题解 | #毕业旅行问题#

import java.util.*;
public class Main {
    private static int N;
    private static int[][] price;

    private static boolean[] visited;
    private static int result = Integer.MAX_VALUE;

    public static int[][] dp;

    public static void main(String[] args){
        Scanner in = new Scanner(System.in);

        while(in.hasNext()){
            solution1(in);
            // solution2(in);
        }
    }
    
    /**
     * 动态规划: 状态压缩
     *
     * dp[i][V]: 代表从i城市出发, 经过V中所有节点, 再回到北京的最低费用.
     * dp[i][V] = min(Price(i,k) + dp[k][V']) for k in V, V'=V-k
     * 
     * @param in
     */
    private static void solution1(Scanner in){
        N = in.nextInt();
        price = new int[N+1][N+1];
        for(int i=0; i<N; i++){
            for(int j=0; j<N; j++){
                price[i][j] = in.nextInt();
            }
        }

        // 对1进行左移n-1位 值等于2^(N-1)
        int V = 1 << (N-1);
        dp = new int[N][V];
        // 初始化
        for (int i=0; i<N; i++) {
            for(int j=0; j<V; j++) {
                dp[i][j] = -1;
            }
        }
        // 2^3 - 1 = 7 -> (二进制111) -> 节点321
        // 从0城市(北京)出发, 经过V中所有节点(城市123), 再回到北京的最低费用.
        int ans = travel1(0 , V-1);
        System.out.println(ans);
    }

    /**
     * DFS
     * @param curr
     * @param cities
     * @return
     */
    public static int travel1(int curr, int cities) {
        if(cities == 0){
            return price[curr][0];
        }

        // 命中返回
        if(dp[curr][cities] != -1){
            return dp[curr][cities];
        }

        int ans = Integer.MAX_VALUE;
        for(int k=1; k<N; k++){
            // i节点在V中
            if(((cities>>(k-1)) & 1) == 1){
                // 异或 去掉i节点
                cities ^= (1<<(k-1));
                // 记录该轮的最小答案
                ans = Math.min(ans, price[curr][k]+travel1(k, cities));
                // 异或 恢复i节点
                cities ^= (1<<(k-1));
            }
        }

        dp[curr][cities] = ans;
        return ans;
    }


    /**
     * DFS: 超时
     * @param in
     */
    private static void solution2(Scanner in){
        N = in.nextInt();
        visited = new boolean[N+1];
        price = new int[N+1][N+1];
        for(int i=1; i<=N; i++){
            for(int j=1; j<=N; j++){
                price[i][j] = in.nextInt();
            }
        }

        travel2(0, 0, 1);

        System.out.println(result);
    }

    private static void travel2(int cities, int total, int curr){
        if(cities==N && curr==1){
            result = Math.min(result, total);
        }

        for(int i=1; i<=N; i++){
            if(i!=curr && !visited[i]){
                visited[i] = true;

                travel2(cities+1, total+price[curr][i], i);

                visited[i] = false;
            }
        }
    }
}