You are given a 2D array of integers coordinates of length n and an integer k, where 0 <= k < n.
coordinates[i] = [xi, yi] indicates the point (xi, yi) in a 2D plane.
An increasing path of length m is defined as a list of points (x1, y1), (x2, y2), (x3, y3), ..., (xm, ym) such that:
xi < xi + 1 and yi < yi + 1 for all i where 1 <= i < m.(xi, yi) is in the given coordinates for all i where 1 <= i <= m.Return the maximum length of an increasing path that contains coordinates[k].
\n
Example 1:
\n\nInput: coordinates = [[3,1],[2,2],[4,1],[0,0],[5,3]], k = 1
\n\nOutput: 3
\n\nExplanation:
\n\n(0, 0), (2, 2), (5, 3) is the longest increasing path that contains (2, 2).
Example 2:
\n\nInput: coordinates = [[2,1],[7,0],[5,6]], k = 2
\n\nOutput: 2
\n\nExplanation:
\n\n(2, 1), (5, 6) is the longest increasing path that contains (5, 6).
\n
Constraints:
\n\n1 <= n == coordinates.length <= 105coordinates[i].length == 20 <= coordinates[i][0], coordinates[i][1] <= 109coordinates are distinct.0 <= k <= n - 1x and y being strictly less than coordinates[k].",
"Sort them by x’s, in the case of equal, the y values should be decreasing.",
"Calculate LIS only using y values.",
"Do the same for coordinates with both x and y being strictly larger than coordinates[k]."
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