LeetCode Entry

1964. Find the Longest Valid Obstacle Course at Each Position

7.05.2023 hard 2023 kotlin

google what is the solution of LIS

1964. Find the Longest Valid Obstacle Course at Each Position hard

fun longestObstacleCourseAtEachPosition(obstacles: IntArray): IntArray {
    // 2 3 1 3
    // 2          2
    //   3        2 3
    //     1      1 3    (pos = 1)
    //       3    1 3 3

    // 5 2 5 4 1 1 1 5 3 1
    // 5       .             5
    //   2     .             2
    //     5   .             2 5
    //       4 .             2 4
    //         1             1 4 (pos = 1)
    //           1           1 1
    //             1         1 1 1
    //               5       1 1 1 5
    //                 3     1 1 1 3
    //                   1   1 1 1 1

    val lis = IntArray(obstacles.size)
    var end = 0
    return obstacles.map { x ->
        var pos = -1
        var lo = 0
        var hi = end - 1
        while (lo <= hi) {
            val mid = lo + (hi - lo) / 2
            if (lis[mid] > x) {
                hi = mid - 1
                pos = mid
            } else lo = mid + 1
        }
        if (pos == -1) {
            lis[end++] = x
            end
        } else {
            lis[pos] = x
            pos + 1
        }
    }.toIntArray()
}

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Intuition

This is the Longest Increasing Subsequence length problem, that have a classic algorithm, which must be learned and understood.

The trivial case of any increasing subsequence is broken by example: 2 3 1 3, when we consider the last 3 result must be: 233 instead of 13. So, we must track all the sequences.

To track all the sequences, we can use TreeMap that will hold the largest element and length of any subsequence. Adding a new element will take \(O(n^2)\).

The optimal LIS solution is to keep the largest increasing subsequence so far and cleverly add new elements:

1. for a new element, search for the smallest element that is larger than it
2. if found, replace
3. if not, append

Approach

• google what is the solution of LIS
• use an array for lis
• carefully write binary search

  Complexity

• Time complexity: \(O(nlog(n))\)
• Space complexity: \(O(n)\)