feat: Add Prefix Sum category with 1D and 2D implementations (#7220)

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

src/main/java/com/thealgorithms/prefixsum/PrefixSum.java

@@ -0,0 +1,54 @@
+package com.thealgorithms.prefixsum;
+
+/**
+ * A class that implements the Prefix Sum algorithm.
+ *
+ * <p>Prefix Sum is a technique used to preprocess an array such that
+ * range sum queries can be answered in O(1) time.
+ * The preprocessing step takes O(N) time.
+ *
+ * <p>This implementation uses a long array for the prefix sums to prevent
+ * integer overflow when the sum of elements exceeds Integer.MAX_VALUE.
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Prefix_sum">Prefix Sum (Wikipedia)</a>
+ * @author Chahat Sandhu, <a href="https://github.com/singhc7">singhc7</a>
+ */
+public class PrefixSum {
+
+    private final long[] prefixSums;
+
+    /**
+     * Constructor to preprocess the input array.
+     *
+     * @param array The input integer array.
+     * @throws IllegalArgumentException if the array is null.
+     */
+    public PrefixSum(int[] array) {
+        if (array == null) {
+            throw new IllegalArgumentException("Input array cannot be null");
+        }
+        this.prefixSums = new long[array.length + 1];
+        this.prefixSums[0] = 0;
+
+        for (int i = 0; i < array.length; i++) {
+            // Automatically promotes int to long during addition
+            this.prefixSums[i + 1] = this.prefixSums[i] + array[i];
+        }
+    }
+
+    /**
+     * Calculates the sum of elements in the range [left, right].
+     * Indices are 0-based.
+     *
+     * @param left  The starting index (inclusive).
+     * @param right The ending index (inclusive).
+     * @return The sum of elements from index left to right as a long.
+     * @throws IndexOutOfBoundsException if indices are out of valid range.
+     */
+    public long sumRange(int left, int right) {
+        if (left < 0 || right >= prefixSums.length - 1 || left > right) {
+            throw new IndexOutOfBoundsException("Invalid range indices");
+        }
+        return prefixSums[right + 1] - prefixSums[left];
+    }
+}