{"id":150267,"date":"2020-09-03T00:02:02","date_gmt":"2020-09-02T16:02:02","guid":{"rendered":"http:\/\/4563.org\/?p=150267"},"modified":"2020-09-03T00:02:02","modified_gmt":"2020-09-02T16:02:02","slug":"%e9%98%bf%e9%87%8c-2020-%e5%8a%a8%e6%80%81%e8%a7%84%e5%88%92%e9%a2%98%ef%bc%9a%e8%83%8c%e5%8c%85%e9%97%ae%e9%a2%98","status":"publish","type":"post","link":"http:\/\/4563.org\/?p=150267","title":{"rendered":"\u963f\u91cc 2020 \u52a8\u6001\u89c4\u5212\u9898\uff1a\u80cc\u5305\u95ee\u9898"},"content":{"rendered":"<div>\n<div>\n<div>\n<h1>                  \u963f\u91cc 2020 \u52a8\u6001\u89c4\u5212\u9898\uff1a\u80cc\u5305\u95ee\u9898               <\/h1>\n<p> <\/p>\n<div>\n<div> <span>\u8cc7\u6df1\u5927\u4f6c : zzzrf <\/span>  <span><i><\/i> 12<\/span> <\/div>\n<div> <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<\/p><\/div>\n<div isfirst=\"1\"> <\/p>\n<p>\u5728 n \u4e2a\u7269\u54c1\u4e2d\u6311\u9009\u82e5\u5e72\u7269\u54c1\u88c5\u5165\u80cc\u5305\uff0c\u6700\u591a\u80fd\u88c5\u591a\u6ee1\uff1f\u5047\u8bbe\u80cc\u5305\u7684\u5927\u5c0f\u4e3a m\uff0c\u6bcf\u4e2a\u7269\u54c1\u7684\u5927\u5c0f\u4e3a A[i]\u3002 \u4f60\u4e0d\u53ef\u4ee5\u5c06\u7269\u54c1\u8fdb\u884c\u5207\u5272\u3002<\/p>\n<p>\u70b9\u6b64\u5728\u7ebf\u505a\u9898<\/p>\n<h2>\u6837\u4f8b 1:<\/h2>\n<pre><code>\u8f93\u5165:  [3,4,8,5], backpack size=10 \u8f93\u51fa:  9 <\/code><\/pre>\n<h2>\u6837\u4f8b 2:<\/h2>\n<pre><code>\u8f93\u5165:  [2,3,5,7], backpack size=12 \u8f93\u51fa:  12 <\/code><\/pre>\n<h2>\u7b97\u6cd5\uff1aDP<\/h2>\n<p>\u4ece\u5df2\u77e5\u7684\u9898\u76ee\u4e2d\uff0c\u53ef\u4ee5\u603b\u7ed3\u51fa\u4ee5\u4e0b\u4e24\u70b9\uff1a<\/p>\n<ul>\n<li>\u6bcf\u4ef6\u7269\u54c1\u53ea\u6709\u4e00\u79cd<\/li>\n<li>\u6bcf\u4ef6\u7269\u54c1\u6700\u591a\u9009\u62e9\u4e00\u6b21 \u90a3\u4e48\u8003\u8651\u5bf9\u4e8e\u524d i \u4ef6\u7684\u7269\u54c1\u5728\u5bb9\u91cf\u4e3a w \u7684\u80cc\u5305\u4e0b\uff0c\u6700\u5927\u7684\u88c5\u8f7d\u91cf\u662f\u591a\u5c11\uff0c\u7531\u6b64\u53ef\u4ee5\u603b\u7ed3\u51fa\u5bf9\u5e94\u7684\u5b50\u7ed3\u6784\uff0c\u8fdb\u884c\u52a8\u6001\u89c4\u5212\u3002<\/li>\n<\/ul>\n<h2>\u7b97\u6cd5\u601d\u8def<\/h2>\n<p>\u8bbe\u8ba1 dp \u6570\u7ec4 dp[n][m]\uff0c\u7528 dp[i][j]\u8868\u793a\u7b2c i \u4e2a\u7269\u54c1\u5728\u5bb9\u91cf\u4e3a j \u7684\u80cc\u5305\u4e0b\uff0c\u6700\u5927\u7684\u88c5\u8f7d\u91cf\u3002<\/p>\n<p>\u5728\u8fd9\u4e2a\u95ee\u9898\u4e2d\uff0c\u82e5\u53ea\u8003\u8651\u7b2c i \u4ef6\u7269\u54c1\u7684\u7b56\u7565\uff08\u653e\u6216\u4e0d\u653e\uff09\uff0c\u90a3\u4e48\u5c31\u53ef\u4ee5\u8f6c\u5316\u4e3a\u4e00\u4e2a\u53ea\u7275\u626f\u524d i\u22121 \u4ef6\u7269\u54c1\u7684\u95ee\u9898\uff1a<\/p>\n<ul>\n<li>\u5982\u679c\u4e0d\u653e\u7b2c i \u4ef6\u7269\u54c1\uff0c\u53ef\u5f97 dp[i][j]=dp[i\u22121][j]<\/li>\n<li>\u5982\u679c\u653e\u4e86\u7b2c i \u4ef6\u7269\u54c1\uff0c\u53ef\u5f97 dp[i][j]=dp[i\u22121][j\u2212A[i]]+Ai \u603b\u7ed3\u72b6\u6001\u8f6c\u4e49\u65b9\u7a0b\u4e3a\uff1adp[i][j]=max(dp[i\u22121][j],dp[i\u22121][j\u2212A[i]]+A[i])<\/li>\n<\/ul>\n<h2>\u590d\u6742\u5ea6\u5206\u6790<\/h2>\n<p>n \u8868\u793a\u7269\u54c1\u4ef6\u6570\uff0cm \u8868\u793a\u80cc\u5305\u5bb9\u91cf<\/p>\n<ul>\n<li>\u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(nm)<\/li>\n<li>\u7a7a\u95f4\u590d\u6742\u5ea6\uff1aO(nm)<\/li>\n<\/ul>\n<p>\u7b97\u6cd5\u4f18\u5316\u89c2\u5bdf\u4e0a\u65b9\u7684\u72b6\u6001\u8f6c\u4e49\u65b9\u7a0b\uff0c\u53ef\u4ee5\u53d1\u73b0 dp[i][j]\u65b9\u7a0b\u7684\u4e24\u4e2a\u72b6\u6001\u90fd\u53ea\u548c dp[i-1]\u6709\u5173\uff0c\u663e\u7136\u901a\u8fc7 O(nm)\u7684\u7a7a\u95f4\u590d\u6742\u5ea6\uff0c\u96be\u514d\u4f1a\u6d6a\u8d39\u4e00\u4e9b\u7a7a\u95f4\u3002<\/p>\n<p>\u53ef\u4ee5\u8003\u8651\u4f7f\u7528\u6eda\u52a8\u6570\u7ec4\u4f18\u5316\uff0c\u5efa\u7acb dp \u6570\u7ec4 dp[m]\uff0c\u4f7f\u7528 dp[j-A[i]]\u4ee3\u66ff dp[i-1][j-A[i]]\u3002\u4f18\u5316\u540e\u72b6\u6001\u8f6c\u4e49\u65b9\u7a0b\u4e3a dp[j]=max(dp[j],dp[j\u2212A[i]]+A[i])<\/p>\n<h2>\u4f18\u5316\u540e\u590d\u6742\u5ea6\u5206\u6790<\/h2>\n<p>\u65f6\u95f4\u590d\u6742\u5ea6\uff1aO(nm) \u7a7a\u95f4\u590d\u6742\u5ea6\uff1aO(m)<\/p>\n<h2>\u4ee3\u7801\u601d\u8def\u5206\u6790<\/h2>\n<p>\u5efa\u7acb\u6570\u7ec4 dp[m]\u8868\u793a\u80cc\u5305\u5bb9\u91cf\u4e3a m \u7684\u60c5\u51b5\u4e0b\uff0c\u6700\u5927\u7684\u88c5\u8f7d\u91cf \u521d\u59cb\u5316 dp[0]=0 \u6b63\u5e8f\u679a\u4e3e A[i]\uff0c\u5e76\u5012\u53d9\u679a\u4e3e j\uff0c\u8fd9\u6837\u6240\u9700\u8981\u7684 dp[j-A[i]]\u4e0d\u4f1a\u88ab\u63d0\u524d\u66f4\u65b0 \u6700\u540e\u8fd4\u56de dp[m]\uff0c\u8868\u793a\u80cc\u5305\u5bb9\u91cf\u5728 m \u4e0b\u7684\u7b54\u6848<\/p>\n<pre><code>public class Solution {     \/**      * @param m: An integer m denotes the size of a backpack      * @param A: Given n items with size A[i]      * @return: The maximum size      *\/     public int backPack(int m, int[] A) {         \/\/ write your code here         \/\/ \u5982\u679c\u80cc\u5305\u5bb9\u91cf\u6216\u8005\u7269\u54c1\u6570\u91cf\u4e3a 0\uff0c\u5219\u76f4\u63a5\u8fd4\u56de         if (A.length == 0 || m == 0) {             return 0;         }         int n = A.length;         int[] dp = new int[m + 1];         for (int i = 0; i &lt; n; i++) {             \/\/ \u6eda\u52a8\u6570\u7ec4\u4f18\u5316 \u5012\u5e8f\u679a\u4e3e j             for (int j = m; j &gt;= A[i]; j--) {                 dp[j] = Integer.max(dp[j], dp[j - A[i]] + A[i]);             }         }         return dp[m];     } }   <\/code><\/pre>\n<p>\u70b9\u6b64\u83b7\u53d6\u66f4\u591a\u5927\u5382\u9762\u8bd5\u52a8\u6001\u89c4\u5212\u9898\u89e3<\/p>\n<\/p><\/div>\n<div> <b>\u5927\u4f6c\u6709\u8a71\u8aaa<\/b> (<span>0<\/span>)        <\/div>\n<div> <\/div>\n<\/p><\/div>\n<\/p><\/div>\n<ul>\n<li>\n","protected":false},"excerpt":{"rendered":"<p>\u963f\u91cc 2020 \u52a8\u6001\u89c4\u5212\u9898\uff1a\u80cc\u5305\u95ee&hellip;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[],"tags":[],"_links":{"self":[{"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts\/150267"}],"collection":[{"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=150267"}],"version-history":[{"count":0,"href":"http:\/\/4563.org\/index.php?rest_route=\/wp\/v2\/posts\/150267\/revisions"}],"wp:attachment":[{"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=150267"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=150267"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/4563.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=150267"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}