feat(heap): max subsequence score

puzzles/heap/maximum_subsequence_score/README.md

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+# Maximum Subsequence Score
+
+You are given two 0-indexed integer arrays nums1 and nums2 of equal length n and a positive integer k. You must choose a
+subsequence of indices from nums1 of length k.
+
+For chosen indices i0, i1, ..., ik - 1, your score is defined as:
+
+The sum of the selected elements from nums1 multiplied with the minimum of the selected elements from nums2.
+It can be defined simply as: (nums1[i0] + nums1[i1] +...+ nums1[ik - 1]) * min(nums2[i0] , nums2[i1], ...
+,nums2[ik - 1]).
+Return the maximum possible score.
+
+A subsequence of indices of an array is a set that can be derived from the set {0, 1, ..., n-1} by deleting some or no
+elements.
+
+```plain
+Example 1:
+
+Input: nums1 = [1,3,3,2], nums2 = [2,1,3,4], k = 3
+Output: 12
+Explanation: 
+The four possible subsequence scores are:
+- We choose the indices 0, 1, and 2 with score = (1+3+3) * min(2,1,3) = 7.
+- We choose the indices 0, 1, and 3 with score = (1+3+2) * min(2,1,4) = 6. 
+- We choose the indices 0, 2, and 3 with score = (1+3+2) * min(2,3,4) = 12. 
+- We choose the indices 1, 2, and 3 with score = (3+3+2) * min(1,3,4) = 8.
+Therefore, we return the max score, which is 12.
+Example 2:
+
+Input: nums1 = [4,2,3,1,1], nums2 = [7,5,10,9,6], k = 1
+Output: 30
+Explanation: 
+Choosing index 2 is optimal: nums1[2] * nums2[2] = 3 * 10 = 30 is the maximum possible score.
+```
+
+## Related Topics
+
+- Array
+- Greedy
+- Sorting
+- Heap (Priority Queue)

puzzles/heap/maximum_subsequence_score/__init__.py

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+from typing import List
+from heapq import heappush, heappop
+from operator import itemgetter
+
+
+def max_score(nums1: List[int], nums2: List[int], k: int) -> int:
+    result, total_sum, min_heap = 0, 0, []
+    merged = sorted(list(zip(nums1, nums2)), key=itemgetter(1), reverse=True)
+
+    for num_1_value, max_of_2 in merged:
+        total_sum += num_1_value
+        heappush(min_heap, num_1_value)
+        if len(min_heap) == k:
+            result = max(result, total_sum * max_of_2)
+            total_sum -= heappop(min_heap)
+
+    return result

puzzles/heap/maximum_subsequence_score/test_max_subsequence_score.py

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+import unittest
+
+from . import max_score
+
+
+class MaxSubsequenceScoreTestCase(unittest.TestCase):
+    def test_1(self):
+        """nums1 = [1,3,3,2], nums2 = [2,1,3,4], k = 3 returns 12"""
+        nums1 = [1, 3, 3, 2]
+        nums2 = [2, 1, 3, 4]
+        k = 3
+        expected = 12
+        actual = max_score(nums1, nums2, k)
+        self.assertEqual(expected, actual)
+
+    def test_2(self):
+        """nums1 = [4,2,3,1,1], nums2 = [7,5,10,9,6], k = 1 returns 30"""
+        nums1 = [4, 2, 3, 1, 1]
+        nums2 = [7, 5, 10, 9, 6]
+        k = 1
+        expected = 30
+        actual = max_score(nums1, nums2, k)
+        self.assertEqual(expected, actual)
+
+
+if __name__ == '__main__':
+    unittest.main()