Program to find all missing numbers from 1 to N in Python

Finding missing numbers from a range is a common programming problem. Given a list of numbers where each number should be in the range [1, N], we need to identify which numbers are missing. Some numbers may appear multiple times while others are missing entirely.

So, if the input is like [4, 4, 2, 2, 6, 6], then the output will be [1, 3, 5] since these numbers are missing from the range [1, 6].

Using Array Counting Method

This approach uses an auxiliary array to count occurrences of each number ?

def find_missing_numbers(nums):
    # Create array of size n+1 to handle indices 1 to n
    n = len(nums)
    count = [0] * (n + 1)
    
    # Count occurrences of each number
    for num in nums:
        count[num] += 1
    
    # Find missing numbers (count = 0, excluding index 0)
    missing = []
    for i in range(1, len(count)):
        if count[i] == 0:
            missing.append(i)
    
    return missing

# Test the function
numbers = [4, 4, 2, 2, 6, 6]
result = find_missing_numbers(numbers)
print("Input:", numbers)
print("Missing numbers:", result)

Input: [4, 4, 2, 2, 6, 6]
Missing numbers: [1, 3, 5]

Using Set Difference Method

A more Pythonic approach using sets to find the difference ?

def find_missing_with_set(nums):
    n = len(nums)
    # Create set of all numbers from 1 to n
    complete_set = set(range(1, n + 1))
    # Create set from input numbers
    nums_set = set(nums)
    # Find missing numbers using set difference
    missing = sorted(list(complete_set - nums_set))
    return missing

# Test the function
numbers = [4, 4, 2, 2, 6, 6]
result = find_missing_with_set(numbers)
print("Input:", numbers)
print("Missing numbers:", result)

Input: [4, 4, 2, 2, 6, 6]
Missing numbers: [1, 3, 5]

Using List Comprehension

A concise one-liner solution using list comprehension ?

def find_missing_comprehension(nums):
    n = len(nums)
    nums_set = set(nums)
    return [i for i in range(1, n + 1) if i not in nums_set]

# Test the function
numbers = [4, 4, 2, 2, 6, 6]
result = find_missing_comprehension(numbers)
print("Input:", numbers)
print("Missing numbers:", result)

Input: [4, 4, 2, 2, 6, 6]
Missing numbers: [1, 3, 5]

Comparison

Conclusion

The set difference method is the most Pythonic and readable solution. All approaches have O(n) time complexity, but the set-based solutions are more intuitive and easier to understand.