integer replace

Author: jackzhenguo

BitManipulation/BitManipulation/IntegerReplacement.cs

@@ -0,0 +1,37 @@
+namespace BitManipulation
+{
+// Given a positive integer n and you can do operations as follow:
+
+// If n is even, replace n with n/2. 
+// If n is odd, you can replace n with either n + 1 or n - 1. 
+// What is the minimum number of replacements needed for n to become 1?
+    public class Solution
+    {
+		// Following coding refers to 
+		// A couple of Java solutions with explanations 
+		// But it has a bug of overflowing and I fix it.
+		public int IntegerReplacement(int n) {
+			int cnt = 0;
+			long bign = (long)n; //n = Int32.MaxValue(2147483647),adds 1 and would overflow
+			while (bign != 1) {
+			if ((bign & 1) == 0) { //even number
+				bign >>= 1;
+			  } 
+			  //It is enough to examine the last two digits to figure out 
+			  //whether incrementing or decrementing will give more 1's. Indeed, 
+			  //if a number ends with 01, 
+			  //then certainly decrementing is the way to go. Otherwise, if it ends with 11, 
+			  //then certainly incrementing is at least as good as decrementing (*011 -> *010 / *100) or
+			  // even better (if there are three or more 1's).
+			  else if (bign == 3|| ((bign >> 1) & 1) == 0) { //*01
+				--bign;
+			  }
+			  else { //*11
+				++bign;
+			}
+			++cnt;
+		   } 
+		   return cnt;
+		}
+    }
+}