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g1401_1500.s1499_max_value_of_equation.readme.md Maven / Gradle / Ivy

1499\. Max Value of Equation

Hard

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

Return _the maximum value of the equation_ yi + yj + |xi - xj| where |xi - xj| <= k and `1 <= i < j <= points.length`.

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

**Example 1:**

**Input:** points = [[1,3],[2,0],[5,10],[6,-10]], k = 1

**Output:** 4

**Explanation:** The first two points satisfy the condition |xi - xj| <= 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

**Explanation:** 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 <= 105
*   `points[i].length == 2`
*   -108 <= xi, yi <= 108
*   0 <= k <= 2 * 108
*   xi < xj for all `1 <= i < j <= points.length`
*   xi form a strictly increasing sequence.