hdu 4777 树状数组+合数分解

Rabbit Kingdom

Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 1999    Accepted Submission(s): 689

Problem Description

　　Long long ago, there was an ancient rabbit kingdom in the forest. Every rabbit in this kingdom was not cute but totally pugnacious, so the kingdom was in chaos in season and out of season.
　　n rabbits were numbered form 1 to n. All rabbits' weight is an integer. For some unknown reason, two rabbits would fight each other if and only if their weight is NOT co-prime.
　　Now the king had arranged the n rabbits in a line ordered by their numbers. The king planned to send some rabbits into prison. He wanted to know that, if he sent all rabbits between the i-th one and the j-th one(including the i-th one and the j-th one) into
prison, how many rabbits in the prison would not fight with others.
　　Please note that a rabbit would not fight with himself.

 

Input

　　The input consists of several test cases.
　　The first line of each test case contains two integer n, m, indicating the number of rabbits and the queries.
　　The following line contains n integers, and the i-th integer W_i indicates the weight of the i-th rabbit.
　　Then m lines follow. Each line represents a query. It contains two integers L and R, meaning the king wanted to ask about the situation that if he sent all rabbits from the L-th one to the R-th one into prison.
　　(1 <= n, m, W_i <= 200000, 1 <= L <= R <= n)
　　The input ends with n = 0 and m = 0.

 

Output

　　For every query, output one line indicating the answer.

/*
hdu 4777 树状数组+合数分解

给你n个数，然后是q个询问，每次[l,r]中与区间内其它所有数互质的数的个数

感觉有点像查找区间内不同数的个数，于是用了l[i]表示左边最近与它不互质的数的
位置，本来想到是只要有互质的 就表为1，但是区间查询出现了问题(与i不互质的
l[i]如果不在区间内，i仍然被标记为1，- -2了)。

当遇到i时，只有当l[i]也在区间中的时候才能算，所以在l[i]上加1。当遇到r[i]时，就算没有l[i]
i也有r[i],所有l[i]减1，i上加1.
至于r[i]本身，已经被加到l[r[i]]上去了

所以大致思路就是：
先处理出l[i]和r[i](可以考虑求出质因子然后判断).
然后把查询按照r的从小到大排序，有点像往后递推的感觉
最后按照上面的思路求出区间[l,r]中不与其它互质的个数，再减去即可

//表示一直没看懂别人的报告(主要是不理解为什么这样插入删除)，这还是偶然间想通的QAQ

hhh-2016-03-06 14:01:51
*/
#include <algorithm>
#include <cmath>
#include <queue>
#include <iostream>
#include <cstring>
#include <map>
#include <cstdio>
#include <vector>
#include <functional>
#define lson (i<<1)
#define rson ((i<<1)|1)
using namespace std;
typedef long long ll;
const int maxn = 200050;
int vis[maxn];
const int inf = 0x3f3f3f3f;
int prime[maxn+1],factor[maxn],s[maxn];
int n,q;
void get_prime()
{
    memset(prime,0,sizeof(prime));
    for(int i =2 ; i <= maxn; i++)
    {
        if(!prime[i])
            prime[++prime[0]] = i;
        for(int j = 1; j <= prime[0] && prime[j] <= maxn/i; j++)
        {
            prime[i*prime[j]] = 1;
            if(i % prime[j] == 0)break;
        }
    }
}
int facnt;
int getFactor(int x)
{
    facnt = 0;
    int tmp = x;
    for(int i = 1; prime[i] <= tmp/prime[i]; i++)
    {
        if(tmp % prime[i] == 0)
        {
            factor[facnt]= prime[i];
            while(tmp%prime[i] == 0)
            {
                tmp/=prime[i];
            }
            facnt ++;
        }
    }
    if(tmp != 1)
    {
        factor[facnt++] = tmp;
    }
}

int lowbit(int x)
{
    return x&(-x);
}

void add(int x,int val)
{
    if(x == 0) return ;
    while(x <= n)
    {
        s[x] += val;
        x += lowbit(x);
    }
}

int sum(int x)
{
    int cnt = 0;
    while(x)
    {
        cnt += s[x];
        x -= lowbit(x);
    }
    return cnt;
}

int t[maxn];
int l[maxn],r[maxn];
int ans[maxn],a[maxn];

struct node
{
    int l,r;
    int id;
} opr[maxn];

bool cmp(node a,node b)
{
    return a.r < b.r;
}
vector<int>c[maxn];
int main()
{
    int T;
    int cas = 1;
    get_prime();
    while(scanf("%d%d",&n,&q) != EOF)
    {
        memset(s,0,sizeof(s));

        if(n == 0 && q == 0)
            break;
        for(int i =1; i <= n; i++)
            scanf("%d",&a[i]);

        for(int i =1; i <= q; i++)
        {
            scanf("%d%d",&opr[i].l,&opr[i].r);
            opr[i].id = i;
        }

        memset(t,0,sizeof(t));
        for(int i =1; i <= n; i++)
        {
            l[i] = 0;
            getFactor(a[i]);
            for(int j = 0; j < facnt; j++)
            {
                l[i] = max(l[i],t[factor[j]]);
                t[factor[j]] = i;
            }
        }
        for(int i =0 ; i < maxn; i++) t[i] = n+1;
        for(int i =n; i >= 1 ; i--)
        {
            r[i] = n+1;
            getFactor(a[i]);
            for(int j = 0; j < facnt; j++)
            {
                r[i] = min(r[i],t[factor[j]]);
                t[factor[j]] = i;
            }
        }
        for(int i = 0; i <= n+2; i++)
        {
            c[i].clear();
        }
        for(int i = 1; i <= n; i++)
            c[r[i]].push_back(i);
        //memset(vis,0,sizeof(vis));

        sort(opr+1,opr+q+1,cmp);
        for(int i = 1,k = 1; i <= q; i++)
        {
            while(k <= n && k <= opr[i].r)
            {
                add(l[k],1);
                for(int o = 0; o < c[k].size(); o++)
                {
                    int v = c[k][o];
                    add(v,1);
                    add(l[v],-1);
                }
                k++;
            }
            ans[opr[i].id] = opr[i].r-opr[i].l+1-(sum(opr[i].r)-sum(opr[i].l-1));
        }
        for(int i =1; i <= q; i++)
        {
            printf("%d\n",ans[i]);
        }
    }
    return 0;
}

/*
input:
3 2
2 1 4
1 2
1 3
6 4
3 6 1 2 5 3
1 3
4 6
4 4
2 6
0 0

output:
2
1
1
3
1
2
*/