【BZOJ】2038: [2009国家集训队]小Z的袜子(hose)（组合计数+概率+莫队算法+分块）

#include <cstdio>
#include <cstring>
#include <cmath>
#include <string>
#include <iostream>
#include <algorithm>
#include <queue>
#include <set>
#include <map>
using namespace std;
typedef unsigned int ll;
#define rep(i, n) for(int i=0; i<(n); ++i)
#define for1(i,a,n) for(int i=(a);i<=(n);++i)
#define for2(i,a,n) for(int i=(a);i<(n);++i)
#define for3(i,a,n) for(int i=(a);i>=(n);--i)
#define for4(i,a,n) for(int i=(a);i>(n);--i)
#define CC(i,a) memset(i,a,sizeof(i))
#define read(a) a=getint()
#define print(a) printf("%d", a)
#define dbg(x) cout << (#x) << " = " << (x) << endl
#define error(x) (!(x)?puts("error"):0)
#define rdm(x, i) for(int i=ihead[x]; i; i=e[i].next)
inline const int getint() { int r=0, k=1; char c=getchar(); for(; c<‘0‘||c>‘9‘; c=getchar()) if(c==‘-‘) k=-1; for(; c>=‘0‘&&c<=‘9‘; c=getchar()) r=r*10+c-‘0‘; return k*r; }

const int N=50005;
struct dat { int l, r, id; }q[N];
int a[N], n, m, blc[N];
ll sum, x[N], y[N], s[N];

inline ll gcd(const ll &a, const ll &b) { return b?gcd(b, a%b):a; }
inline bool cmp(const dat &a, const dat &b) { return blc[a.l]==blc[b.l]?a.r<b.r:a.l<b.l; }
inline void fix(const int &x, const int &f) {
	sum-=s[x]*s[x];
	s[x]+=f;
	sum+=s[x]*s[x];
}
void init() {
	int sz=sqrt(0.5+n), now=0, tot=0;
	for1(i, 1, n) {
		++now;
		blc[i]=tot;
		if(now==sz) now=0, ++tot;
	}
	sort(q+1, q+1+m, cmp);
}
int main() {
	read(n); read(m);
	for1(i, 1, n) read(a[i]);
	for1(i, 1, m) read(q[i].l), read(q[i].r), q[i].id=i;
	init();
	int l=q[1].l, r=q[1].r;
	for1(i, l, r) fix(a[i], 1);
	x[q[1].id]=sum-(r-l+1);
	y[q[1].id]=(r-l+1)*(r-l);
	for1(i, 2, m) {
		int xl=q[i].l, xr=q[i].r, id=q[i].id;
		ll rg=(xr-xl+1);
		while(l<xl) fix(a[l++], -1);
		while(l>xl) fix(a[--l], 1);
		while(r<xr) fix(a[++r], 1);
		while(r>xr) fix(a[r--], -1);
		x[id]=sum-rg;
		y[id]=rg*(rg-1);
	}
	for1(i, 1, m) { if(x[i]<=0 || y[i]<=0) { puts("0/1"); continue; } ll g=gcd(x[i], y[i]); printf("%u/%u\n", x[i]/g, y[i]/g); }
	return 0;
}