Package g1401_1500.s1499_max_value_of_equation

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    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 <code>pointsi = x<sub>i</sub>, y<sub>i</sub></code> such that <code>x<sub>i</sub>< x<sub>j</sub></code> for all 1 &lt;= i &lt; j &lt;= points.length. You are also given an integer k.

    Return the maximum value of the equation <code>y<sub>i</sub> + y<sub>j</sub> + |x<sub>i</sub> - x<sub>j</sub>|</code> where <code>|x<sub>i</sub> - x<sub>j</sub>| <= k</code> and 1 &lt;= i &lt; j &lt;= points.length.

    It is guaranteed that there exists at least one pair of points that satisfy the constraint <code>|x<sub>i</sub> - x<sub>j</sub>| <= k</code>.

    Example 1:

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

    Output: 4

    Explanation: The first two points satisfy the condition |x<sub>i</sub> - x<sub>j</sub>| <= 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:

    • <code>2 <= points.length <= 10<sup>5</sup></code>

    • points[i].length == 2

    • <code>-10<sup>8</sup><= x<sub>i</sub>, y<sub>i</sub><= 10<sup>8</sup></code>

    • <code>0 <= k <= 2 * 10<sup>8</sup></code>

    • <code>x<sub>i</sub>< x<sub>j</sub></code> for all 1 &lt;= i &lt; j &lt;= points.length

    • <code>x<sub>i</sub></code> form a strictly increasing sequence.

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Integer findMaxValueOfEquation(Array<IntArray> points, Integer k)

      • Methods inherited from class java.lang.Object

        clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait