LeetCode #1539 — EASY

Kth Missing Positive Number

Build confidence with an intuition-first walkthrough focused on array fundamentals.

The Problem

Problem Statement

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

Return the k^th 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 5^th 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 2^nd 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

Follow up:

Could you solve this problem in less than O(n) complexity?

Step 01

Brute Force Baseline

Problem summary: 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.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array · Binary Search

Example 1

[2,3,4,7,11]
5

Example 2

[1,2,3,4]
2

Core Insight

What unlocks the optimal approach

Keep track of how many positive numbers are missing as you scan the array.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #1539: Kth Missing Positive Number
class Solution {
    public int findKthPositive(int[] arr, int k) {
        if (arr[0] > k) {
            return k;
        }
        int left = 0, right = arr.length;
        while (left < right) {
            int mid = (left + right) >> 1;
            if (arr[mid] - mid - 1 >= k) {
                right = mid;
            } else {
                left = mid + 1;
            }
        }
        return arr[left - 1] + k - (arr[left - 1] - (left - 1) - 1);
    }
}

// Accepted solution for LeetCode #1539: Kth Missing Positive Number
func findKthPositive(arr []int, k int) int {
	if arr[0] > k {
		return k
	}
	left, right := 0, len(arr)
	for left < right {
		mid := (left + right) >> 1
		if arr[mid]-mid-1 >= k {
			right = mid
		} else {
			left = mid + 1
		}
	}
	return arr[left-1] + k - (arr[left-1] - (left - 1) - 1)
}

# Accepted solution for LeetCode #1539: Kth Missing Positive Number
class Solution:
    def findKthPositive(self, arr: List[int], k: int) -> int:
        if arr[0] > k:
            return k
        left, right = 0, len(arr)
        while left < right:
            mid = (left + right) >> 1
            if arr[mid] - mid - 1 >= k:
                right = mid
            else:
                left = mid + 1
        return arr[left - 1] + k - (arr[left - 1] - (left - 1) - 1)

// Accepted solution for LeetCode #1539: Kth Missing Positive Number
struct Solution;

impl Solution {
    fn find_kth_positive(arr: Vec<i32>, mut k: i32) -> i32 {
        let mut x = 1;
        let mut i = 0;
        let n = arr.len();
        loop {
            if i < n && x == arr[i] {
                i += 1;
            } else {
                k -= 1;
            }
            if k == 0 {
                break;
            }
            x += 1;
        }
        x
    }
}

#[test]
fn test() {
    let arr = vec![2, 3, 4, 7, 11];
    let k = 5;
    let res = 9;
    assert_eq!(Solution::find_kth_positive(arr, k), res);
    let arr = vec![1, 2, 3, 4];
    let k = 2;
    let res = 6;
    assert_eq!(Solution::find_kth_positive(arr, k), res);
}

// Accepted solution for LeetCode #1539: Kth Missing Positive Number
// Auto-generated TypeScript example from java.
function exampleSolution(): void {
}
// Reference (java):
// // Accepted solution for LeetCode #1539: Kth Missing Positive Number
// class Solution {
//     public int findKthPositive(int[] arr, int k) {
//         if (arr[0] > k) {
//             return k;
//         }
//         int left = 0, right = arr.length;
//         while (left < right) {
//             int mid = (left + right) >> 1;
//             if (arr[mid] - mid - 1 >= k) {
//                 right = mid;
//             } else {
//                 left = mid + 1;
//             }
//         }
//         return arr[left - 1] + k - (arr[left - 1] - (left - 1) - 1);
//     }
// }

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(log n)

Space

O(1)

Approach Breakdown

LINEAR SCAN

O(n) time

O(1) space

Check every element from left to right until we find the target or exhaust the array. Each comparison is O(1), and we may visit all n elements, giving O(n). No extra space needed.

BINARY SEARCH

O(log n) time

O(1) space

Each comparison eliminates half the remaining search space. After k comparisons, the space is n/2ᵏ. We stop when the space is 1, so k = log₂ n. No extra memory needed — just two pointers (lo, hi).

Shortcut: Halving the input each step → O(log n). Works on any monotonic condition, not just sorted arrays.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.

Boundary update without `+1` / `-1`

Wrong move: Setting `lo = mid` or `hi = mid` can stall and create an infinite loop.

Usually fails on: Two-element ranges never converge.

Fix: Use `lo = mid + 1` or `hi = mid - 1` where appropriate.