Find All Numbers Disappeared in an Array

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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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

✓ Brute Force - Check Each Number

⏱️ Time: O(n²) Space: O(1)

Iterate through each possible number from 1 to n, and for each number, scan the entire input array to check if it exists. If not found, add to result.

Cyclic Sort / Index Marking

⏱️ Time: O(n) Space: O(1)

Since numbers are in range [1,n], we can use the array itself as a hash table. For each number x, mark position x-1 as visited by negating it. Then scan for positive values which indicate missing numbers.

Hash Set Approach

⏱️ Time: O(n) Space: O(n)

First pass: add all numbers to a hash set for O(1) lookup. Second pass: check each number from 1 to n against the set.

Brute Force - Check Each Number — Algorithm Steps

Iterate through numbers 1 to n
For each number, scan entire array to check existence
If number not found, add to missing list

Visualization

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Step-by-Step Walkthrough

Check Number 1

Scan entire array looking for 1

Check Number 2

Scan entire array looking for 2 - not found!

Continue for All

Repeat for numbers 3, 4, etc.

Code -

solution.c — C

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

int* solution(int* nums, int numsSize, int* returnSize) {
    int* missing = (int*)malloc(numsSize * sizeof(int));
    int count = 0;
    
    // Check each number from 1 to n
    for (int i = 1; i <= numsSize; i++) {
        int found = 0;
        // Scan array to see if number i exists
        for (int j = 0; j < numsSize; j++) {
            if (nums[j] == i) {
                found = 1;
                break;
            }
        }
        if (!found) {
            missing[count++] = i;
        }
    }
    
    *returnSize = count;
    return missing;
}

void parseArray(const char* str, int* arr, int* size) {
    *size = 0;
    const char* p = str;
    while (*p && *p != '[') p++;
    if (*p == '[') p++;
    while (*p && *p != ']') {
        while (*p == ' ' || *p == ',') p++;
        if (*p == ']' || *p == '\0') break;
        arr[(*size)++] = (int)strtol(p, (char**)&p, 10);
    }
}

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(n²)

Outer loop runs n times, inner scan takes O(n) time for each number

⚠ Quadratic Growth

Space Complexity

O(1)

Only using result array and loop variables, no extra data structures

✓ Linear Space

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Input & Output

Constraints

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Related Problems

Common Approaches

Brute Force - Check Each Number — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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