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Adarshsingh99Adarshsingh99
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feat: Add Kadane's 2D algorithm for maximum sum rectangle
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‎src/main/java/com/thealgorithms/matrix/Kadane2D.java‎

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package com.thealgorithms.matrix;
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/**
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* Kadane's Algorithm for 2D arrays (Maximum Sum Rectangle in a 2D Matrix)
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*
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* This algorithm finds the maximum sum of elements in a rectangular submatrix
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* of a given 2D matrix. It uses Kadane's algorithm for 1D arrays extended to 2D.
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*
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* Time Complexity: O(n^2 * m) where n is the number of columns and m is the number of rows
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* Space Complexity: O(m) for the temporary array
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*
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* @author Adarsh Singh
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*/
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public final class Kadane2D {
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/**
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* Finds the maximum sum rectangle in a 2D matrix
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*
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* @param matrix The input 2D matrix
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* @return The maximum sum found in any rectangular submatrix
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* @throws IllegalArgumentException if matrix is null or empty
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*/
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public static int maxSumRectangle(int[][] matrix) {
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if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
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throw new IllegalArgumentException("Matrix cannot be null or empty");
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}
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int rows = matrix.length;
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int cols = matrix[0].length;
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int maxSum = Integer.MIN_VALUE;
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// Fix the left column
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for (int left = 0; left < cols; left++) {
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int[] temp = new int[rows];
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// Calculate sum between left and right columns
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for (int right = left; right < cols; right++) {
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// Add elements of current column to temp array
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for (int i = 0; i < rows; i++) {
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temp[i] += matrix[i][right];
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}
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// Apply Kadane's 1D algorithm on temp array
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int currentMax = kadane1D(temp);
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maxSum = Math.max(maxSum, currentMax);
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}
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}
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return maxSum;
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}
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/**
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* Kadane's algorithm for 1D array
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* Finds maximum sum of contiguous subarray
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*
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* @param arr The input array
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* @return Maximum sum of contiguous subarray
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*/
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private static int kadane1D(int[] arr) {
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int maxSoFar = arr[0];
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int maxEndingHere = arr[0];
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for (int i = 1; i < arr.length; i++) {
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maxEndingHere = Math.max(arr[i], maxEndingHere + arr[i]);
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maxSoFar = Math.max(maxSoFar, maxEndingHere);
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}
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return maxSoFar;
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}
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/**
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* Result class to store coordinates along with maximum sum
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*/
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public static class Result {
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public final int maxSum;
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public final int topRow;
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public final int leftCol;
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public final int bottomRow;
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public final int rightCol;
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public Result(int maxSum, int topRow, int leftCol, int bottomRow, int rightCol) {
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this.maxSum = maxSum;
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this.topRow = topRow;
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this.leftCol = leftCol;
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this.bottomRow = bottomRow;
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this.rightCol = rightCol;
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}
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@Override
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public String toString() {
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return String.format("Max Sum: %d, Top-Left: (%d, %d), Bottom-Right: (%d, %d)",
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maxSum, topRow, leftCol, bottomRow, rightCol);
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}
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}
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/**
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* Finds the maximum sum rectangle along with its coordinates
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*
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* @param matrix The input 2D matrix
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* @return Result object containing maximum sum and rectangle coordinates
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* @throws IllegalArgumentException if matrix is null or empty
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*/
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public static Result maxSumRectangleWithCoordinates(int[][] matrix) {
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if (matrix == null || matrix.length == 0 || matrix[0].length == 0) {
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throw new IllegalArgumentException("Matrix cannot be null or empty");
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}
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int rows = matrix.length;
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int cols = matrix[0].length;
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int maxSum = Integer.MIN_VALUE;
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int finalLeft = 0, finalRight = 0, finalTop = 0, finalBottom = 0;
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for (int left = 0; left < cols; left++) {
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int[] temp = new int[rows];
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for (int right = left; right < cols; right++) {
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for (int i = 0; i < rows; i++) {
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temp[i] += matrix[i][right];
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}
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// Modified Kadane's to track row positions
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int currentSum = temp[0];
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int maxTemp = temp[0];
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int start = 0, end = 0, s = 0;
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for (int i = 1; i < rows; i++) {
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if (currentSum < 0) {
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currentSum = temp[i];
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s = i;
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} else {
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currentSum += temp[i];
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}
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if (currentSum > maxTemp) {
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maxTemp = currentSum;
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start = s;
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end = i;
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}
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}
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if (maxTemp > maxSum) {
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maxSum = maxTemp;
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finalLeft = left;
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finalRight = right;
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finalTop = start;
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finalBottom = end;
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}
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}
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}
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return new Result(maxSum, finalTop, finalLeft, finalBottom, finalRight);
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}
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}

