Maximize Win From Two Segments
There are some prizes on the X-axis. You are given an integer array prizePositions that is sorted in non-decreasing order, where prizePositions[i] is the position of the i^th prize. There could be different prizes at the same position on the line. You are also given an integer k.
You are allowed to select two segments with integer endpoints. The length of each segment must be k. You will collect all prizes whose position falls within at least one of the two selected segments, including the endpoints of the segments. The two selected segments may intersect.
Return the maximum number of prizes you can win if you choose the two segments optimally.
Example 1
Input
prizePositions = [1,1,2,2,3,3,5], k = 2Output
7In this example, you can win all 7 prizes by selecting two segments [1, 3] and [3, 5].
Example 2
Input
prizePositions = [1,2,3,4], k = 0Output
2One choice for the segments is [3, 3] and [4, 4], which lets you get 2 prizes.
Constraints
- 1 <= prizePositions.length <= 10^5
- 1 <= prizePositions[i] <= 10^9
- 0 <= k <= 10^9
- prizePositions is sorted in non-decreasing order.