Count Odd Numbers in an Interval Range Python C++ Java

1523 Count Odd Numbers in an Interval Range

Count Odd Numbers in an Interval Range  Python C++ Java

In this article, we'll explore the solution to LeetCode problem 1523: Count Odd Numbers in an Interval Range. Given two non-negative integers, low and high, the task is to return the count of odd numbers between the two values (inclusive).

🧠 What are Odd Numbers?

Odd numbers are numbers that are not divisible by 2. That means if a number leaves a remainder of 1 when divided by 2, it is considered odd.
Example:

 1, 3, 5, 7, 9...

📝 Problem Statement

Given two non-negative integers low and high, return the total count of odd numbers in the inclusive range [low, high].

🔢 Example 1

Input:

low = 3, high = 7

Output: 3 Explanation:

The odd numbers in this range are [3, 5, 7].

🔢 Example 2

  Input: 
low = 8, high = 10
  Output: 1
  Explanation: 
Only 9 is an odd number between 8 and 10.
  

✅ Optimized Approach

Instead of checking each number individually, we can use a mathematical formula to calculate the count of odd numbers:

 Count = ((high - low) // 2) + (1 if low % 2 != 0 or high % 2 != 0 else 0)
  

This works because odd numbers alternate every two steps, and if either boundary is odd, we add one extra.

💻 Python Code

def countOdds(low: int, high: int) -> int:
    return ((high - low) // 2) + (1 if low % 2 != 0 or high % 2 != 0 else 0)
  

💻 C++ Code

class Solution {
public:
    int findOddCount(int min, int max) {
        if (!(min & 1)) {
            min++;
        }
        return min > max ? 0 : (max - min) / 2 + 1;
    }
};
  

💻 Java Code

class Solution {
  public int countOddNumbers(int start, int end) {
    // Increment start if it's even.
    if ((start & 1) == 0) {
      start++;
    }

    // Calculate the number of odd numbers in the range.
    return start > end ? 0 : (end - start) / 2 + 1;
  }
}
  

🧠 Time and Space Complexity

• Time Complexity: O(1) – No loops, just arithmetic operations.
• Space Complexity: O(1) – No extra memory used.

🎯 Conclusion

This problem teaches how simple mathematical reasoning can replace brute-force loops. It’s a perfect example of writing efficient, optimized code for a seemingly simple problem. Try implementing it in your favorite language and practice edge cases!