‎src/test/java/com/thealgorithms/matrix/Kadane2DTest.java‎

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package com.thealgorithms.matrix;
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import org.junit.jupiter.api.Test;
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import static org.junit.jupiter.api.Assertions.*;
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/**
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* Test cases for Kadane2D algorithm
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*/
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class Kadane2DTest {
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@Test
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void testBasicMatrix() {
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int[][] matrix = {
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{1, 2, -1, -4, -20},
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{-8, -3, 4, 2, 1},
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{3, 8, 10, 1, 3},
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{-4, -1, 1, 7, -6}
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};
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assertEquals(29, Kadane2D.maxSumRectangle(matrix));
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}
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@Test
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void testAllPositive() {
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int[][] matrix = {
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{1, 2, 3},
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{4, 5, 6},
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{7, 8, 9}
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};
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// Sum of all elements
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assertEquals(45, Kadane2D.maxSumRectangle(matrix));
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}
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@Test
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void testAllNegative() {
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int[][] matrix = {
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{-1, -2, -3},
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{-4, -5, -6},
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{-7, -8, -9}
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};
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// Maximum single element (least negative)
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assertEquals(-1, Kadane2D.maxSumRectangle(matrix));
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}
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@Test
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void testSingleElement() {
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int[][] matrix = {{5}};
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assertEquals(5, Kadane2D.maxSumRectangle(matrix));
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}
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@Test
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void testSingleRow() {
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int[][] matrix = {{-2, 1, -3, 4, -1, 2, 1, -5, 4}};
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assertEquals(6, Kadane2D.maxSumRectangle(matrix));
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}
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@Test
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void testSingleColumn() {
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int[][] matrix = {{-2}, {1}, {-3}, {4}, {-1}, {2}, {1}, {-5}, {4}};
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assertEquals(6, Kadane2D.maxSumRectangle(matrix));
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}
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@Test
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void testMixedValues() {
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int[][] matrix = {
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{2, 1, -3, -4},
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{-5, -1, 4, 0},
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{1, 2, 3, -2}
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};
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assertEquals(9, Kadane2D.maxSumRectangle(matrix));
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}
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@Test
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void testWithCoordinates() {
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int[][] matrix = {
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{1, 2, -1, -4, -20},
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{-8, -3, 4, 2, 1},
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{3, 8, 10, 1, 3},
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{-4, -1, 1, 7, -6}
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};
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Kadane2D.Result result = Kadane2D.maxSumRectangleWithCoordinates(matrix);
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assertEquals(29, result.maxSum);
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assertEquals(1, result.topRow);
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assertEquals(1, result.leftCol);
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assertEquals(2, result.bottomRow);
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assertEquals(3, result.rightCol);
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}
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@Test
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void testNullMatrix() {
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assertThrows(IllegalArgumentException.class, () -> {
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Kadane2D.maxSumRectangle(null);
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});
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}
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@Test
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void testEmptyMatrix() {
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assertThrows(IllegalArgumentException.class, () -> {
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Kadane2D.maxSumRectangle(new int[0][0]);
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});
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}
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@Test
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void testZeroMatrix() {
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int[][] matrix = {
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{0, 0, 0},
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{0, 0, 0},
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{0, 0, 0}
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};
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assertEquals(0, Kadane2D.maxSumRectangle(matrix));
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}
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}

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