背包问题(2)01背包 Bone Collector
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Bone Collector
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)Total Submission(s): 22998 Accepted Submission(s): 9320
Problem Description
Many years ago , in Teddy’s hometown there was a man who was called “Bone Collector”. This man like to collect varies of bones , such as dog’s , cow’s , also he went to the grave …
The bone collector had a big bag with a volume of V ,and along his trip of collecting there are a lot of bones , obviously , different bone has different value and different volume, now given the each bone’s value along his trip , can you calculate out the maximum of the total value the bone collector can get ?
The bone collector had a big bag with a volume of V ,and along his trip of collecting there are a lot of bones , obviously , different bone has different value and different volume, now given the each bone’s value along his trip , can you calculate out the maximum of the total value the bone collector can get ?
Input
The first line contain a integer T , the number of cases.
Followed by T cases , each case three lines , the first line contain two integer N , V, (N <= 1000 , V <= 1000 )representing the number of bones and the volume of his bag. And the second line contain N integers representing the value of each bone. The third line contain N integers representing the volume of each bone.
Followed by T cases , each case three lines , the first line contain two integer N , V, (N <= 1000 , V <= 1000 )representing the number of bones and the volume of his bag. And the second line contain N integers representing the value of each bone. The third line contain N integers representing the volume of each bone.
Output
One integer per line representing the maximum of the total value (this number will be less than 231).
Sample Input
15 101 2 3 4 55 4 3 2 1
Sample Output
14思路:比上个问题更水的背包问题, 因看错了volume 和 value 而抑郁了半天(侧面说明English
is very important!!!), 用 ans[i][j] 表示前i个物品在容量为j的背包里的最优解, 每个问题可以分解成两个子问题的和(第i个物品放或不放):ans[i-1][j] 前i-1个物品放入容量为j的背包里的最优解, 和ans[i-1][j - weight[i]] + value[i], 将第i个物品加入到背包内, 递推式为:f[i][v]=max{f[i-1][v],f[i-1][v-c[i]]+w[i]}。
#include <stdio.h>#include <string.h>#include <stdlib.h>#define MAX 1005int ans[MAX][MAX], weight[MAX], value[MAX];int mymax(int a, int b){ return a > b ? a : b;}int main(){ int t, n, v, i, j; //变量见题目scanf("%d", &t);while(t--){memset(ans, 0, sizeof(ans)); //每次清空scanf("%d%d", &n, &v);for(i = 1; i <= n; i++){ scanf("%d", &value[i]);}for(i = 1; i <= n; i++){ scanf("%d", &weight[i]);}for(i = 1; i <= n; i++){ for(j = 0; j <= v; j++){if(j < weight[i]) //在j < weight[i] 时无法加入, 保存(i-1)的解{ ans[i][j] = ans[i-1][j];}else //否则取最优解(加或不加){ ans[i][j] = mymax(ans[i-1][j], ans[i-1][j-weight[i]] + value[i]);}}}printf("%d\n", ans[n][v]); //最优解} return 0;}
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