1499. Max Value of Equation

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.

Find 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 <= 10^5
  • points[i].length == 2
  • -10^8 <= points[i][0], points[i][1] <= 10^8
  • 0 <= k <= 2 * 10^8
  • points[i][0] < points[j][0] for all 1 <= i < j <= points.length
  • xi form a strictly increasing sequence.

Rust Solution

struct Solution;

use std::collections::VecDeque;

impl Solution {
    fn find_max_value_of_equation(points: Vec<Vec<i32>>, k: i32) -> i32 {
        let n = points.len();
        let mut queue: VecDeque<(i32, i32)> = VecDeque::new();
        let mut res = std::i32::MIN;
        for j in 0..n {
            let xj = points[j][0];
            let yj = points[j][1];
            while let Some(&(_, xi)) = queue.front() {
                if xi + k < xj {
                    queue.pop_front();
                } else {
                    break;
                }
            }
            if let Some(&(diff, _)) = queue.front() {
                res = res.max(diff + yj + xj);
            }
            while let Some(&(diff, xi)) = queue.back() {
                if (diff, xi) < (yj - xj, xj) {
                    queue.pop_back();
                } else {
                    break;
                }
            }
            queue.push_back((yj - xj, xj));
        }
        res
    }
}

#[test]
fn test() {
    let points = vec_vec_i32![[1, 3], [2, 0], [5, 10], [6, -10]];
    let k = 1;
    let res = 4;
    assert_eq!(Solution::find_max_value_of_equation(points, k), res);
    let points = vec_vec_i32![[0, 0], [3, 0], [9, 2]];
    let k = 3;
    let res = 3;
    assert_eq!(Solution::find_max_value_of_equation(points, k), res);
}

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