HDU 5145 NPY and girls（组合+莫队）

Posted 2020-09-24 mfmdaoyou

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pid=5145">【HDU 5145】 NPY and girls（组合+莫队）

NPY and girls

Time Limit: 8000/4000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 593    Accepted Submission(s): 179

Problem Description

NPY‘s girlfriend blew him out!His honey doesn‘t love him any more!However, he has so many girlfriend candidates.Because there are too many girls and for the convenience of management, NPY numbered the girls from 1 to n.These girls are in different classes(some girls may be in the same class).And the i-th girl is in class ai.NPY wants to visit his girls frequently.Each time he visits some girls numbered consecutively from L to R in some order. He can only visit one girl every time he goes into a classroom,otherwise the girls may fight with each other(-_-!).And he can visit the class in any order.
Here comes the problem,(NPY doesn‘t want to learn how to use excavator),he wonders how many different ways there can be in which he can visit his girls.The different ways are different means he visits these classrooms in different order.

 

Input

The first line contains the number of test cases T(1≤T≤10).
For each test case,there are two integers n,m(0<n,m≤30000) in the first line.N is the number of girls,and M is the number of times that NPY want to visit his girls.
The following single line contains N integers, a1,a2,a3,…,an, which indicates the class number of each girl. (0<ai≤30000)
The following m lines,each line contains two integers l,r(1≤l≤r≤n),which indicates the interval NPY wants to visit.

 

Output

For each visit,print how many ways can NPY visit his girls.Because the ans may be too large,print the ans mod 1000000007.

 

Sample Input

2
4 2
1 2 1 3
1 3
1 4
1 1
1
1 1

 

Sample Output

3
12
1

 

Source

BestCoder Round #22

 

Recommend

heyang

 

题目大意：T组输入

每组两个数 n m分别表示人数n和询问次数m

之后n个数 表示n个女孩所在教室

对于m次询问 每次一个[L,R]（1 <= L <= R <= n） 问为了訪问到每一个女孩 訪问教室的方案有几种（会出现几个女孩在一个教室的情况 但每次訪问教室仅仅能找一个女孩 同一个编号的教室是同样的）

对于单组询问[L,R] 如果有n中班级 每一个班级有c个女生 总共m个女生 那么答案就是C(m,c1)*C(m-c1,c2)*C(m-c1-c2,c3)*....*C(cn,cn)

但假设每次都暴力的进行统计然后求组合数 果果的会超时

这样就要用莫队 把区间n进行分块 分成n/sqrt(n)份 进行分块排序

然后按分好的顺序进行区间的扩大或缩小 这样能够发现对组合数的求解也能够在区间转换的过程中进行

由于C(m+1,n+1) = C(m,n)*(m+1/n+1)

相同的 C(m,n) = C(m+1,n+1)*(n+1/m+1) （对于缩小的过程而言）

这样 因为n和m的范围都在30000之内 并且要求最后对一个大素数取余 能够用费马小定理高速求出范围内全部数的逆元

然后就像上面说的对区间进行转换 然后离线处理存储答案 最后输出就可以 记得答案要存在排序前的位置中。。。由于这个WA找了好久错误=.=

代码例如以下：

#include <iostream>
#include <cmath>
#include <vector>
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <queue>
#include <stack>
#include <list>
#include <algorithm>
#include <map>
#include <set>
#define LL long long
#define Pr pair<int,int>
#define fread() freopen("in.in","r",stdin)
#define fwrite() freopen("out.out","w",stdout)

using namespace std;
const int INF = 0x3f3f3f3f;
const int msz = 10000;
const LL mod = 1e9+7;
const double eps = 1e-8;

LL pow_m(LL a,LL b)
{
	LL ans = 1;
	while(b)
	{
		if(b&1) ans = (ans*a)%mod;
		b >>= 1;
		a = (a*a)%mod;
	}
	return ans;
}

LL Inv(LL a)
{
	return pow_m(a,mod-2);
}

int per;
struct Range
{
	int l,r,id;
	bool operator < (const struct Range a)const
	{
		return l/per == a.l/per?
 r < a.r: l/per < a.l/per;
	}
};

Range rg[30030];
LL ans[30030];
LL inv[30030];
int cla[30030];
int cnt[30030];

int main()
{
	//fread();
	//fwrite();

	for(int i = 1; i <= 30000; ++i)
		inv[i] = Inv(i);

	int t,n,q;

	scanf("%d",&t);
	while(t--)
	{
		scanf("%d%d",&n,&q);
		per = sqrt(n*1.0);

		for(int i = 1; i <= n; ++i)
			scanf("%d",&cla[i]);

		for(int i = 0; i < q; ++i)
		{
			scanf("%d%d",&rg[i].l,&rg[i].r);
			rg[i].id = i;
		}

		sort(rg,rg+q);

		int l = 1, r = 0;
		LL tmp = 1;
		memset(cnt,0,sizeof(cnt));
		for(int i = 0; i < q; ++i)
		{
			while(r < rg[i].r)
			{
				++r;
				cnt[cla[r]]++;
				tmp = tmp*(r-l+1)%mod*inv[cnt[cla[r]]]%mod;
			}
			while(l > rg[i].l)
			{
				--l;
				cnt[cla[l]]++;
				tmp = tmp*(r-l+1)%mod*inv[cnt[cla[l]]]%mod;
			}

			while(r > rg[i].r)
			{
				tmp = tmp*cnt[cla[r]]%mod*inv[r-l+1]%mod;
				cnt[cla[r]]--;
				--r;
			}

			while(l < rg[i].l)
			{
				tmp = tmp*cnt[cla[l]]%mod*inv[r-l+1]%mod;
				cnt[cla[l]]--;
				++l;
			}
			ans[rg[i].id] = tmp;
		}
		for(int i = 0; i < q; ++i)
			printf("%I64d\n",ans[i]);

	}

	return 0;
}