From b7cff04574f5288c0483040c11be3bcc2b396a32 Mon Sep 17 00:00:00 2001
From: wuminbin <wuminbin@yeah.net>
Date: Mon, 24 Jun 2019 18:11:07 +0800
Subject: [PATCH] better implementation for midpoint (#914)

---
 arithmetic_analysis/bisection.py | 4 ++--
 searches/binary_search.py        | 2 +-
 2 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/arithmetic_analysis/bisection.py b/arithmetic_analysis/bisection.py
index c81fa84f8..8bf3f0978 100644
--- a/arithmetic_analysis/bisection.py
+++ b/arithmetic_analysis/bisection.py
@@ -14,7 +14,7 @@ def bisection(function, a, b):  # finds where the function becomes 0 in [a,b] us
         print("couldn't find root in [a,b]")
         return
     else:
-        mid = (start + end) / 2
+        mid = start + (end - start) / 2.0
         while abs(start - mid) > 10**-7:  # until we achieve precise equals to 10^-7
             if function(mid) == 0:
                 return mid
@@ -22,7 +22,7 @@ def bisection(function, a, b):  # finds where the function becomes 0 in [a,b] us
                 end = mid
             else:
                 start = mid
-            mid = (start + end) / 2
+            mid = start + (end - start) / 2.0
         return mid
 
 
diff --git a/searches/binary_search.py b/searches/binary_search.py
index 1d5da9658..e658dac2a 100644
--- a/searches/binary_search.py
+++ b/searches/binary_search.py
@@ -45,7 +45,7 @@ def binary_search(sorted_collection, item):
     right = len(sorted_collection) - 1
 
     while left <= right:
-        midpoint = (left + right) // 2
+        midpoint = left + (right - left) // 2
         current_item = sorted_collection[midpoint]
         if current_item == item:
             return midpoint