1014 Best Sightseeing Pair.py

Author: rajeevranjancom

1014 Best Sightseeing Pair.py

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+#!/usr/bin/python3
+"""
+Given an array A of positive integers, A[i] represents the value of the i-th
+sightseeing spot, and two sightseeing spots i and j have distance j - i between
+them.
+
+The score of a pair (i < j) of sightseeing spots is (A[i] + A[j] + i - j) : the
+sum of the values of the sightseeing spots, minus the distance between them.
+
+Return the maximum score of a pair of sightseeing spots.
+
+Example 1:
+
+Input: [8,1,5,2,6]
+Output: 11
+Explanation: i = 0, j = 2, A[i] + A[j] + i - j = 8 + 5 + 0 - 2 = 11
+
+
+Note:
+2 <= A.length <= 50000
+1 <= A[i] <= 1000
+"""
+from typing import List
+
+
+class Solution:
+    def maxScoreSightseeingPair(self, A: List[int]) -> int:
+        """
+        Attribute the result to the ending element
+
+        Count the current best score in all previous.
+        Distance will increase, then the score will decay
+        """
+        ret = -float("inf")
+        prev_max = A[0]
+        for a in A[1:]:
+            ret = max(ret, prev_max - 1 + a)
+            prev_max = max(prev_max - 1, a)
+
+        return ret
+
+    def maxScoreSightseeingPair_error(self, A: List[int]) -> int:
+        """
+        brute force O(N^2)
+
+        pre-processing, adjust A[i] as A[i] - i
+        error, no direction
+        """
+        n = len(A)
+        B = []
+        for i in range(n):
+            B.append(A[i] - i)
+
+        # find top 2
+        m1, m2 = None, None
+        for i in range(n):
+            if m1 is None:
+                m1 = i
+            elif m2 is None:
+                m2 = i
+            elif B[i] + (i - m1) > B[m1]:
+                m1 = i
+            elif B[i] + (i - m2) > B[m2]:
+                m2 = i
+        return A[m2] + A[m1] - abs(m2 - m1)
+
+
+if __name__ == "__main__":
+    assert Solution().maxScoreSightseeingPair([8,1,5,2,6]) == 11