TOJ 10008 a^b mod c

題目鏈接 : TOJ10008

10008 - a^b mod c

Time Limit: 1000MS
Memory Limit: 65536KB

Description
The calculation of a^b mod c arises in many fields of computer science, this time we brought it to you, can you prove us your talent?


Input
Three integers, a, b, c. (1<=a,b,c<=2³¹-1)



Output
One integer, the result of a^b mod c.


Sample Input
3 7 15



Sample Output
12



Hint

• The operator mod is defined as calculating the reminder of a divides b. For example, 5 mod 1 = 0, 5 mod 2 = 1, 5 mod 3 = 2, 5 mod 4 = 1, 5 mod 5 = 0, 5 mod 6 = 5, 5 mod 7 = 5, 5 mod 8 = 5, etc.
  
• The operator mod has following properties:
  
  • (a + b) mod c = ((a mod c) + b) mod c
    
  • (a - b) mod c = ((a mod c) - b) mod c
    
  • (a * b) mod c = ((a mod c) * b) mod c
    
  • It is obvious that (a + b) mod c = ((a mod c) + (b mod c)) mod c, and etc.

 

簡單的快速冪

 

#include<cstdio>


int pow_mod(int a,int b,int c)
{
	long long d=1,e=a%c;
	while(b)
	{
		if(b%2) d=(d*e)%c;
		b/=2;
		e=(e*e)%c;
	}
	return d;
}
int main()
{
	int a,b,c;
	scanf("%d%d%d",&a,&b,&c);
	printf("%d\n",pow_mod(a,b,c));
	return 0;
}