Merge pull request #1996 from T-Fathima/branch_2

Added Count set bits in bit Manipulation

docs/bit-manipulation/count-set-bits.md

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+---
+id: count-set-bits
+title: Counting Set Bits
+sidebar_label: Count Set Bits
+sidebar_position: 5
+Description: This algorithm counts the number of set bits (1s) in the binary representation of a number. Utilizing bit manipulation, it efficiently clears the rightmost set bit repeatedly to quickly calculate the total number of 1s in the binary form, commonly used in applications requiring binary analysis.
+
+Tags: [dsa, bit manipulation, algorithm, set bits, efficiency]
+---
+# Counting the Number of Set Bits in a Number
+
+## Introduction
+
+The **Count Set Bits** algorithm calculates the number of 1s in the binary representation of a given integer. This is particularly useful in digital signal processing, cryptography, and data compression, where binary data operations are essential.
+
+## How it Works
+
+The algorithm leverages bit manipulation to clear the rightmost set bit until no bits remain. The key operation, `n & (n - 1)`, removes the lowest set bit, allowing us to count the total set bits with minimal operations.
+
+### Steps in the Algorithm:
+1. Initialize a counter.
+2. While `n` is greater than zero:
+   - Perform `n = n & (n - 1)` to remove the lowest set bit.
+   - Increment the counter.
+3. Return the counter as the count of set bits.
+
+### Example Walkthrough
+
+Consider the example where `n = 13` (binary `1101`):
+
+- **Step 1**:  
+  `n = 1101`  
+  `n - 1 = 1100`  
+  `n & (n - 1) = 1100`  
+  Counter = 1
+
+- **Step 2**:  
+  `n = 1100`  
+  `n - 1 = 1011`  
+  `n & (n - 1) = 1000`  
+  Counter = 2
+
+- **Step 3**:  
+  `n = 1000`  
+  `n - 1 = 0111`  
+  `n & (n - 1) = 0000`  
+  Counter = 3
+
+Thus, `13` has three set bits.
+
+### C++ Implementation
+
+```cpp
+#include <iostream>
+using namespace std;
+
+// Function to count the number of set bits
+int countSetBits(int n) {
+    int count = 0;
+    while (n > 0) {
+        n = n & (n - 1);
+        count++;
+    }
+    return count;
+}
+
+int main() {
+    int n = 13;
+    cout << "Number of set bits in " << n << " is " << countSetBits(n) << endl;
+    return 0;
+}
+```
+# Python Implementation
+```python
+def count_set_bits(n):
+    count = 0
+    while n > 0:
+        n &= (n - 1)
+        count += 1
+    return count
+
+# Test the function
+n = 13
+print(f"Number of set bits in {n} is {count_set_bits(n)}")
+```
+
+# Time Complexity
+This algorithm runs in O(k), where k is the number of set bits, making it efficient compared to simple bit counting methods.
+
+# Why It's Efficient
+The algorithm focuses only on set bits, skipping zero bits entirely, which significantly reduces the number of operations.
+
+# Conclusion
+The Count Set Bits technique is a highly efficient bit manipulation strategy for determining the number of set bits in a binary number, widely used in low-level programming and binary data manipulation.