binary exponentiation

other/binary_exponentiation.java

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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;
+        }
+        */
+    }
+}