Add Fenwick tree implementation and tests

Author: Rohan45create

src/main/java/com/thealgorithms/datastructures/trees/FenwickTree.java

@@ -1,29 +1,33 @@
 package com.thealgorithms.datastructures.trees;
 
+/** Fenwick Tree for point updates and prefix-sum queries in O(log n). */
 public class FenwickTree {
 
-    private int n;
-    private int[] fenTree;
+    private final int n;
+    private final int[] fenTree;
 
-    /* Constructor which takes the size of the array as a parameter */
+    /** Creates a Fenwick tree with n elements, all initialized to zero. */
     public FenwickTree(int n) {
+        if (n < 0) {
+            throw new IllegalArgumentException("Size must be non-negative");
+        }
         this.n = n;
         this.fenTree = new int[n + 1];
     }
 
-    /* A function which will add the element val at index i*/
+    /** Adds val to the element at index i. */
     public void update(int i, int val) {
-        // As index starts from 0, increment the index by 1
-        i += 1;
+        checkIndex(i);
+        i += 1; // Convert to the internal 1-based index
         while (i <= n) {
             fenTree[i] += val;
             i += i & (-i);
         }
     }
 
-    /* A function which will return the cumulative sum from index 1 to index i*/
+    /** Returns the sum of elements from index 0 to i. */
     public int query(int i) {
-        // As index starts from 0, increment the index by 1
+        checkIndex(i);
         i += 1;
         int cumSum = 0;
         while (i > 0) {
@@ -32,4 +36,11 @@ public int query(int i) {
         }
         return cumSum;
     }
+
+    // Check that the index is within the valid range.
+    private void checkIndex(int i) {
+        if (i < 0 || i >= n) {
+            throw new IndexOutOfBoundsException("Index " + i + " out of bounds for size " + n);
+        }
+    }
 }

src/test/java/com/thealgorithms/datastructures/trees/FenwickTree.java

@@ -0,0 +1,115 @@
+package com.thealgorithms.datastructures.trees;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import java.util.Random;
+import org.junit.jupiter.api.Test;
+
+class FenwickTreeTest {
+
+    @Test
+    void queryOnFreshTreeReturnsZero() {
+        FenwickTree tree = new FenwickTree(5);
+        for (int i = 0; i < 5; i++) {
+            assertEquals(0, tree.query(i));
+        }
+    }
+
+    @Test
+    void singleElementTree() {
+        FenwickTree tree = new FenwickTree(1);
+        tree.update(0, 7);
+        assertEquals(7, tree.query(0));
+    }
+
+    @Test
+    void prefixSumsAfterUpdates() {
+        FenwickTree tree = new FenwickTree(5);
+        int[] values = {3, 2, -1, 6, 5};
+        for (int i = 0; i < values.length; i++) {
+            tree.update(i, values[i]);
+        }
+        assertEquals(3, tree.query(0));
+        assertEquals(5, tree.query(1));
+        assertEquals(4, tree.query(2));
+        assertEquals(10, tree.query(3));
+        assertEquals(15, tree.query(4));
+    }
+
+    @Test
+    void repeatedUpdatesOnSameIndexAccumulate() {
+        FenwickTree tree = new FenwickTree(4);
+        tree.update(2, 5);
+        tree.update(2, 3);
+        tree.update(2, -2);
+        assertEquals(0, tree.query(1));
+        assertEquals(6, tree.query(2));
+        assertEquals(6, tree.query(3));
+    }
+
+    @Test
+    void negativeValues() {
+        FenwickTree tree = new FenwickTree(3);
+        tree.update(0, -4);
+        tree.update(1, -6);
+        tree.update(2, 10);
+        assertEquals(-4, tree.query(0));
+        assertEquals(-10, tree.query(1));
+        assertEquals(0, tree.query(2));
+    }
+
+    @Test
+    void nonPowerOfTwoSize() {
+        int size = 13;
+        FenwickTree tree = new FenwickTree(size);
+        for (int i = 0; i < size; i++) {
+            tree.update(i, 1);
+        }
+        for (int i = 0; i < size; i++) {
+            assertEquals(i + 1, tree.query(i));
+        }
+    }
+
+    @Test
+    void matchesNaivePrefixSumOnRandomData() {
+        Random random = new Random(42);
+        int size = 100;
+        FenwickTree tree = new FenwickTree(size);
+        int[] naive = new int[size];
+
+        for (int step = 0; step < 500; step++) {
+            int index = random.nextInt(size);
+            int delta = random.nextInt(21) - 10;
+            tree.update(index, delta);
+            naive[index] += delta;
+        }
+
+        int running = 0;
+        for (int i = 0; i < size; i++) {
+            running += naive[i];
+            assertEquals(running, tree.query(i), "Mismatch at index " + i);
+        }
+    }
+
+    @Test
+    void zeroSizeTreeRejectsAnyIndex() {
+        FenwickTree tree = new FenwickTree(0);
+        assertThrows(IndexOutOfBoundsException.class, () -> tree.update(0, 1));
+        assertThrows(IndexOutOfBoundsException.class, () -> tree.query(0));
+    }
+
+    @Test
+    void negativeSizeThrows() {
+        assertThrows(IllegalArgumentException.class, () -> new FenwickTree(-1));
+    }
+
+    @Test
+    void outOfBoundsIndicesThrow() {
+        FenwickTree tree = new FenwickTree(5);
+        assertThrows(IndexOutOfBoundsException.class, () -> tree.update(-1, 1));
+        assertThrows(IndexOutOfBoundsException.class, () -> tree.update(5, 1));
+        assertThrows(IndexOutOfBoundsException.class, () -> tree.query(-1));
+        assertThrows(IndexOutOfBoundsException.class, () -> tree.query(5));
+    }
+}