2546 饭卡（01背包，挺好的）

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题目地址：http://acm.hdu.edu.cn/showproblem.php?pid=2546

思路：刚开始直接把背包的容量搞为m-5+max1（max1的值为最贵的菜的价格），因为他最多的能花这么多，结果错了，应该把最大的单独提出来，用5块来买,剩下的钱做背包

AC代码：

#include <iostream>#include <cstdio>#include <cstdlib>#include <algorithm>#include <queue>#include <stack>#include <map>#include <cstring>#include <climits>#include <cmath>#include <cctype>const int inf = 0x3f3f3f3f;//1061109567typedef long long LL;#define lson l,m,rt<<1#define rson m+1,r,rt<<1|1using namespace std;int dp[1000];int a[1010];int main(){    int n;    while(scanf("%d",&n) && n)    {        memset(dp,0,sizeof(dp));        int max1 = -1;        int k;        for(int i=1; i<=n; i++)        {            scanf("%d",&a[i]);            if(a[i] > max1)            {                max1 = a[i];                k = i;            }        }        int x;        scanf("%d",&x);        if(x < 5)        {            printf("%d\n",x);            continue;        }        x -= 5;        for(int i=1; i<=n; i++)        {            if(i == k)                continue;            for(int j=x; j>=a[i]; j--)            {                dp[j] = max(dp[j],dp[j-a[i]] + a[i]);            }        }        printf("%d\n",x+5-dp[x]-max1);    }    return 0;}

错误代码：（这个会造成价值最大的有可能没有选，逻辑不对）

#include <iostream>#include <cstdio>#include <cstdlib>#include <algorithm>#include <queue>#include <stack>#include <map>#include <cstring>#include <climits>#include <cmath>#include <cctype>const int inf = 0x3f3f3f3f;//1061109567typedef long long LL;#define lson l,m,rt<<1#define rson m+1,r,rt<<1|1using namespace std;int dp[1060];int a[1010];int main(){    int n;    while(scanf("%d",&n) && n)    {        memset(dp,0,sizeof(dp));        int max1 = 0;        for(int i=1; i<=n; i++)        {             scanf("%d",&a[i]);             if(a[i] > max1)                max1 = a[i];        }        int cost;        scanf("%d",&cost);        int x = cost;        if(cost < 5)        {            printf("%d\n",cost);            continue;        }        cost = cost - 5 + max1;        for(int i=1; i<=n; i++)        {            for(int j=cost; j>=a[i]; j--)            {                dp[j] = max(dp[j],dp[j-a[i]]+a[i]);            }        }        printf("%d\n",x-dp[cost]);    }    return 0;}

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