ORIGIN

String HDU-6572

2019-11-11

String

Problem Description

Avin has a string. He would like to uniform-randomly select four characters (selecting the same character is allowed) from it. You are asked to calculate the probability of the four characters being ”avin” in order.

Input

The first line contains n (1 ≤ n ≤ 100), the length of the string. The second line contains the string. To simplify the problem, the characters of the string are from ’a’, ’v’, ’i’, ’n’.

Output

Print the reduced fraction (the greatest common divisor of the numerator and denominator is 1), representing the probability. If the answer is 0, you should output “0/1”.

Sample Input

4
avin
4
aaaa

Sample Output

1
2

1/256
0/1

Analysis

Because of selecting the same character is allowed, so the probability of one character is
$$
P_{a_i}=\frac{1}{a.length}
$$
And if there are more than one ‘a’ or ‘v’ or so on, like n ‘a’, the probability is
$$
P_{‘a’}=\frac{n}{a.length}
$$

Code

#include<bits/stdc++.h>

using namespace std;
map<char,int> num;
int main() {
	int n;
	string s;
	cin >> n >> s;
	for(int i = 0; i < n; i ++){
		num[s[i]] ++;
	}
	int ga = __gcd(num['a'], n);
	int gv = __gcd(num['v'], n);
	int gi = __gcd(num['i'], n);
	int gn = __gcd(num['n'], n);
	int na = n / ga; num['a'] /= ga;
	int nv = n / gv; num['v'] /= gv;
	int ni = n / gi; num['i'] /= gi;
	int nn = n / gn; num['n'] /= gn;
	int son = num['a'] * num['v'] * num['i'] * num['n'];
	int fa = na * nv * ni * nn;
	int g = __gcd(son, fa);
	cout << son / g << '/' << fa / g << endl;
	return 0;
}