First Missing Positive

First Missing Positive - Problem

Given an unsorted integer array nums, return the smallest positive integer that is not present in nums.

Important: You must implement an algorithm that runs in O(n) time and uses O(1) auxiliary space.

The problem asks you to find the first missing positive number from 1, 2, 3, ... that doesn't exist in the array.

Input & Output

Example 1 — Basic Case

$ Input: nums = [1,2,0]

› Output: 3

💡 Note: The numbers 1 and 2 are present, but 3 is the first missing positive integer.

Example 2 — Negative and Large Numbers

$ Input: nums = [3,4,-1,1]

› Output: 2

💡 Note: We have 1, 3, and 4, but 2 is missing. Negative numbers don't affect the result.

Example 3 — All Numbers Present

$ Input: nums = [7,8,9,11,12]

› Output: 1

💡 Note: The smallest positive integer 1 is not present in the array.

Constraints

1 ≤ nums.length ≤ 10⁵
-2³¹ ≤ nums[i] ≤ 2³¹ - 1

Visualization

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Asked in

A Amazon 45 M Microsoft 38 G Google 32 F Facebook 28

The key insight is to use the array itself as a hash table by placing each number n at index n-1. The optimal Cyclic Sort approach achieves O(n) time and O(1) space by rearranging elements in-place, then finding the first position where the expected value is missing.

Common Approaches

✓ Brute Force - Linear Search

⏱️ Time: O(n²) Space: O(1)

For each positive integer starting from 1, scan the entire array to see if it exists. Return the first integer that's not found.

Cyclic Sort (In-Place)

⏱️ Time: O(n) Space: O(1)

Place each positive number n at index n-1. After rearrangement, scan the array to find the first position where nums[i] != i+1.

Hash Set Lookup

⏱️ Time: O(n) Space: O(n)

First pass: insert all positive numbers into a hash set. Second pass: check integers 1, 2, 3... until we find one not in the set.

Brute Force - Linear Search — Algorithm Steps

Start with candidate = 1
For each candidate, scan entire array to check if it exists
If not found, return candidate
If found, increment candidate and repeat

Visualization

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Step-by-Step Walkthrough

Check 1

Scan array for 1

Check 2

Scan array for 2

Found Missing

First number not in array

Code -

solution.c — C

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

int solution(int* nums, int numsSize) {
    int candidate = 1;
    while (true) {
        bool found = false;
        for (int i = 0; i < numsSize; i++) {
            if (nums[i] == candidate) {
                found = true;
                break;
            }
        }
        if (!found) {
            return candidate;
        }
        candidate++;
    }
}

int main() {
    char line[10000];
    fgets(line, sizeof(line), stdin);
    
    // Parse JSON array
    int nums[1000];
    int numsSize = 0;
    char* token = strtok(line + 1, ",]");
    while (token != NULL) {
        nums[numsSize++] = atoi(token);
        token = strtok(NULL, ",]");
    }
    
    int result = solution(nums, numsSize);
    printf("%d\n", result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n²)

For each of potentially n candidates, we scan the entire array of size n

✓ Linear Growth

Space Complexity

O(1)

Only using a few variables, no extra data structures

⚡ Linearithmic Space

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Input & Output

Constraints

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Related Problems

Common Approaches

Brute Force - Linear Search — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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