Rightmost Digit

最新推荐文章于 2018-10-26 20:31:00 发布

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Rightmost Digit

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 31938 Accepted Submission(s): 12240

Problem Description

Given a positive integer N, you should output the most right digit of N^N.

Input

The input contains several test cases. The first line of the input is a single integer T which is the number of test cases. T test cases follow.
Each test case contains a single positive integer N(1<=N<=1,000,000,000).

Output

For each test case, you should output the rightmost digit of N^N.

Sample Input

2
3
4

Sample Output

7
6

Hint

In the first case, 3 * 3 * 3 = 27, so the rightmost digit is 7.
In the second case, 4 * 4 * 4 * 4 = 256, so the rightmost digit is 6.

幂取模，利用分治法

例如a^29=(a^14)^2*a----->a^14=(a^7)^2----->a^7=(a^3)^2*a----->a^3=a^2*a;

<span style="font-size:18px;">#include <iostream>
#include<stdio.h>
#include<string.h>
#include<math.h>
using namespace std;
int fenzhi(int a,int n,int m)
{
    int k=1;
    while(n>0)
    {
        if(n%2==1)
        k=k*a%m;
        a=a*a;
        a%=m;
        n=n/2;
    }
    return k;
}
int main()
{
    int n,t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%d",&n);
        printf("%d\n",fenzhi(n%10,n,10));
    }
    return 0;
}</span>