added a problem on kadane's algo and its solution.

dynamic_programming/max_product_subarray.py

@@ -0,0 +1,33 @@
+def max_product_subarray(nums: list[int]) -> int:
+    """
+    Returns the maximum product that can be obtained by multiplying a
+    contiguous subarray of the given integer list `nums`.
+
+    Example:
+    >>> max_product_subarray([2, 3, -2, 4])
+    6
+    >>> max_product_subarray([-2, 0, -1])
+    0
+    >>> max_product_subarray([2, 3, -2, 4, -1])
+    48
+    """
+    n = len(nums)
+
+    if n == 0:
+        return 0
+
+    max_till_now = nums[0]
+    min_till_now = nums[0]
+    max_prod = nums[0]
+
+    for i in range(1, n):
+        # update the maximum and minimum subarray products
+        if nums[i] < 0:
+            max_till_now, min_till_now = min_till_now, max_till_now
+        max_till_now = max(nums[i], max_till_now * nums[i])
+        min_till_now = min(nums[i], min_till_now * nums[i])
+
+        # update the maximum product found till now
+        max_prod = max(max_prod, max_till_now)
+
+    return max_prod