UVA116 Unidirectional TSP 单向TSP

分阶段的DAG，注意字典序的处理和路径的保存。

定义状态d[i][j]为从i,j 出发到最后一列的最小花费，转移的时候只有三种，向上，向下，或平移。

#include<bits/stdc++.h>
using namespace std;

const int maxm = 11;
const int maxn = 101;

int G[maxm][maxn];
const int INF = 1e9;
int d[maxm][maxn];
int path[maxn][maxn];

int main()
{
    //freopen("in.txt","r",stdin);
    int m,n;
    while(~scanf("%d%d",&m,&n)){
        for(int i = 0; i < m; i++)
        for(int j = 0; j < n ;j++){
            scanf("%d",G[i]+j);
        }
        int ans = INF,head = 0;
        for(int i = 0; i < m; i++) d[i][n-1] = G[i][n-1];
        if(n == 1){
            for(int i = 0; i < m; i++){
                if(d[i][0]<ans) { ans = d[i][0]; head = i; }
            }
        }else {
            for(int j = n-2; j >= 0; j--){
                for(int i = 0; i < m; i++){
                    int nxt[] = {i,i+1,i-1};
                    if(i == 0) nxt[2] = m-1;
                    if(i == m-1) nxt[1] = 0;
                    sort(nxt,nxt+3);
                    d[i][j] = d[nxt[0]][j+1];
                    path[i][j] = nxt[0];
                    for(int k = 1; k < 3; k++){
                        int t = d[nxt[k]][j+1];
                        if(t < d[i][j]){
                            d[i][j] = t; path[i][j] = nxt[k];
                        }
                    }
                    d[i][j] += G[i][j];
                    if(j == 0 && d[i][j] < ans) { ans = d[i][j]; head = i; }
                }
            }
        }

        printf("%d",head+1);
        for(int i = path[head][0],j = 1; j < n; i = path[i][j], j++){
            printf(" %d",i+1);
        }
        printf("
%d
",ans);
    }
    return 0;
}