HDU - 5666 Segment （大数位运算）好题

HDU
- 5666

Segment

Submit Status

Description

Silen
August does not like to talk with others.She like to find some interesting problems.

Today
she finds an interesting problem.She finds a segment .The
segment intersect the axis and produce a delta.She links some line between  and
the node on the segment whose coordinate are integers.

Please
calculate how many nodes are in the delta and not on the segments,output answer mod P.

Input

First
line has a number,T,means testcase number.

Then,each
line has two integers q,P.

 is
a prime number,and 

Output

Output
1 number to each testcase,answer mod P.

Sample Input

1
2 107 

Sample Output

0 

Source

BestCoder Round #80

//题意：方程x+y=q;

告诉你q，然你求这条直线在第一象限有多少个整数坐标，在直线上的不算。

//思路：

很容易找出规律[(q-2)*(q-1)/2]%p,但是因为数太大，所以在大数取余时得用一个技巧，就是把其中一个大数化小，再逐个相乘取余。

#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<iostream>
#define ll __int64
using namespace std;
ll p_mod(ll q1,ll q2,ll p)
{
	ll sum=0;
	while(q2)
	{
		if(q2&1)
		{
			sum+=q1;
			sum%=p;
		}
		q1<<=1;
		q1%=p;
		q2>>=1;
	}
	return sum;
}
int main()
{
	int t,n,m;
	ll p,q;
	ll q1,q2,pp;
	int i,j,k;
	scanf("%d",&t);
	while(t--)
	{
		scanf("%lld%lld",&q,&p);
		q1=q-1;q2=q-2;
		if(q1&1)
			q2>>=1;
		else
			q1>>=1;
		printf("%lld\n",p_mod(q1,q2,p));
	}
	return 0;
}