dp背包价值过大的求解，结果关键在“优化”

A Bank plans to install a machine for cash withdrawal. The machine is able to deliver appropriate @ bills for a requested cash amount. The machine uses exactly N distinct bill denominations, say Dk, k=1,N, and for each denomination Dk the machine has a supply of nk bills. For example,

N=3, n1=10, D1=100, n2=4, D2=50, n3=5, D3=10

means the machine has a supply of 10 bills of @100 each, 4 bills of @50 each, and 5 bills of @10 each.

Call cash the requested amount of cash the machine should deliver and write a program that computes the maximum amount of cash less than or equal to cash that can be effectively delivered according to the available bill supply of the machine.

Notes:
@ is the symbol of the currency delivered by the machine. For instance, @ may stand for dollar, euro, pound etc.

Input

The program input is from standard input. Each data set in the input stands for a particular transaction and has the format:

cash N n1 D1 n2 D2 ... nN DN

where 0 <= cash <= 100000 is the amount of cash requested, 0 <=N <= 10 is the number of bill denominations and 0 <= nk <= 1000 is the number of available bills for the Dk denomination, 1 <= Dk <= 1000, k=1,N. White spaces can occur freely between the numbers in the input. The input data are correct.

Output

For each set of data the program prints the result to the standard output on a separate line as shown in the examples below.

Sample Input

735 3  4 125  6 5  3 350633 4  500 30  6 100  1 5  0 1735 00 3  10 100  10 50  10 10

Sample Output

73563000

这道题中的价值太大，解法就是01背包或者完全背包，但是需要优化！

因为其中在每次循环中，对于大于现阶段的最大能获得的值的dp数组是不用扫过的，因为它们全为0，即使扫过一遍也无法更新其他值，于是在第二个循环用ans代替了cash

结果就顺利ac

贴下代码：

#include <stdio.h>#include <iostream>#include <cstring>#include <stdlib.h>#include <algorithm>#include <queue>#include <math.h>#define INF 1e8using namespace std;//FILE *fp;int n,cash;struct P{    int val,vol;}s[15];int dp[100005];int ans;int main(void){    //fp=fopen("123.txt","r");    while (scanf("%d %d",&cash,&n)!=EOF)    {        for (int i = 0;i < n;i++)            scanf("%d %d",&s[i].vol,&s[i].val);        memset(dp,0,sizeof(dp));        dp[0]=1;        ans = 0;        for (int i = 0;i < n;i++)        {            for (int j = ans;j >=0 ;j--)            {                if(dp[j])                {                    for (int k = 1;k <= s[i].vol;k++)                    {                        if(j+k*s[i].val<=cash&&dp[j+k*s[i].val]!=1)                        {                            dp[j+k*s[i].val]=1;                            ans=max(j+k*s[i].val,ans);                        }                    }                }            }        }        cout<<ans<<endl;    }    return 0;}

cheer up！！！