HDOJ 5381 The sum of gcd 莫队算法

Posted 2020-09-17 gavanwanggw

大神题解:

http://blog.csdn.net/u014800748/article/details/47680899

The sum of gcd

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/65536 K (Java/Others)
Total Submission(s): 526    Accepted Submission(s): 226

Problem Description

You have an array ,the length of  is 
Let 

 

Input

There are multiple test cases. The first line of input contains an integer T, indicating the number of test cases. For each test case:
First line has one integers 
Second line has  integers 
Third line has one integers ,the number of questions
Next there are Q lines,each line has two integers ,

 

Output

For each question,you need to print 

 

Sample Input

2
5
1 2 3 4 5
3
1 3
2 3
1 4
4
4 2 6 9
3
1 3
2 4
2 3

 

Sample Output

9
6
16
18
23
10

 

Author

SXYZ

 

Source

2015 Multi-University Training Contest 8

 

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>

using namespace std;

const int maxn=10100;
typedef long long int LL;

struct G
{
    G(){}
    G(int _id,LL _g):id(_id),g(_g){}

    int id;
	LL g;

	void toString()
	{
		printf("id: %d g: %lld\n",id,g);
	}
};

int n,a[maxn],Q;
vector<G> VL[maxn],VR[maxn];
struct Que
{
    int L,R,id;
    bool operator<(const Que& que) const
    {
        if(L!=que.L) return L<que.L;
        return R<que.R;
    }
}que[maxn];

void PreInit()
{
    /// get Left Point
    /// 以i为右端点,预处理出左边的段
    for(int i=1;i<=n;i++)
    {
        VL[i].clear();
        if(i==1)
        {
            VL[i].push_back(G(i,a[i]));
        }
        else
        {
			LL curg=a[i];int L=i;
			for(auto &it : VL[i-1])
			{
				int g=__gcd(it.g,curg);
				if(g!=curg) VL[i].push_back(G(L,curg));
				curg=g; L=it.id;
			}
			VL[i].push_back(G(L,curg));
        }
    }
    /// get Right Point
    /// 以i为左端点,预处理出右边的段
	for(int i=n;i>=1;i--)
	{
		VR[i].clear();
		if(i==n)
		{
			VR[i].push_back(G(i,a[i]));
		}
		else
		{
			LL curg=a[i];int R=i;
			for(auto &it : VR[i+1])
			{
				int g=__gcd(curg,it.g);
				if(g!=curg) VR[i].push_back(G(R,curg));
				curg=g; R=it.id;
			}
			VR[i].push_back(G(R,curg));
		}
	}
}

/// 计算L,R之间的值
LL calu(int type,int L,int R)
{
	LL ret=0;
	if(type==0)
	{
		int tr=R;
		for(auto &it : VL[R])
		{
			if(it.id>=L)
			{
				ret+=(tr-it.id+1)*it.g;
				tr=it.id-1;
			}
			else
			{
				ret+=(tr-L+1)*it.g;
				break;
			}
		}
	}
	else if(type==1)
	{
		int tr=L;
		for(auto &it : VR[L])
		{
			if(it.id<=R)
			{
				ret+=(it.id-tr+1)*it.g;
				tr=it.id+1;
			}
			else
			{
				ret+=(R-tr+1)*it.g;
				break;
			}
		}
	}
	return ret;
}

LL ans[maxn];

int main()
{
	int T_T;
	scanf("%d",&T_T);
    while(T_T--)
    {
        scanf("%d",&n);
        for(int i=1;i<=n;i++)
            scanf("%d",a+i);
        PreInit();

		scanf("%d",&Q);
        for(int i=0,l,r;i<Q;i++)
        {
            scanf("%d%d",&l,&r);
            que[i].L=l; que[i].R=r; que[i].id=i;
        }
        sort(que,que+Q);

		int L=1,R=0; LL ret=0;
		for(int i=0;i<Q;i++)
		{
			while(R<que[i].R)
			{
				R++;
				ret+=calu(0,L,R);
			}
			while(R>que[i].R)
			{
				ret-=calu(0,L,R);
				R--;
			}
			while(L<que[i].L)
			{
				ret-=calu(1,L,R);
				L++;
			}
			while(L>que[i].L)
			{
				L--;
				ret+=calu(1,L,R);
			}
			ans[que[i].id]=ret;
		}

		for(int i=0;i<Q;i++)
			cout<<ans[i]<<endl;
    }
    return 0;
}