状压TSP问题

TSP问题

从一个点出发经过所有的点回到这个点的最短路径

洛谷模板P1171

dp[i][j] 表示的是从起点出发到达 i 点, 且状态为 j 是的最小花费
答案取 \(min_{i = 1}^n(dp[i][(1<<n) - 1] + G[i][st])\)

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

const int N = 21;
int dp[N][(1 << 20) + 20];
int G[N][N];

int n;
int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; i++) {
		for (int j = 1; j <= n; j++) {
			scanf("%d", &G[i][j]);
		}
	}
	memset(dp, 0x3f, sizeof dp);
	dp[1][1] = 0;
	for (int i = 0; i < (1 << n); i++) {
		for (int j = 1; j <= n; j++) {
			if (i & (1 << (j - 1)))continue;
			for (int k = 1; k <= n; k++) {
				if (i & (1 << (k - 1)) == 0)continue;
				dp[j][i | (1 << (j - 1))] = min(dp[j][i | (1 << (j - 1))], dp[k][i] + G[k][j]);
			}
		}
	}
	int ans = 0x3f3f3f3f;
	for (int i = 1; i <= n; i++) {
		ans = min(ans, dp[i][(1 << n) - 1] + G[i][1]);
	}
	printf("%d\n", ans);
}

就可以解决牛客day2 的B题了