Python: Find the first missing positive integer that does not exist in a given list

Last update on March 21 2025 12:42:21 (UTC/GMT +8 hours)

First Missing Positive Integer

Write a Python program to find the first missing positive integer that does not exist in a given list.

Sample Solution:

Python Code:

# Define a function to find the first missing positive integer in a list
def first_missing_number(nums):
    # Check if the list is empty, return 1 if it is
    if len(nums) == 0:
        return 1
        
    # Sort the list in ascending order
    nums.sort()
    
    # Initialize the smallest positive integer as 0
    smallest_int_num = 0
    
    # Iterate through the sorted list
    for i in range(len(nums) - 1):
        # Skip non-positive or duplicate numbers
        if nums[i] <= 0 or nums[i] == nums[i + 1]:
            continue
        else:
            # Check for a gap between consecutive numbers
            if nums[i + 1] - nums[i] != 1:
                smallest_int_num = nums[i] + 1
                return smallest_int_num
    
    # If no gap is found, the smallest missing positive integer is after the last element
    if smallest_int_num == 0:
        smallest_int_num = nums[-1] + 1
    
    # Return the smallest missing positive integer
    return smallest_int_num

# Test the function with different lists of numbers
print(first_missing_number([2, 3, 7, 6, 8, -1, -10, 15, 16])) 
print(first_missing_number([1, 2, 4, -7, 6, 8, 1, -10, 15]))
print(first_missing_number([1, 2, 3, 4, 5, 6, 7]))
print(first_missing_number([-2, -3, -1, 1, 2, 3]))

Sample Output:

4
3
8
4

Explanation:

Here is a breakdown of the above Python code:

• The function "first_missing_number()" takes a list of numbers ('nums') as input.
• It checks if the list is empty and returns 1 if it is.
• The function sorts the list in ascending order.
• It initializes the smallest positive integer as 0.
• It iterates through the sorted list, skipping non-positive or duplicate numbers.
• It checks for a gap between consecutive numbers, indicating a missing positive integer.
• If a gap is found, the smallest missing positive integer is determined and returned.
• If no gap is found, the smallest missing positive integer is after the last element.
• The function is tested with different lists of numbers.

Flowchart:

For more Practice: Solve these Related Problems:

• Write a Python program to find the smallest missing positive integer in an unsorted array in O(n) time.
• Write a Python program to identify the first missing positive number by rearranging the array elements in-place.
• Write a Python program to determine the smallest positive integer that does not appear in a given list using index mapping.
• Write a Python program to compute the first absent positive number using a constant space solution.

Python Code Editor:

Have another way to solve this solution? Contribute your code (and comments) through Disqus.

Previous: Write a Python program to compute the largest product of three integers from a given list of integers.
Next: Write a Python program to randomly generate a list with 10 even numbers between 1 and 100 inclusive.