Codeforces Round #388 (Div. 2)E Inversions After Shuffle

題目解法：

      好大一道數學題，看了半天什麼都不會觀摩了別的題解才勉強寫的：

      公式是：

代碼：

#include "iostream"
#include "cstdio"
#include "math.h"
#include "algorithm"
#include "string"
#include "string.h"
#include "vector"
#include "map"
#include "queue"
#include "bitset"
#include "set"
using namespace std;
int n;
long long a[100010], tree[100010];
void add(int x, long long y) {
	for (int i = x;i <= n;i += i&(-i))
		tree[i] += y;
}
long long get(int x) {
	long long ret = 0;
	for (int i = x;i;i -= i&(-i))
		ret += tree[i];
	return ret;
}
int main() {
	scanf("%d", &n);
	for (int i = 1;i <= n;i++)
		scanf("%lld", &a[i]);
	long long cnt = 0;
	for (int i = 1;i <= n;i++) {
		cnt += get(n) - get(a[i]);
		add(a[i], 1);
	}
	double ans = 0, now =0, pre = 0;
	for (int i = 1;i <= n;i++)
		ans += (n - i + 1)*((double)i*(i - 1) / 4 + cnt);
	memset(tree, 0, sizeof(tree));
	for (int i = 1;i <= n;i++) {
		now = get(n) - get(a[i]) + pre;
		ans -= now;
		pre = now;
		add(a[i], i);
	}
	ans /= (double)n*(n + 1) / 2;
	printf("%.10f\n", ans);
	return 0;
}