UVa 116 单向TSP（多段图最短路）

https://cn.vjudge.net/problem/UVA-116

题意：给出m行n列的整数矩阵，从第一列任何一个位置出发每次往右，右上或右下走一格，最终到达最后一列，要求经过的整数之和最小。

#include<iostream> 
#include<algorithm>
using namespace std;

const int INF = 0x7FFFFFFF;
const int maxn = 1000 + 5;

int m, n;
int a[maxn][maxn];
int dp[maxn][maxn];
int next[maxn][maxn];

int main()
{
    //freopen("D:\txt.txt", "r", stdin);
    while (cin >> m >> n && m && n)
    {
        for (int i = 0; i < m;i++)
        for (int j = 0; j < n; j++)
            cin >> a[i][j];
        int first = 0;
        int ans = INF;
        for (int j = n - 1; j >= 0; j--)
        {
            for (int i = 0; i < m; i++)
            {
                if (j == n - 1)  dp[i][j] = a[i][j];  //边界
                else
                {
                    dp[i][j] = INF;
                    int row[3] = { i, i + 1, i - 1 };
                    if (i == 0)       row[2] = m - 1;
                    if (i == m - 1)   row[1] = 0;
                    sort(row, row + 3);   //重新排序，以便找到字典序最小的
                    for (int k = 0; k < 3; k++)
                    {
                        int v = dp[row[k]][j + 1] + a[i][j];
                        if (v < dp[i][j])      { dp[i][j] = v; ::next[i][j] = row[k];}
                    }
                }
                if (j == 0 && dp[i][j] < ans)  {
                    ans = dp[i][j]; first = i;
                }
            }
        }
        cout << first + 1;
        for (int i = ::next[first][0], j = 1; j < n; i = ::next[i][j], j++)
            cout << " " << i + 1;
        cout << endl << ans << endl;
    }
    return 0;
}