Best Sightseeing Pair

Description

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:

1. 2 <= A.length <= 50000
2. 1 <= A[i] <= 1000

Solution(javascript)

/** 暴力解法 O(n^2)
 * @param {number[]} A
 * @return {number}
 */
// const maxScoreSightseeingPair = function (A = []) {
//   let max = -Infinity
//   for (let i = 0; i < A.length; i++) {
//     for (let j = i + 1; j < A.length; j++) {
//       max = Math.max(
//         max,
//         A[i] + A[j] + i - j,
//       )
//     }
//   }
//   return max
// }

// O(n) 解法，存储最大的 A[i] + i
const maxScoreSightseeingPair = function (A = []) {
  let max = A[0] + 0
  let result = -Infinity
  for (let i = 1; i < A.length; i++) {
    result = Math.max(result, max + A[i] - i)
    max = Math.max(A[i] + i, max)
  }
  return result
}