Max subarray sum

Author: ratulb

codes/max_sum_sub_array.mojo

@@ -0,0 +1,33 @@
+# Given an integer array nums, find the subarray with the largest sum, and return its sum.
+
+
+# Function to find the subarray with the maximum sum
+fn max_sum_sub_array(nums: List[Int]) -> Int:
+    # If the list is empty, return 0 as no subarray exists
+    if len(nums) == 0:
+        return 0
+
+    # Initialize the running sum and max sum with the first element
+    # running_sum: current subarray sum being tracked
+    # max_sum: maximum subarray sum seen so far
+    running_sum, max_sum = nums[0], nums[0]
+
+    # Iterate over the list starting from the second element
+    for idx in range(1, len(nums)):
+        # Decide whether to extend the previous subarray or start a new subarray at current index
+        running_sum = max(running_sum + nums[idx], nums[idx])
+
+        # Update max_sum if the current running_sum is greater
+        max_sum = max(max_sum, running_sum)
+
+    # Return the maximum subarray sum found
+    return max_sum
+
+
+def main():
+    nums = List(-2, 1, -3, 4, -1, 2, 1, -5, 4)
+    max_sum = max_sum_sub_array(nums)
+    debug_assert(max_sum == 6, "Assertion failed")
+    nums = List(5,4,-1,7,8)
+    max_sum = max_sum_sub_array(nums)
+    debug_assert(max_sum == 23, "Assertion failed")

docs/index.md

@@ -6,3 +6,4 @@
 - [ Buy and Sell Stock 2](buy_and_sell_stock_2.md) ➔ Maximize profit by buying and selling multiple times.
 - [ Longest Substring Without Repeating Characters](longest_substr_no_char_repeats.md) ➔ Given a string s, find the length of the longest substring without duplicate characters.
 - [ Product of Array Except Self](product_of_array_except_self.md) ➔ Return an array where each element is the product of all others in the input array.
+- [ Maximum Subarray](max_sum_sub_array.md) ➔ Given an integer array nums, find the subarray with the largest sum, and return its sum.

docs/max_sum_sub_array.md

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+### Given an integer array nums, find the subarray with the largest sum, and return its sum.
+
+### Kadane’s Algorithm: At each step, you decide whether to include the current number in the previous subarray (i.e., running_sum + nums[idx]) or start a new subarray from the current number (nums[idx]).
+
+### It maintains the maximum sum seen so far and runs in O(n) time with O(1) space.
+
+# Function to find the subarray with the maximum sum
+fn max_sum_sub_array(nums: List[Int]) -> Int:
+    # If the list is empty, return 0 as no subarray exists
+    if len(nums) == 0:
+        return 0
+
+    # Initialize the running sum and max sum with the first element
+    # running_sum: current subarray sum being tracked
+    # max_sum: maximum subarray sum seen so far
+    running_sum, max_sum = nums[0], nums[0]
+
+    # Iterate over the list starting from the second element
+    for idx in range(1, len(nums)):
+        # Decide whether to extend the previous subarray or start a new subarray at current index
+        running_sum = max(running_sum + nums[idx], nums[idx])
+
+        # Update max_sum if the current running_sum is greater
+        max_sum = max(max_sum, running_sum)
+
+    return max_sum
+
+def main():
+    nums = List(-2, 1, -3, 4, -1, 2, 1, -5, 4)
+    max_sum = max_sum_sub_array(nums)
+    debug_assert(max_sum == 6, "Assertion failed")
+    nums = List(5,4,-1,7,8)
+    max_sum = max_sum_sub_array(nums)
+    debug_assert(max_sum == 23, "Assertion failed")