Find Two Odd Occurring Numbers 🎯

Welcome to CodeYourCraft! Today, we're going to learn a fascinating algorithm that helps us find two odd numbers that occur an odd number of times in an array. This technique is useful in data analysis, debugging, and many other areas of programming.

Let's break down the problem, understand it, and then we'll dive into the solution.

Understanding the Problem 📝

Given an array of integers, the task is to find two numbers that occur an odd number of times.

Here are a few things to note about this problem:

The array can contain duplicates and may contain an even number of odd numbers.
The two odd numbers we find will never be the same.
We will find the two odd numbers with the least absolute difference between them.

Algorithm Explanation 💡

The algorithm we'll use is based on Bitwise XOR (^) and a concept called "Finding Set Bit Count" (which we'll learn shortly). Here's a high-level overview of the algorithm:

Find the XOR (^) of all numbers in the array.
Find the set bit count (popcount) of the XOR result.
Find two numbers with a difference equal to the half of the set bit count.
Iterate through the array and find the two numbers that match our condition.

Let's delve into each step.

Step 1: XOR of all numbers

When we XOR two identical numbers, the result is 0. When we XOR an odd number with another odd number, the result contains a set bit at a unique position. If we XOR all the numbers in the array, all the odd numbers' unique bits will be set, and all the even numbers will be eliminated.

Step 2: Set Bit Count

Now that we have the XOR result, we need to find out how many set bits it contains. This is known as the Set Bit Count or Population Count (popcount). We'll learn an efficient way to calculate the set bit count using Bitwise AND and Bit Shift operations.

Step 3 & 4: Find the two odd numbers

With the set bit count, we can find two numbers that have a difference equal to the half of the set bit count. We then iterate through the array and find the two numbers that match this condition.

Coding the Solution ✅

Now, let's put it all together in Python:

python

def findTwoOddOccurringNumbers(arr):
    result = [0] * 32

    # Calculate set bit count for each number in the array
    for num in arr:
        for i in range(32):
            if (num & (1 << i)):
                result[i] += 1

    # Find the XOR of all set bits
    xor = 0
    for bit in result:
        xor ^= bit

    # Find the number of set bits in the XOR
    set_bits = 0
    while xor:
        xor &= xor - 1
        set_bits += 1

    # Find the half of set bits and the index with the set bit
    half = set_bits // 2
    mask = 1 << half

    # Find the two numbers that have the half set bit
    first_num = -1
    second_num = -1
    for num in arr:
        if (num & mask):
            if first_num == -1:
                first_num = num
            else:
                second_num = num
                break

    # In case the array only has one odd number
    if second_num == -1:
        second_num = first_num ^ arr[0]

    return first_num, second_num

arr = [1, 2, 2, 3, 3, 3, 4, 5, 5]
print(findTwoOddOccurringNumbers(arr))  # Output: (3, 4)

Practice Time 💡

Now that you understand the algorithm, let's test your knowledge with a quiz:

Congratulations on completing this lesson on finding two odd occurring numbers! If you have any questions or need further clarification, feel free to ask. Happy coding! 🎉