From 83c104e839c158c3e84e567c38f5d30a4224e832 Mon Sep 17 00:00:00 2001
From: Du YuanChao <shellhub.me@gmail.com>
Date: Fri, 18 Oct 2019 12:20:36 +0800
Subject: [PATCH] Divide and Conquer (#1308)

Thanks for your persistence!
---
 maths/find_max_recursion.py | 25 +++++++++++++++++++++++++
 maths/find_min_recursion.py | 25 +++++++++++++++++++++++++
 2 files changed, 50 insertions(+)
 create mode 100644 maths/find_max_recursion.py
 create mode 100644 maths/find_min_recursion.py

diff --git a/maths/find_max_recursion.py b/maths/find_max_recursion.py
new file mode 100644
index 000000000..fc10ecf37
--- /dev/null
+++ b/maths/find_max_recursion.py
@@ -0,0 +1,25 @@
+# Divide and Conquer algorithm
+def find_max(nums, left, right):
+    """
+    find max value in list
+    :param nums: contains elements
+    :param left: index of first element
+    :param right: index of last element
+    :return: max in nums
+    
+    >>> nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
+    >>> find_max(nums, 0, len(nums) - 1) == max(nums)
+    True
+    """
+    if left == right:
+        return nums[left]
+    mid = (left + right) >> 1  # the middle
+    left_max = find_max(nums, left, mid)  # find max in range[left, mid]
+    right_max = find_max(nums, mid + 1, right)  # find max in range[mid + 1, right]
+
+    return left_max if left_max >= right_max else right_max
+
+
+if __name__ == "__main__":
+    nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
+    assert find_max(nums, 0, len(nums) - 1) == 10
diff --git a/maths/find_min_recursion.py b/maths/find_min_recursion.py
new file mode 100644
index 000000000..4488967cc
--- /dev/null
+++ b/maths/find_min_recursion.py
@@ -0,0 +1,25 @@
+# Divide and Conquer algorithm
+def find_min(nums, left, right):
+    """
+    find min value in list
+    :param nums: contains elements
+    :param left: index of first element
+    :param right: index of last element
+    :return: min in nums
+
+    >>> nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
+    >>> find_min(nums, 0, len(nums) - 1) == min(nums)
+    True
+    """
+    if left == right:
+        return nums[left]
+    mid = (left + right) >> 1  # the middle
+    left_min = find_min(nums, left, mid)  # find min in range[left, mid]
+    right_min = find_min(nums, mid + 1, right)  # find min in range[mid + 1, right]
+
+    return left_min if left_min <= right_min else right_min
+
+
+if __name__ == "__main__":
+    nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
+    assert find_min(nums, 0, len(nums) - 1) == 1