1a6
<\/em> \u89e3\u91ca\uff1a
<\/em> \u5220\u9664 4 \u83b7\u5f97 4 \u4e2a\u70b9\u6570\uff0c\u56e0\u6b64 3 \u4e5f\u88ab\u5220\u9664\u3002
<\/em> \u4e4b\u540e\uff0c\u5220\u9664 2 \u83b7\u5f97 2 \u4e2a\u70b9\u6570\u3002\u603b\u5171\u83b7\u5f97 6 \u4e2a\u70b9\u6570\u3002
<\/em> \u793a\u4f8b 2\uff1a
<\/em>
<\/em> \u8f93\u5165\uff1anums = [2,2,3,3,3,4]
<\/em> \u8f93\u51fa\uff1a9
<\/em> \u89e3\u91ca\uff1a
<\/em> \u5220\u9664 3 \u83b7\u5f97 3 \u4e2a\u70b9\u6570\uff0c\u63a5\u7740\u8981\u5220\u9664\u4e24\u4e2a 2 \u548c 4 \u3002
<\/em> \u4e4b\u540e\uff0c\u518d\u6b21\u5220\u9664 3 \u83b7\u5f97 3 \u4e2a\u70b9\u6570\uff0c\u518d\u6b21\u5220\u9664 3 \u83b7\u5f97 3 \u4e2a\u70b9\u6570\u3002
<\/em> \u603b\u5171\u83b7\u5f97 9 \u4e2a\u70b9\u6570\u3002
<\/em>
<\/em>
<\/em> \u63d0\u793a\uff1a
<\/em>
<\/em> 1 <= nums.length <= 2 * 10^4
<\/em> 1 <= nums[i] <= 10^4
<\/em>
<\/em> * <\/em>@author <\/em><\/strong>zeroheart
<\/em> *
<\/em> *\/
<\/em>public class Question740 {
    public int deleteAndEarn(int[] nums) {
        \/\/ nums = [2,2,3,3,3,4]
        \/\/ \u8fd9\u9898\u9700\u8981\u4e00\u4e2a\u8f6c\u5316\uff0c\u5b9a\u4e49\u6570\u7ec4arr[]\uff0c\u5b58\u653e\u6bcf\u4e2a\u70b9\u6570\u7684\u548c\uff0carr[0] = 0, arr[1] = 0, arr[2] = 4, arr[3] = 9, arr[4] = 4
        \/\/ \u7531\u4e8e\u53d6\u5230nums[i]\u4e4b\u540e\uff0c\u8981\u5220\u9664nums[i] + 1 \u548c nums[i] - 1\u7684\uff0c\u5728\u65b0\u7684\u6570\u7ec4\u91cc\u9762\uff0c\u76f8\u5f53\u4e8e\u4e0d\u80fd\u53d6\u76f8\u90bb\u7684\u503c\uff0c\u6253\u5bb6\u52ab\u820d\u3002\u3002\u3002\u3002\u3002

        \/\/ 1 <= nums[i] <= 10^4
        int[] trans = new int[10001];

        for(int i = 0; i<nums.length; i++){
            trans[nums[i]] += nums[i];
        }

        if(trans.length == 0) return 0;
        if(trans.length == 1) return trans[0];
        if(trans.length == 2) return Math.max<\/em>(trans[0], trans[1]);

        int[] dp = new int[trans.length];
        dp[0] = trans[0];
        dp[1] = Math.max<\/em>(trans[0], trans[1]);
        for(int i = 2; i<trans.length; i++){
            dp[i] = Math.max<\/em>(dp[i-1], dp[i-2] + trans[i]);
        }
        return dp[trans.length - 1];
    }
}<\/pre>\n\n\n\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
\u300c\u52a8\u6001\u89c4\u5212\u300d – \u5b66\u4e60\u8ba1\u5212 – \u529b\u6263\uff08LeetCode\uff09\u5168\u7403\u6781\u5ba2\u631a\u7231\u7684\u6280\u672f\u6210\u957f\u5e73\u53f0 ( […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[155],"tags":[158,165],"_links":{"self":[{"href":"https:\/\/www.zeroheart.xyz\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/2497"}],"collection":[{"href":"https:\/\/www.zeroheart.xyz\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.zeroheart.xyz\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.zeroheart.xyz\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.zeroheart.xyz\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2497"}],"version-history":[{"count":12,"href":"https:\/\/www.zeroheart.xyz\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/2497\/revisions"}],"predecessor-version":[{"id":2509,"href":"https:\/\/www.zeroheart.xyz\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/2497\/revisions\/2509"}],"wp:attachment":[{"href":"https:\/\/www.zeroheart.xyz\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2497"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.zeroheart.xyz\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2497"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.zeroheart.xyz\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2497"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}