【luogu P1494 [国家集训队]小Z的袜子】 题解

题目链接：https://www.luogu.org/problemnew/show/P1494

#include <cstdio>
#include <algorithm>
#include <iostream>
#include <cmath>
using namespace std;
const int maxn =  50000+10;
inline long long read()
{
    long long k=0;
    char c;
    c=getchar();
    while(!isdigit(c))c=getchar();
    while(isdigit(c)){k=(k<<3)+(k<<1)+c-'0';c=getchar();}
    return k;
}
long long n, m, bl, answer, curL = 1, curR = 0, cnt[maxn], a[maxn], gg;

struct query{
	long long p, l, r;
}e[maxn];

struct answers{
	long long x, y;
}ans[maxn], now;

long long gcd(long long x, long long y)
{
	if(x%y == 0) return y;
	else return gcd(y,x%y);
}

bool cmp(query a, query b)
{
	return (a.l/bl) == (b.l/bl) ? a.r < b.r : a.l < b.l;
}

void add(long long pos)
{
	cnt[a[pos]]++;
	if(cnt[a[pos]] > 1)
	now.x = now.x + cnt[a[pos]]*(cnt[a[pos]]-1)-(cnt[a[pos]]-1)*(cnt[a[pos]]-2);

}

void remove(long long pos)
{
	cnt[a[pos]]--;
	if(cnt[a[pos]] > 0)
	now.x = now.x + cnt[a[pos]]*(cnt[a[pos]]-1)-(cnt[a[pos]]+1)*cnt[a[pos]];
}

int main()
{
	n = read(); m = read();

	bl = sqrt(n);

	for(long long i = 1; i <= n; i++)
	a[i] = read();

	for(long long i = 1; i <= m; i++)
	{
		e[i].l = read(); e[i].r = read(); e[i].p = i;
	}

	sort(e+1,e+1+m,cmp);

	for(long long i = 1; i <= m; i++)
	{
		long long L = e[i].l, R = e[i].r;
		while(curL < L)
			remove(curL++);
		while(curL > L)
			add(--curL);
		while(curR < R)
			add(++curR);
		while(curR > R)
			remove(curR--);
		now.y = (e[i].r-e[i].l+1)*(e[i].r-e[i].l);
		if (!now.x)
		{
			now.x=0;
			now.y=1;
		}
		gg = gcd(now.x, now.y);
		ans[e[i].p].x = now.x/gg;
		ans[e[i].p].y = now.y/gg;
	}
	for(long long i = 1; i <= m; i++)
	printf("%lld/%lld\n",ans[i].x,ans[i].y);
	return 0;
}