added 0069_sqrt.py

Author: nyierr

problems/easy/0069_sqrt.py

@@ -0,0 +1,52 @@
+"""
+Given a non-negative integer x, compute and return the
+square root of x.
+
+Since the return type is an integer, the decimal digits
+are truncated, and only the integer part of the result
+is returned.
+
+Note: You are not allowed to use any built-in exponent
+function or operator, such as pow(x, 0.5) or x ** 0.5.
+
+Example 1:
+  Input: x = 4
+  Output: 2
+
+Example 2:
+  Input: x = 8
+  Output: 2
+  Explanation: The square root of 8 is 2.82842..., and
+  since the decimal part is truncated, 2 is returned. 
+
+Constraints:
+  * 0 <= x <= 2^31 - 1
+"""
+
+class Solution:   
+    # O(log n) solution using Newton's algorithm
+    #def mySqrt(self, x: int) -> int:
+    #    ap = x
+    #    
+    #    while abs(x - ap * ap) >= 1:
+    #        ap = (ap + (x / ap)) / 2
+    #
+    #    return int(ap)
+    
+    # O(log n) solution
+    def mySqrt(self, x: int) -> int:
+        half = x // 2
+        
+        while half * half > x:
+            half = half // 2
+            
+        if half * half == x:
+            return half
+                
+        while half * half < x: 
+            half += 1
+            
+        if half * half == x:
+            return half
+        
+        return half - 1