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Title: Add Efficient Algorithm to Count Total Set Bits from 1 to N

🧠 Overview

This contribution adds a bit manipulation algorithm that counts the total number of set bits (1s) in binary representation of all numbers from 1 to N efficiently — much faster than naive iteration.

🧩 Problem Description

Given an integer N, compute the total count of bits set to 1 in all numbers from 1 up to N.
For example, N = 3 → Binary(1)=1, Binary(2)=10, Binary(3)=11 → Total set bits = 4.

📂 Implementation Details

• Folder: src/main/java/com/thealgorithms/bitmanipulation/
• Filename: CountTotalSetBits.java
• Approach: Use recursion or bit-pattern observation (N/2, N/4, etc.) to reduce time complexity to O(log N).

✅ Expected Deliverables

• Well-commented Java code with clear explanation of logic.
• Unit tests for small and large values of N.
• Comparison with naive loop-based method (optional).
• Include complexity analysis in code comments.

🧑‍💻 Additional Notes

This algorithm provides an elegant use of bit patterns and helps learners understand bitwise counting techniques.

Issue details

🧩 Problem Description

Given an integer N, compute the total count of bits set to 1 in all numbers from 1 up to N.
For example, N = 3 → Binary(1)=1, Binary(2)=10, Binary(3)=11 → Total set bits = 4.

Additional Information

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