add Subarray Sum Equals K using prefix sum (#7252)

Co-authored-by: Deniz Altunkapan <deniz.altunkapan@outlook.com>

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;
+    }
+}