01背包（打印路径） 之 uva 624

//  [7/21/2014 Sjm]
/*
此题直接根据01背包的求解思路，记录路径，再递归输出。。1A。。
注：
对于最后一个测试用例 43 2 也是满足题目要求的，输出它也是对的。
*/

#include <iostream>
#include <cstdlib>
#include <cstdio>
#include <algorithm>
#include <cstring>
using namespace std;
const int MAX_NUM = 25;
const int MAX_N = 100005;
struct node {
    int t_n; // 得到它前面那个所取节点的位置
    bool Judge;  // 判断当前节点是否被选择
};
int N, num;
int dp[MAX_NUM][MAX_N], arr[MAX_NUM];
node vis[MAX_NUM][MAX_N];

void output(int mynum, int myN, int sum) {
    if (sum == 0) {
        return;
    }
    if (vis[mynum][myN].Judge) {
        output(mynum - 1, vis[mynum][myN].t_n, sum - arr[mynum]);
        printf("%d ", arr[mynum]);
    }
    else {
        output(mynum - 1, myN, sum);
    }
}

void Solve() {
    for (int i = 1; i <= num; ++i) {
        for (int k = 0; k < arr[i]; ++k) {
            dp[i][k] = dp[i - 1][k];
        }
        for (int j = arr[i]; j <= N; ++j) {
            if (dp[i - 1][j - arr[i]] + arr[i] > dp[i - 1][j]) {
                dp[i][j] = dp[i - 1][j - arr[i]] + arr[i];
                vis[i][j].Judge = true;
                vis[i][j].t_n = j - arr[i];
            }
            else { dp[i][j] = dp[i - 1][j]; }
        }
    }

    int start;
    for (start = num; start >= 0; --start) {
        if (vis[start][N].Judge) {
            break;
        }
    }
    output(start, N, dp[start][N]);

    printf("sum:%d
", dp[num][N]);
}

int main()
{
    //freopen("input.txt", "r", stdin);
    while (~scanf("%d %d", &N, &num)) {
        for (int i = 0; i <= num; ++i) {
            for (int j = 0; j <= N; ++j) {
                dp[i][j] = 0;
                vis[i][j].Judge = false;
                vis[i][j].t_n = -1;
            }
        }
        for (int i = 1; i <= num; ++i) {
            scanf("%d", &arr[i]);
        }
        Solve();
    }
    return 0;
}