From 6f468c4c98bf72f386944bb3a09dbed45e9f0408 Mon Sep 17 00:00:00 2001
From: ktkovachev <143198904+ktkovachev@users.noreply.github.com>
Date: Mon, 8 Apr 2024 16:56:16 +0100
Subject: [PATCH] Solve 69. Sqrt(x)

---
 python/69_sqrtx.py | 12 ++++++++++++
 1 file changed, 12 insertions(+)
 create mode 100644 python/69_sqrtx.py

diff --git a/python/69_sqrtx.py b/python/69_sqrtx.py
new file mode 100644
index 0000000..6db86e1
--- /dev/null
+++ b/python/69_sqrtx.py
@@ -0,0 +1,12 @@
+class Solution:
+    def mySqrt(self, x: int) -> int:
+        # Use Newton-Raphson iteration
+        # y**2 - x = 0 = f(y)
+        # f'(y) = 2y
+        # y = y - (y**2 - x)/(2y)
+        y = 1
+        close_enough = False
+        while not close_enough:
+            y -= (y*y-x)/(2*y)
+            close_enough = y*y - x <= 0.1 and (y+1)*(y+1) > x
+        return floor(y)