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Delete binary_exponentiation.java

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Chinmoy Das 2017-10-08 12:58:59 +05:30 committed by GitHub
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/**
* Binary Exponentiation
* This is a method to find a^b in a time complexity of O(log b)
* This is one of the most commonly used methods of finding powers.
* Also useful in cases where solution to (a^b)%c is required,
* where a,b,c can be numbers over the computers calculation limits.
*/
/**
* @author chinmoy159
* @version 1.0 dated 10/08/2017
*/
public class bin_expo
{
/**
* function :- b_expo (int a, int b)
* returns a^b
*/
public static int b_expo(int a, int b)
{
/*
* iterative solution
*/
int res;
for (res = 1; b > 0; a *=a, b >>= 1) {
if ((b&1) == 1) {
res *= a;
}
}
return res;
/*
* recursive solution
if (b == 0) {
return 1;
}
if (b == 1) {
return a;
}
if ((b & 1) == 1) {
return a * b_expo(a*a, b >> 1);
} else {
return b_expo (a*a, b >> 1);
}
*/
}
/**
* function :- b_expo (long a, long b, long c)
* return (a^b)%c
*/
public static long b_expo(long a, long b, long c)
{
/*
* iterative solution
*/
long res;
for (res = 1l; b > 0; a *=a, b >>= 1) {
if ((b&1) == 1) {
res = ((res%c) * (a%c)) % c;
}
}
return res;
/*
* recursive solution
if (b == 0) {
return 1;
}
if (b == 1) {
return a;
}
if ((b & 1) == 1) {
return ((a%c) * (b_expo(a*a, b >> 1)%c))%c;
} else {
return b_expo (a*a, b >> 1)%c;
}
*/
}
}