From 839c7e56c4915c24220089caba1e46de2edc4474 Mon Sep 17 00:00:00 2001
From: Kyle Lobo <kylelobo11898@gmail.com>
Date: Sat, 25 May 2019 11:30:31 +0530
Subject: [PATCH] Added explanation for O(logn) solution in "Exponentiation"
 (#28807)

---
 guide/english/algorithms/exponentiation/index.md | 10 +++++++++-
 1 file changed, 9 insertions(+), 1 deletion(-)

diff --git a/guide/english/algorithms/exponentiation/index.md b/guide/english/algorithms/exponentiation/index.md
index c32ca84488..32f9dc63e8 100644
--- a/guide/english/algorithms/exponentiation/index.md
+++ b/guide/english/algorithms/exponentiation/index.md
@@ -35,6 +35,14 @@ int power(int x, unsigned int y) {
         return x*temp*temp; 
 } 
 ```
+Why is this faster?
+
+Suppose we have x = 5, y = 4, we know that our answer is going to be (5 * 5 * 5 * 5). 
+
+If we break this down, we notice that we can write (5 * 5 * 5 * 5) as (5 * 5) * 2 and further, we can write (5 * 5) as 5 * 2.
+
+Through this observation, we can optimize our function to O(log n) by calculating power(x, y/2) only once and storing it. 
+
 
 ## Modular Exponentiation
 
@@ -49,7 +57,7 @@ int power(int x, unsigned int y, int p) {
             res = (res*x) % p; 
   
         // y must be even now 
-        y = y>>1; 
+        y = y >> 1; 
         x = (x*x) % p;   
     } 
     return res;