Max Value of Equation

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Problem Statement

You are given an array points containing the coordinates of points on a 2D plane, sorted by the x-values, where points[i] = [x _i , y _i ] such that x _i < x _j for all 1 <= i < j <= points.length . You are also given an integer k .

Return the maximum value of the equation y _i + y _j + |x _i - x _j | where |x _i - x _j | <= k and 1 <= i < j <= points.length .

It is guaranteed that there exists at least one pair of points that satisfy the constraint |x _i - x _j | <= k .

Examples

Example 1

Input: points = [[1,3],[2,0],[5,10],[6,-10]], k = 1
Output: 4
The first two points satisfy the condition |x _i - x _j | <= 1 and if we calculate the equation we get 3 + 0 + |1 - 2| = 4. Third and fourth points also satisfy the condition and give a value of 10 + -10 + |5 - 6| = 1.
No other pairs satisfy the condition, so we return the max of 4 and 1.

Example 2

Input: points = [[0,0],[3,0],[9,2]], k = 3
Output: 3
Only the first two points have an absolute difference of 3 or less in the x-values, and give the value of 0 + 0 + |0 - 3| = 3.

Constraints

2 <= points.length <= 10 ^5

points[i].length == 2

-10 ^8 <= x _i , y _i <= 10 ^8

0 <= k <= 2 * 10 ^8

x _i < x _j for all 1 <= i < j <= points.length

x _i form a strictly increasing sequence.

😤

Hard

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicQueue