UVa 103 Stacking Boxes --- DAG上的动态规划

/* UVa 103 Stacking Boxes --- DAG上的动态规划 */
#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

int n, m;    //n为结点数,m为维度(n <= 30, m <= 10)
int G[35][35];    //DAG, G[i][j]为1表示 盒子i可以嵌套在盒子j中
int vec[35][15];
int dp[35];

//判断x是否小于y
bool is_small(int x, int y){
    for (int i = 1; i <= m; ++i){
        //有一个大于等于则返回0
        if (vec[x][i] >= vec[y][i]){
            return 0;
        }
    }//for(i)
    return 1;
}

void CMAX(int&x, int y){
    if (y > x){
        x = y;
    }
}

int DP(int i){
    int &ans = dp[i];
    if (ans > 0){
        //记忆化搜索,避免重复计算
        return ans;
    }
    ans = 1;
    for (int j = 1; j <= n; ++j){
        if (G[i][j]){
            //递归求解
            CMAX(ans, DP(j) + 1);
        }
    }//for(j)
    return ans;
}

//输出序列
void print_ans(int i){
    if (dp[i] == 1){
        //最后一个节点了
        printf("%d", i);
    }
    else{
        for (int j = 1; j <= n; ++j){
            if (G[i][j] && dp[j] + 1 == dp[i]){
                printf("%d ", i);
                print_ans(j);
                break;
            }    
        }//for(j)    
    }
}

int main()
{
#ifdef _LOCAL
    freopen("D:\\input.txt", "r", stdin);
#endif
    while (scanf("%d%d", &n, &m) == 2){
        for (int i = 1; i <= n; ++i){
            for (int j = 1; j <= m; ++j){
                scanf("%d", vec[i] + j);
            }//for(j)
            sort(vec[i] + 1, vec[i] + m + 1);
        }//for(i)
        
        //建DAG
        memset(G, 0, sizeof G);
        for (int i = 1; i <= n; ++i){
            for (int j = 1; j <= n; ++j){
                //G[i][j]为1表示盒子i可以嵌套在盒子j中
                if (is_small(i, j)){
                    G[i][j] = 1;    
                }
            }//for(j)
        }//for(i)

        //求最长路径
        int ans = 0;
        int best;
        memset(dp, 0, sizeof dp);
        for (int i = 1; i <= n; ++i){
            if (DP(i) > ans){
                ans = dp[i];
                best = i;
            }
        }//for(i)
        printf("%d\n", ans);
        print_ans(best);
        printf("\n");
    }//while(scanf)

    return 0;
}