背包问题及其变形

hdu 2546 

题目意思：食堂买菜，只要余额大于5圆就可以买任意的菜，问最少余额为多少。

思路：把5圆留着购买最贵的菜，其余的直接0-1背包即可，有点贪心的思想。

#include <iostream>
#include <cstdio>
#include <cstring>
#include<algorithm>
#define maxn 1010
#define INF 0x3ffffff
using namespace std;
int dp[maxn];
int n,m;
int w[maxn];
int main ()
{
    while(scanf("%d",&n),n)
    {
        for(int i=0;i<n;++i)scanf("%d",&w[i]);
        sort(w,w+n);
        scanf("%d",&m);
        if(m<5){printf("%d
",m);continue;}
        m-=5;
        for(int i=0;i<=m;++i)dp[i]=m;
        for(int i=n-2;i>=0;--i)
        {
            for(int j =m;j>=w[i];--j)
            {
                dp[j]=min(dp[j],dp[j-w[i]]-w[i]);
            }
        }
        int ans = INF;
        for(int i=0;i<=m;++i)ans = min(ans,dp[i]);
        printf("%d
",ans+5-w[n-1]);
    }
}

uva 624

0-1背包记录路径

#include <iostream>
#include <cstdio>
#include <cstring>
#define maxn 1010
using namespace std;
int dp[maxn];
int n,m;
int w[maxn];
int path[maxn][maxn];
int main ()
{
    while(scanf("%d%d",&m,&n)!=EOF)
    {
        for(int i=1; i<=n; ++i)scanf("%d",&w[i]);
        memset(dp,0,sizeof(dp));
        memset(path,0,sizeof(path));
        for(int i=n; i>=1;--i)
        {
            for(int j =m; j>=w[i]; --j)
            {
                if(dp[j-w[i]]+w[i]>dp[j])
                {
                    dp[j]=dp[j-w[i]]+w[i];
                    path[i][j]=1;
                }
            }
        }
        for(int i=1,j=m;i<=n;++i)
        {
            if(path[i][j]){printf("%d ",w[i]);j-=w[i];}
        }
        printf("sum:%d
",dp[m]);
    }
}

hdu 2126 

0-1 背包记录方案数

#include <iostream>
#include <cstdio>
#include <cstring>
#define maxn 5010
#include<algorithm>
using namespace std;
int dp[maxn];
int n,m;
int w[maxn];
int path[maxn];
int used[maxn];
int main ()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d%d",&n,&m);
        for(int i=1;i<=n;++i)scanf("%d",&w[i]);
        memset(dp,0,sizeof(dp));
        memset(path,0,sizeof(path));
        for(int i=0;i<=m;++i)path[i]=1;
        for(int i=1;i<=n;++i)
        {
            for(int j=m;j>=w[i];--j)
            {
                if(dp[j-w[i]]+1>dp[j])
                {
                    dp[j]=dp[j-w[i]]+1;
                    path[j]=path[j-w[i]];
                }
                else if(dp[j-w[i]]+1==dp[j])
                {
                    path[j]+=path[j-w[i]];
                }
            }
        }
        if(dp[m]==0){printf("Sorry, you can't buy anything.
");continue;}
        printf("You have %d selection(s) to buy with %d kind(s) of souvenirs.
",path[m],dp[m]);
    }
}