0-1背包问题,poj 3624 Charm Bracelet动态规划-解题报告,增加最优路径构建
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1)0-1背包问题和 零碎背包问题是不同的,前者只能用动态规划来做, 后者可以用贪心算法。
2)动态规划的核心是 “有多个重叠子问题”,“自底向上”解决问题。
3) 0-1背包问题 ,W为最大重量,n为物体个数,求最大的价值Value,可在O(nW)的时间复杂度内解算出来。
Language:Default
Charm Bracelet
Time Limit: 1000MS
Memory Limit: 65536K
Total Submissions: 10014
Accepted: 4498
Description
Bessie has gone to the mall's jewelry store and spies a charm bracelet. Of course, she'd like to fill it with the best charms possible from theN (1 ≤N ≤ 3,402) available charms. Each charm i in the supplied list has a weightWi (1 ≤Wi ≤ 400), a 'desirability' factorDi (1 ≤Di ≤ 100), and can be used at most once. Bessie can only support a charm bracelet whose weight is no more thanM (1 ≤M ≤ 12,880).
Given that weight limit as a constraint and a list of the charms with their weights and desirability rating, deduce the maximum possible sum of ratings.
Input
* Line 1: Two space-separated integers: N and M
* Lines 2..N+1: Line i+1 describes charm i with two space-separated integers:Wi andDi
Output
* Line 1: A single integer that is the greatest sum of charm desirabilities that can be achieved given the weight constraints
Sample Input
4 61 42 63 122 7
Sample Output
23
Source
USACO 2007 December Silver
#include <stdio.h>int N,M;int W[3410],D[3410];int f[12882];int rout[12882]; //寻根,帮助重建 int main(){ scanf("%d%d",&N,&M); for(int i=1;i<=N;i++) { scanf("%d%d",&W[i],&D[i]); } for(int i=1;i<=M;i++) { f[i]=0; rout[i]=-1; } for(int i=1;i<=N;i++) //注意不是从W[i]到M,而是从M到W[i],因为这次是基于上次的基础(后者),而不是重复算两次当下(前者) for(int j=M;j>=W[i];j--) { if(f[j-W[i]] +D[i]>f[j]) { f[j]=f[j-W[i]]+D[i]; rout[j]=W[i]; } } int ma=-1; int pos=-1; for(int i=1;i<=M;i++) if(f[i]>ma) { ma=f[i]; pos=i; } printf("%d\n",ma); int j=pos; while(rout[j]!=-1 && j>0) { printf("%d\n",rout[j]); j=j-rout[j]; } scanf("%d",&N); return 0;}
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