Find All Numbers Disappeared in an Array - Practice Coding Problems

Find All Numbers Disappeared in an Array - Problem

Given an array nums of n integers where nums[i] is in the range [1, n], return an array of all the integers in the range [1, n] that do not appear in nums.

Follow up: Could you do it without extra space and in O(n) runtime? You may assume the returned list does not count as extra space.

Input & Output

Example 1 — Basic Case

$ Input: nums = [4,3,2,7,8,2,3,1]

› Output: [5,6]

💡 Note: The array has length 8, so numbers should be in range [1,8]. Numbers 1,2,3,4,7,8 are present (with duplicates). Numbers 5 and 6 are missing.

Example 2 — Single Missing

$ Input: nums = [1,1]

› Output: [2]

💡 Note: Array length is 2, so range is [1,2]. Number 1 appears twice, number 2 is missing.

Example 3 — No Missing Numbers

$ Input: nums = [1,2,3]

› Output: []

💡 Note: All numbers from 1 to 3 are present, so no numbers are missing.

Constraints

n == nums.length
1 ≤ n ≤ 10⁴
1 ≤ nums[i] ≤ n

Visualization

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Understanding the Visualization

Input Analysis

Array of length n with numbers in range [1,n]

Key Insight

Use array indices as hash table to track presence

Output

List of missing numbers from the expected range

Key Takeaway

🎯 Key Insight: Since numbers are in range [1,n], we can use array indices as a hash table to mark presence without extra space

Asked in

G Google 15 a Amazon 12 M Microsoft 8 A Apple 6

The key insight is to use the array indices as a hash table since numbers are in range [1,n]. The optimal approach marks presence by negating values at corresponding indices, achieving O(n) time and O(1) space.

Common Approaches

Approach	Time	Space	Notes
✓ Cyclic Sort / Index Marking	O(n)	O(1)	Use array indices as hash table by negating values at corresponding positions
Brute Force - Check Each Number	O(n²)	O(1)	For each number 1 to n, scan entire array to check if it exists
Hash Set Approach	O(n)	O(n)	Use hash set for O(1) lookup to check which numbers 1-n are missing

Cyclic Sort / Index Marking — Algorithm Steps

For each number x in array, negate nums[x-1] to mark as seen
Scan array - positive values at index i mean number i+1 is missing
Collect indices+1 where values are still positive

Visualization

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Step-by-Step Walkthrough

Mark Present

For each number x, negate nums[x-1]

Scan Array

Positive values indicate missing numbers

Collect Missing

Convert indices back to 1-based numbers

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

int abs_val(int x) {
    return x < 0 ? -x : x;
}

int* solution(int* nums, int numsSize, int* returnSize) {
    int* missing = (int*)malloc(numsSize * sizeof(int));
    int count = 0;
    
    // Mark numbers as seen by negating value at corresponding index
    for (int i = 0; i < numsSize; i++) {
        int index = abs_val(nums[i]) - 1; // Convert 1-based to 0-based
        if (nums[index] > 0) {
            nums[index] = -nums[index];
        }
    }
    
    // Find missing numbers (positive values indicate missing)
    for (int i = 0; i < numsSize; i++) {
        if (nums[i] > 0) {
            missing[count++] = i + 1; // Convert back to 1-based
        }
    }
    
    *returnSize = count;
    return missing;
}

int main() {
    char line[10000];
    fgets(line, sizeof(line), stdin);
    
    // Simple parsing for [1,2,3] format
    int nums[1000];
    int size = 0;
    char* ptr = strchr(line, '[');
    ptr++;
    
    char* token = strtok(ptr, ",]");
    while (token != NULL) {
        nums[size++] = atoi(token);
        token = strtok(NULL, ",]");
    }
    
    int returnSize;
    int* result = solution(nums, size, &returnSize);
    
    printf("[");
    for (int i = 0; i < returnSize; i++) {
        printf("%d", result[i]);
        if (i < returnSize - 1) printf(",");
    }
    printf("]\n");
    
    free(result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n)

Two passes: first pass marks seen numbers, second pass finds positive values

✓ Linear Growth

Space Complexity

O(1)

Only using result array (doesn't count) and loop variables, no extra data structures

✓ Linear Space

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Cyclic Sort / Index Marking — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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