LeetCode 1964: Find the Longest Valid Obstacle Course at Each Position Solution

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1964. Find the Longest Valid Obstacle Course at Each Position

Hard

Array Binary Search Binary Indexed Tree

Problem Explanation

Explanation:

To solve this problem, we can use a dynamic programming approach. We will iterate through the obstacles and for each obstacle, we will find the longest increasing subsequence of obstacles up to that point. We will store the lengths of the longest obstacle courses ending at each position in an array. At each position, we will consider the current obstacle and check how it can be added to the longest increasing subsequence ending at the previous obstacles.

We will iterate through the obstacles from left to right.
For each obstacle, we will find the longest increasing subsequence ending at that obstacle.
We will update the length of the longest increasing subsequence ending at the current obstacle.
Finally, we will return the array containing the lengths of the longest obstacle courses ending at each position.

Time Complexity: O(n^2) Space Complexity: O(n)

Solution Code

public int[] longestObstacleCourseAtEachPosition(int[] obstacles) {
    int n = obstacles.length;
    int[] dp = new int[n];
    Arrays.fill(dp, 1);
    
    for (int i = 1; i < n; i++) {
        for (int j = 0; j < i; j++) {
            if (obstacles[i] >= obstacles[j]) {
                dp[i] = Math.max(dp[i], dp[j] + 1);
            }
        }
    }
    
    return dp;
}

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