From 5c2d1fe725ff0281bb1b40efdc2f49461caf1475 Mon Sep 17 00:00:00 2001
From: jbsch <pari.ankana3112@gmail.com>
Date: Thu, 24 Oct 2024 22:06:42 +0530
Subject: [PATCH 1/3] added largest rectangle histogram function

---
 .../stacks/largest_rectangle_histogram.py     | 39 +++++++++++++++++++
 1 file changed, 39 insertions(+)
 create mode 100644 data_structures/stacks/largest_rectangle_histogram.py

diff --git a/data_structures/stacks/largest_rectangle_histogram.py b/data_structures/stacks/largest_rectangle_histogram.py
new file mode 100644
index 000000000..107fb41c4
--- /dev/null
+++ b/data_structures/stacks/largest_rectangle_histogram.py
@@ -0,0 +1,39 @@
+def largest_rectangle_area(heights: list[int]) -> int:
+    """
+    Given an array of integers representing the heights of bars,
+    this function returns the area of the largest rectangle that can be formed
+
+    >>> largest_rectangle_area([2, 1, 5, 6, 2, 3])
+    10
+
+    >>> largest_rectangle_area([2, 4])
+    4
+
+    >>> largest_rectangle_area([6, 2, 5, 4, 5, 1, 6])
+    12
+
+    >>> largest_rectangle_area([1])
+    1
+    """
+    stack: list[int] = []
+    max_area = 0
+    heights = [*heights, 0]  # make a new list by appending the sentinel 0
+    n = len(heights)
+
+    for i in range(n):
+        # make sure the stack remains in increasing order
+        while stack and heights[i] < heights[stack[-1]]:
+            h = heights[stack.pop()]  # height of the bar
+            # if stack is empty, it means entire width can be taken from index 0 to i-1
+            w = i if not stack else i - stack[-1] - 1  # calculate width
+            max_area = max(max_area, h * w)
+
+        stack.append(i)
+
+    return max_area
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()

From 50d5bb1af3cfcf45ae7912b3912f76eb74021f18 Mon Sep 17 00:00:00 2001
From: jbsch <pari.ankana3112@gmail.com>
Date: Thu, 24 Oct 2024 22:13:23 +0530
Subject: [PATCH 2/3] added largest rectangle histogram function

---
 data_structures/stacks/largest_rectangle_histogram.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/data_structures/stacks/largest_rectangle_histogram.py b/data_structures/stacks/largest_rectangle_histogram.py
index 107fb41c4..7575bd9f6 100644
--- a/data_structures/stacks/largest_rectangle_histogram.py
+++ b/data_structures/stacks/largest_rectangle_histogram.py
@@ -1,7 +1,7 @@
 def largest_rectangle_area(heights: list[int]) -> int:
     """
-    Given an array of integers representing the heights of bars,
-    this function returns the area of the largest rectangle that can be formed
+    Inputs an array of integers representing the heights of bars,
+    and returns the area of the largest rectangle that can be formed
 
     >>> largest_rectangle_area([2, 1, 5, 6, 2, 3])
     10

From bfb816781110a87245858e1e7c7313b10c96dbd8 Mon Sep 17 00:00:00 2001
From: jbsch <pari.ankana3112@gmail.com>
Date: Thu, 24 Oct 2024 22:39:56 +0530
Subject: [PATCH 3/3] added kadane's algo

---
 data_structures/arrays/kadanes_algorithm.py | 42 +++++++++++++++++++++
 1 file changed, 42 insertions(+)
 create mode 100644 data_structures/arrays/kadanes_algorithm.py

diff --git a/data_structures/arrays/kadanes_algorithm.py b/data_structures/arrays/kadanes_algorithm.py
new file mode 100644
index 000000000..5ab2b1fd1
--- /dev/null
+++ b/data_structures/arrays/kadanes_algorithm.py
@@ -0,0 +1,42 @@
+# Kadane's algorithm
+
+
+def kadanes_algorithm(arr: list[int]) -> int:
+    """
+    Function to find the maximum sum of a contiguous subarray using Kadane's algorithm
+
+    >>> kadanes_algorithm([-2, 1, -3, 4, -1, 2, 1, -5, 4])
+    6
+
+    >>> kadanes_algorithm([-1, -2, -3, -4])
+    -1
+
+    >>> kadanes_algorithm([5, 4, -1, 7, 8])
+    23
+
+    >>> kadanes_algorithm([1])
+    1
+
+    >>> kadanes_algorithm([-1, 2, 3, -5, 4])
+    5
+    """
+    # initializing variables
+    max_current = arr[0]  # store the current max sum
+    max_global = arr[0]  # store the global max sum
+
+    # looping through the array starting at the second element
+    for i in range(1, len(arr)):
+        # update current max sum by choosing the maximum between
+        # current element alone or current element plus previous max
+        max_current = max(arr[i], max_current + arr[i])
+
+        # update global max sum if current max is larger
+        max_global = max(max_current, max_global)
+
+    return max_global
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()