GCD
Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 405 Accepted Submission(s): 172
Problem Description
The greatest common divisor GCD(a,b) of two positive integers a and b,sometimes written (a,b),is the largest divisor common to a and b,For example,(1,2)=1,(12,18)=6.
(a,b) can be easily found by the Euclidean algorithm. Now Carp is considering a little more difficult problem:
Given integers N and M, how many integer X satisfies 1<=X<=N and (X,N)>=M.
Input
The first line of input is an integer T(T<=100) representing the number of test cases. The following T lines each contains two numbers N and M (2<=N<=1000000000, 1<=M<=N), representing a test case.
Output
For each test case,output the answer on a single line.
Sample Input
Sample Output
题目大意: 给你N和M,求满足1<=X<=N,(X,N)>=M中 x的个数。
思路:要用到欧拉函数,还要算出N的约数,eular(N/约数)且约数>=M就是其中一个数的和。刚好就是,自己推一下就知道。
代码:
#include <iostream>
#include <stdio.h>
#include <algorithm>
using namespace std;
int a[100005];
int cnt;
int eular(int n)
{
int i, ans = n;
for(i = 2; i*i <= n; i++)
{
if(n%i == 0)
{
ans -= ans/i;
while(n%i == 0)
n /= i;
}
}
if(n > 1) ans -= ans/n;
return ans;
}
void init(int n) //找出n的约数并保存于数组a中
{
int i;
cnt = 0;
for(i = 1; i*i < n; i++)
{
if(n%i == 0)
{
a[cnt++] = i;
a[cnt++] = n/i;
}
}
if(n%i == 0) a[cnt++] = i;
sort(a, a+cnt);
}
int main()
{
int i, t, n, m, sum;
scanf("%d", &t);
while(t--)
{
scanf("%d %d", &n, &m);
init(n);
sum = 0;
for(i = 0; i < cnt; i++)
{
if(a[i] >= m)
{
sum += eular(n/a[i]); //总和就是各个eular(n/a[i])的和
}
}
printf("%d\n", sum);
}
return 0;
}
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