KthMissingPositiveNumber.java

/* https://leetcode.com/problems/kth-missing-positive-number/description/ */
/*
1539. Kth Missing Positive Number

Given an array arr of positive integers sorted in a strictly increasing order, and an integer k.

Return the kth positive integer that is missing from this array.

Example 1:
Input: arr = [2,3,4,7,11], k = 5
Output: 9
Explanation: The missing positive integers are [1,5,6,8,9,10,12,13,...]. The 5th missing positive integer is 9.

Example 2:
Input: arr = [1,2,3,4], k = 2
Output: 6
Explanation: The missing positive integers are [5,6,7,...]. The 2nd missing positive integer is 6.
 
Constraints:
1 <= arr.length <= 1000
1 <= arr[i] <= 1000
1 <= k <= 1000
arr[i] < arr[j] for 1 <= i < j <= arr.length
*/

class KthMissingPositiveNumber {
    public int findKthPositive(int[] arr, int k) {
    int l = 0;
    int r = arr.length;

    // Find the first index l s.t. nMissing(l) = A[l] - l - 1 >= k
    while (l < r) {
      final int m = (l + r) / 2;
      if (arr[m] - m - 1 >= k)
        r = m;
      else
        l = m + 1;
    }

    // The k-th missing positive
    // = A[l - 1] + k - nMissing(l - 1)
    // = A[l - 1] + k - (A[l - 1] - (l - 1) - 1)
    // = A[l - 1] + k - (A[l - 1] - l)
    // = l + k
    return l + k;
    }
}