From 03f4d419cc4793e3593355afc04d1508a5bc2db8 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?=E2=80=9C=5Bgithub=5D=E2=80=9D?=
 <ruturajjadhav122@gmail.com>
Date: Sun, 1 Feb 2026 18:56:44 +0530
Subject: [PATCH] add Subarray Sum Equals K using prefix sum

---
 .../prefixsum/SubarraySumEqualsK.java         | 72 +++++++++++++++++++
 .../prefixsum/SubarraySumEqualskTest.java     | 59 +++++++++++++++
 2 files changed, 131 insertions(+)
 create mode 100644 src/main/java/com/thealgorithms/prefixsum/SubarraySumEqualsK.java
 create mode 100644 src/test/java/com/thealgorithms/prefixsum/SubarraySumEqualskTest.java

diff --git a/src/main/java/com/thealgorithms/prefixsum/SubarraySumEqualsK.java b/src/main/java/com/thealgorithms/prefixsum/SubarraySumEqualsK.java
new file mode 100644
index 000000000000..d6a6bbc01663
--- /dev/null
+++ b/src/main/java/com/thealgorithms/prefixsum/SubarraySumEqualsK.java
@@ -0,0 +1,72 @@
+package com.thealgorithms.prefixsum;
+
+import java.util.HashMap;
+import java.util.Map;
+
+/**
+ * Implements an algorithm to count the number of continuous subarrays
+ * whose sum equals a given value k.
+ *
+ * <p>
+ * This algorithm uses the Prefix Sum technique combined with a HashMap
+ * to achieve O(N) time complexity.
+ * </p>
+ *
+ * <p>
+ * Let prefixSum[i] be the sum of elements from index 0 to i.
+ * A subarray (j + 1) to i has sum k if:
+ *
+ * <pre>
+ * prefixSum[i] - prefixSum[j] = k
+ * </pre>
+ * </p>
+ *
+ * <p>
+ * The HashMap stores the frequency of each prefix sum encountered so far.
+ * </p>
+ *
+ * <p>
+ * <strong>Time Complexity:</strong> O(N)<br>
+ * <strong>Space Complexity:</strong> O(N)
+ * </p>
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Prefix_sum">Prefix Sum (Wikipedia)</a>
+ * @author Ruturaj Jadhav, <a href="https://github.com/ruturajjadhav07">ruturajjadhav07</a>
+ */
+public final class SubarraySumEqualsK {
+
+    private SubarraySumEqualsK() {
+        // Utility class; prevent instantiation
+    }
+
+    /**
+     * Counts the number of subarrays whose sum equals k.
+     *
+     * @param nums The input integer array.
+     * @param k    The target sum.
+     * @return The number of continuous subarrays summing to k.
+     * @throws IllegalArgumentException if nums is null.
+     */
+    public static int countSubarrays(int[] nums, int k) {
+        if (nums == null) {
+            throw new IllegalArgumentException("Input array cannot be null");
+        }
+
+        Map<Long, Integer> prefixSumFrequency = new HashMap<>();
+        prefixSumFrequency.put(0L, 1);
+
+        long prefixSum = 0;
+        int count = 0;
+
+        for (int num : nums) {
+            prefixSum += num;
+
+            long requiredSum = prefixSum - k;
+            count += prefixSumFrequency.getOrDefault(requiredSum, 0);
+
+            prefixSumFrequency.put(prefixSum, prefixSumFrequency.getOrDefault(prefixSum, 0) + 1);
+        }
+
+        return count;
+    }
+}
diff --git a/src/test/java/com/thealgorithms/prefixsum/SubarraySumEqualskTest.java b/src/test/java/com/thealgorithms/prefixsum/SubarraySumEqualskTest.java
new file mode 100644
index 000000000000..68f85b713046
--- /dev/null
+++ b/src/test/java/com/thealgorithms/prefixsum/SubarraySumEqualskTest.java
@@ -0,0 +1,59 @@
+package com.thealgorithms.prefixsum;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+import static org.junit.jupiter.api.Assertions.assertThrows;
+
+import org.junit.jupiter.api.Test;
+
+/**
+ * Tests for {@link SubarraySumEqualsK}.
+ */
+class SubarraySumEqualsKTest {
+
+    @Test
+    void testBasicExample() {
+        int[] nums = {1, 1, 1};
+        int k = 2;
+        assertEquals(2, SubarraySumEqualsK.countSubarrays(nums, k));
+    }
+
+    @Test
+    void testWithNegativeNumbers() {
+        int[] nums = {1, -1, 0};
+        int k = 0;
+        assertEquals(3, SubarraySumEqualsK.countSubarrays(nums, k));
+    }
+
+    @Test
+    void testSingleElementEqualToK() {
+        int[] nums = {5};
+        int k = 5;
+        assertEquals(1, SubarraySumEqualsK.countSubarrays(nums, k));
+    }
+
+    @Test
+    void testSingleElementNotEqualToK() {
+        int[] nums = {5};
+        int k = 3;
+        assertEquals(0, SubarraySumEqualsK.countSubarrays(nums, k));
+    }
+
+    @Test
+    void testAllZeros() {
+        int[] nums = {0, 0, 0};
+        int k = 0;
+        assertEquals(6, SubarraySumEqualsK.countSubarrays(nums, k));
+    }
+
+    @Test
+    void testEmptyArray() {
+        int[] nums = {};
+        int k = 0;
+        assertEquals(0, SubarraySumEqualsK.countSubarrays(nums, k));
+    }
+
+    @Test
+    void testNullArrayThrowsException() {
+        assertThrows(IllegalArgumentException.class, () -> SubarraySumEqualsK.countSubarrays(null, 0));
+    }
+}