678E - Another Sith Tournament - CodeForces Solution

#include <cstdlib>
#include <cctype>
#include <cstring>
#include <cstdio>
#include <cmath>
#include <algorithm>
#include <vector>
#include <string>
#include <iostream>
#include <sstream>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <fstream>
#include <numeric>
#include <iomanip>
#include <bitset>
#include <list>
#include <stdexcept>
#include <functional>
#include <utility>
#include <ctime>
#include <random>
#include <cassert>
using namespace std;
typedef long long LL;
typedef unsigned long long ULL;
#define MEM(a,b) memset((a),(b),sizeof(a))
const LL INF = 1e9 + 7;
const int N = 4e5 + 10;
double dp[N][20];
double p[20][20];
int main()
{
	//freopen("input.txt", "r", stdin);
	//freopen("output.txt", "w", stdout);
	int n;
	scanf("%d", &n);
	for (int i = 0; i < n; i++)
	{
		for (int j = 0; j < n; j++)
		{
			scanf("%lf", &p[i][j]);
		}
	}
	dp[1][0] = 1;
	int tot = 1 << n;
	int mask = tot - 1;
	for (int o = 1; o < tot; o++)
	{
		for (int i = 0; i < n; i++)
		{
			if (o >> i & 1)
			{
				for (int j = 0; j < n; j++)
				{
					if (i == j) continue;
					if (o >> j & 1)
					{
						dp[o][i] = max(dp[o][i],
							dp[1 << i ^ o][j] * p[j][i] + dp[1 << j ^ o][i] * p[i][j]);
					}
				}
			}
		}
	}
	double ans = 0;
	for (int i = 0; i < n; i++)
		ans = max(ans, dp[mask][i]);
	printf("%.15f\n", ans);
	return 0;
}