Add Count Total Set Bits from 1 to N (Bit Manipulation)

Author: Shewale41

src/main/java/com/thealgorithms/bitmanipulation/CountTotalSetBits.java

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+package com.thealgorithms.bitmanipulation;
+
+/**
+ * Count the total number of set bits in binary representations of all numbers from 1 to N.
+ *
+ * <p>This implementation uses bit manipulation and mathematical observation to
+ * efficiently calculate the total number of set bits in O(log N) time.
+ *
+ * <p>Example:
+ * N = 3 -> Binary(1):01, Binary(2):10, Binary(3):11 => Total Set Bits = 4
+ *
+ * <p>Reference: https://www.geeksforgeeks.org/count-total-set-bits-in-all-numbers-from-1-to-n/
+ */
+public final class CountTotalSetBits {
+
+    private CountTotalSetBits() {
+        // utility class
+    }
+
+    /**
+     * Returns the total count of set bits in binary representations of all numbers from 1 to n.
+     *
+     * @param n the upper limit of the range
+     * @return total number of set bits from 1 to n
+     */
+    public static int countTotalSetBits(int n) {
+        if (n == 0) {
+            return 0;
+        }
+
+        int x = largestPowerOf2(n);
+        int bitsTill2x = x * (1 << (x - 1));
+        int msbBits = n - (1 << x) + 1;
+        int rest = n - (1 << x);
+
+        return bitsTill2x + msbBits + countTotalSetBits(rest);
+    }
+
+    /**
+     * Helper function to find the largest power of 2 less than or equal to n.
+     */
+    private static int largestPowerOf2(int n) {
+        int x = 0;
+        while ((1 << x) <= n) {
+            x++;
+        }
+        return x - 1;
+    }
+}

src/test/java/com/thealgorithms/bitmanipulation/CountTotalSetBitsTest.java

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+package com.thealgorithms.bitmanipulation;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import org.junit.jupiter.api.Test;
+
+/**
+ * Test cases for {@link CountTotalSetBits}.
+ */
+public class CountTotalSetBitsTest {
+
+    @Test
+    void testSmallNumbers() {
+        assertEquals(4, CountTotalSetBits.countTotalSetBits(3));  // 1->1,2->1,3->2
+        assertEquals(5, CountTotalSetBits.countTotalSetBits(4));  // 1,2,3,4 -> total 5
+    }
+
+    @Test
+    void testPowerOfTwo() {
+        assertEquals(12, CountTotalSetBits.countTotalSetBits(7));  // from 1 to 7
+    }
+
+    @Test
+    void testLargerNumber() {
+        assertEquals(17, CountTotalSetBits.countTotalSetBits(10)); // verified manually
+    }
+
+    @Test
+    void testZero() {
+        assertEquals(0, CountTotalSetBits.countTotalSetBits(0));
+    }
+}