feat: implement greedy optimization for minimize product sum #1874

Author: Osamsami

exercises/1000_programs/medium/1874_minimize_product_sum.py

@@ -0,0 +1,28 @@
+def minProductSum(nums1, nums2):
+    """
+    Minimizes the product sum of two arrays of equal length.
+    
+    Approach:
+    To minimize the sum, we pair the largest elements of one array with 
+    the smallest elements of the other. This greedy strategy is a 
+    foundational concept in loss optimization and weight adjustment.
+    
+    Args:
+        nums1 (list[int]): First array of integers.
+        nums2 (list[int]): Second array of integers.
+        
+    Returns:
+        int: The minimum possible product sum.
+    """
+    # Sorting nums1 in ascending order (smallest to largest)
+    nums1.sort()
+    
+    # Sorting nums2 in descending order (largest to smallest)
+    nums2.sort(reverse=True)
+    
+    min_sum = 0
+    # Zip pairs the elements together for multiplication
+    for n1, n2 in zip(nums1, nums2):
+        min_sum += n1 * n2
+        
+    return min_sum