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];
+    }
+}

src/main/java/com/thealgorithms/prefixsum/PrefixSum2D.java

@@ -0,0 +1,64 @@
+package com.thealgorithms.prefixsum;
+
+/**
+ * A class that implements the 2D Prefix Sum algorithm.
+ *
+ * <p>2D Prefix Sum is a technique used to preprocess a 2D matrix such that
+ * sub-matrix sum queries can be answered in O(1) time.
+ * The preprocessing step takes O(N*M) time.
+ *
+ * <p>This implementation uses a long array for the prefix sums to prevent
+ * integer overflow.
+ *
+ * @see <a href="https://en.wikipedia.org/wiki/Summed-area_table">Summed-area table (Wikipedia)</a>
+ * @author Chahat Sandhu, <a href="https://github.com/singhc7">singhc7</a>
+ */
+public class PrefixSum2D {
+
+    private final long[][] prefixSums;
+
+    /**
+     * Constructor to preprocess the input matrix.
+     *
+     * @param matrix The input integer matrix.
+     * @throws IllegalArgumentException if the matrix is null or empty.
+     */
+    public PrefixSum2D(int[][] matrix) {
+        if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
+            throw new IllegalArgumentException("Input matrix cannot be null or empty");
+        }
+
+        int rows = matrix.length;
+        int cols = matrix[0].length;
+        this.prefixSums = new long[rows + 1][cols + 1];
+
+        for (int i = 0; i < rows; i++) {
+            for (int j = 0; j < cols; j++) {
+                // P[i+1][j+1] = current + above + left - diagonal_overlap
+                this.prefixSums[i + 1][j + 1] = matrix[i][j] + this.prefixSums[i][j + 1] + this.prefixSums[i + 1][j] - this.prefixSums[i][j];
+            }
+        }
+    }
+
+    /**
+     * Calculates the sum of the sub-matrix defined by (row1, col1) to (row2, col2).
+     * Indices are 0-based.
+     *
+     * @param row1 Top row index.
+     * @param col1 Left column index.
+     * @param row2 Bottom row index.
+     * @param col2 Right column index.
+     * @return The sum of the sub-matrix.
+     * @throws IndexOutOfBoundsException if indices are invalid.
+     */
+    public long sumRegion(int row1, int col1, int row2, int col2) {
+        if (row1 < 0 || row2 >= prefixSums.length - 1 || row2 < row1) {
+            throw new IndexOutOfBoundsException("Invalid row indices");
+        }
+        if (col1 < 0 || col2 >= prefixSums[0].length - 1 || col2 < col1) {
+            throw new IndexOutOfBoundsException("Invalid column indices");
+        }
+
+        return prefixSums[row2 + 1][col2 + 1] - prefixSums[row1][col2 + 1] - prefixSums[row2 + 1][col1] + prefixSums[row1][col1];
+    }
+}