POJ3624背包问题

Charm Bracelet

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 38547 Accepted: 16723

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 the N (1 ≤ N ≤ 3,402) available charms. Each charm i in the supplied list has a weight W_i (1 ≤ W_i ≤ 400), a 'desirability' factor D_i (1 ≤ D_i ≤ 100), and can be used at most once. Bessie can only support a charm bracelet whose weight is no more than M (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: W_i and D_i

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

    拿到这个题目，首先想到的是算出每一个元素的权（平均价值），再排序，再开循环依次判断，输出价值和。以下是我写的代码

#include <stdio.h>#include <stdlib.h>typedef struct about{    int weight;    int vual;    double power;} T;T arr[3500];int cmp(const void*a,const void*b){    T *A=(T *)a;    T *B=(T *)b;    return B->power-A->power>0?1:-1;}int main(){    int n,m;    while(~scanf("%d%d",&n,&m))    {        int sum=0;        for(int i=0; i<n; i++)        {            scanf("%d%d",&arr[i].weight,&arr[i].vual);            arr[i].power=arr[i].vual*1.0/arr[i].weight;        }        qsort(arr,n,sizeof(about),cmp);            //将结构体按照power的从大到小排序        for(int i=0; i<n; i++)        {            if(m>arr[i].weight)                  //依次判断总质量m与每个元素质量的大小            {                m-=arr[i].weight;                sum+=arr[i].vual;            }            else            {                sum+=m*arr[i].power;                break;            }        }        printf("%d\n",sum);    }    return 0;}

   代码写的挺顺手的，结果运行起来WA，搞不清楚为什么。于是就和小组的成员一起讨论了一下，发现了问题，给出的每个物体不能拆分。开始以为这个题目就是个纯粹的贪心，纠结了一下输出的数为什么是整数而不是小数，结果问题果然出现在这里。修改后的代码如下

#include <stdio.h>#include <string.h>int max(int a,int b){    return a>b?a:b;}typedef struct about{    int weight;    int vual;} T;T arr[4000];int main(){    int n,m,i,j;    int dp[40000];    while(~scanf("%d%d",&n,&m))    {        memset(dp,0,sizeof(dp));        for(i = 0; i<n; i++)            scanf("%d%d",&arr[i].weight,&arr[i].vual);        for(i = 0; i<n; i++)            for(j = m; j>=arr[i].weight; j--)                dp[j] = max(dp[j],dp[j-arr[i].weight]+arr[i].vual);        printf("%d\n",dp[m]);    }    return 0;}

    一次AC。有时候看英文的翻译，题目的意思会被曲解，英语不能落下。