Add count bit problem in bit manipulation

bit_manipulation/count_bit.cpp

@@ -0,0 +1,42 @@
+#include <iostream>
+using namespace std;
+
+// Function to count total set bits from 1 to n
+int countSetBits(int n) {
+    int count = 0;
+    for (int i = 1; i <= n; i++) {
+        int num = i;
+        while (num) {
+            count += num & 1; // Increment count if LSB is 1
+            num >>= 1;        // Right shift by 1
+        }
+    }
+    return count;
+}
+
+// Optimized version using Brian Kernighan’s Algorithm
+int countSetBitsOptimized(int n) {
+    int count = 0;
+    for (int i = 1; i <= n; i++) {
+        int num = i;
+        while (num) {
+            num = num & (num - 1); // Remove the rightmost set bit
+            count++;
+        }
+    }
+    return count;
+}
+
+int main() {
+    int n;
+    cout << "Enter a number: ";
+    cin >> n;
+
+    cout << "Total set bits from 1 to " << n << " (simple method): " 
+         << countSetBits(n) << endl;
+
+    cout << "Total set bits from 1 to " << n << " (optimized method): " 
+         << countSetBitsOptimized(n) << endl;
+
+    return 0;
+}