best_sightseeing_pair.py

"""
1014. Best Sightseeing Pair

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
"""

# V0

# V1
# https://github.com/azl397985856/leetcode/blob/master/problems/1014.best-sightseeing-pair.md
class Solution:
    def maxScoreSightseeingPair(self, A: List[int]) -> int:
        n = len(A)
        pre = A[0] + 0
        res = 0
        for i in range(1, n):
            res = max(res, pre + A[i] - i)
            pre = max(pre, A[i] + i)
        return res

# V1'
# https://github.com/azl397985856/leetcode/blob/master/problems/1014.best-sightseeing-pair.md
class Solution:
    def maxScoreSightseeingPair(self, A: List[int]) -> int:
        n = len(A)
        pre = A[0] + 0
        res = 0
        for i in range(1, n):
            # res = max(res, pre + A[i] - i)
            # pre = max(pre, A[i] + i)
            res = res if res > pre + A[i] - i else pre + A[i] - i
            pre = pre if pre > A[i] + i else A[i] + i
        return res

# V2