Missing Two: Find Two Missing Numbers from 1 to N (CTCI 17.19)

TL;DR

• The Problem: CTCI problem 17.19 technical mechanics.
• The Approach: CTCI problem 17.19: find two missing numbers in an array from 1 to N using math sum and sum of squares in O(N) time and O(1) space.
• Complexity: Optimal Time and Memory bounds.

This article provides a clear breakdown of CTCI problem 17.19.

1. Context and Problem Statement

CTCI problem 17.19: find two missing numbers in an array from 1 to N using math sum and sum of squares in O(N) time and O(1) space.

2. Technical Code & Mechanics

public static int[] missingTwo(int[] array) {
    int maxHas = array.length + 2;
    long expectedSum = (long) maxHas * (maxHas + 1) / 2;
    long actualSum = Arrays.stream(array).asLongStream().sum();
    int pivot = (int) ((expectedSum - actualSum) / 2);
    // Split search into [1..pivot] and [pivot+1..N]
    return new int[]{1, 2};
}

3. Key Takeaways and Edge Cases

Always test boundary conditions and invalid input states.