Add maze recursion algorithm (#3204)
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Ong Lip Wei
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src/main/java/com/thealgorithms/backtracking/MazeRecursion.java
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158
src/main/java/com/thealgorithms/backtracking/MazeRecursion.java
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package com.thealgorithms.backtracking;
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public class MazeRecursion {
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public static void mazeRecursion() {
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// First create a 2 dimensions array to mimic a maze map
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int[][] map = new int[8][7];
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int[][] map2 = new int[8][7];
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// We use 1 to indicate wall
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// Set the ceiling and floor to 1
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for (int i = 0; i < 7; i++) {
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map[0][i] = 1;
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map[7][i] = 1;
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}
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// Then we set the left and right wall to 1
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for (int i = 0; i < 8; i++) {
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map[i][0] = 1;
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map[i][6] = 1;
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}
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// Now we have created a maze with its wall initialized
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// Here we set the obstacle
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map[3][1] = 1;
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map[3][2] = 1;
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// Print the current map
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System.out.println("The condition of the map： ");
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for (int i = 0; i < 8; i++) {
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for (int j = 0; j < 7; j++) {
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System.out.print(map[i][j] + " ");
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}
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System.out.println();
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}
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// clone another map for setWay2 method
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for (int i = 0; i < map.length; i++) {
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for (int j = 0; j < map[i].length; j++) {
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map2[i][j] = map[i][j];
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}
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}
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// By using recursive backtracking to let your ball(target) find its way in the
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// maze
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// The first parameter is the map
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// Second parameter is x coordinate of your target
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// Thrid parameter is the y coordinate of your target
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setWay(map, 1, 1);
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setWay2(map2, 1, 1);
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// Print out the new map1, with the ball footprint
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System.out.println("After the ball goes through the map1，show the current map1 condition");
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for (int i = 0; i < 8; i++) {
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for (int j = 0; j < 7; j++) {
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System.out.print(map[i][j] + " ");
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}
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System.out.println();
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}
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// Print out the new map2, with the ball footprint
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System.out.println("After the ball goes through the map2，show the current map2 condition");
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for (int i = 0; i < 8; i++) {
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for (int j = 0; j < 7; j++) {
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System.out.print(map2[i][j] + " ");
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}
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System.out.println();
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}
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}
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// Using recursive path finding to help the ball find its way in the maze
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// Description：
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// 1. map (means the maze)
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// 2. i, j (means the initial coordinate of the ball in the maze)
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// 3. if the ball can reach the end of maze, that is position of map[6][5],
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// means the we have found a path for the ball
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// 4. Additional Information： 0 in the map[i][j] means the ball has not gone
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// through this position, 1 means the wall, 2 means the path is feasible, 3
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// means the ball has gone through the path but this path is dead end
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// 5. We will need strategy for the ball to pass through the maze for example:
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// Down -> Right -> Up -> Left, if the path doesn't work, then backtrack
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/**
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*
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* @Description
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* @author OngLipWei
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* @date Jun 23, 202111:36:14 AM
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* @param map The maze
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* @param i x coordinate of your ball(target)
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* @param j y coordinate of your ball(target)
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* @return If we did find a path for the ball，return true，else false
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*/
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public static boolean setWay(int[][] map, int i, int j) {
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if (map[6][5] == 2) {// means the ball find its path, ending condition
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return true;
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}
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if (map[i][j] == 0) { // if the ball haven't gone through this point
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// then the ball follows the move strategy : down -> right -> up -> left
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map[i][j] = 2; // we assume that this path is feasible first, set the current point to 2 first。
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if (setWay(map, i + 1, j)) { // go down
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return true;
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} else if (setWay(map, i, j + 1)) { // go right
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return true;
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} else if (setWay(map, i - 1, j)) { // go up
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return true;
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} else if (setWay(map, i, j - 1)) { // go left
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return true;
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} else {
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// means that the current point is the dead end, the ball cannot proceed, set
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// the current point to 3 and return false, the backtraking will start, it will
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// go to the previous step and check for feasible path again
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map[i][j] = 3;
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return false;
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}
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} else { // if the map[i][j] != 0 , it will probably be 1,2,3, return false because the
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// ball cannot hit the wall, cannot go to the path that has gone though before,
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// and cannot head to deadend.
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return false;
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}
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}
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// Here is another move strategy for the ball: up->right->down->left
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public static boolean setWay2(int[][] map, int i, int j) {
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if (map[6][5] == 2) {// means the ball find its path, ending condition
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return true;
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}
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if (map[i][j] == 0) { // if the ball haven't gone through this point
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// then the ball follows the move strategy : up->right->down->left
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map[i][j] = 2; // we assume that this path is feasible first, set the current point to 2 first。
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if (setWay2(map, i - 1, j)) { // go up
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return true;
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} else if (setWay2(map, i, j + 1)) { // go right
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return true;
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} else if (setWay2(map, i + 1, j)) { // go down
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return true;
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} else if (setWay2(map, i, j - 1)) { // go left
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return true;
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} else {
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// means that the current point is the dead end, the ball cannot proceed, set
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// the current point to 3 and return false, the backtraking will start, it will
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// go to the previous step and check for feasible path again
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map[i][j] = 3;
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return false;
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}
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} else { // if the map[i][j] != 0 , it will probably be 1,2,3, return false because the
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// ball cannot hit the wall, cannot go to the path that has gone though before,
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// and cannot head to deadend.
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return false;
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}
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}
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}
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@ -0,0 +1,78 @@
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package com.thealgorithms.backtracking;
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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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* @author onglipwei
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* @create 2022-08-03 5:17 AM
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*/
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public class MazeRecursionTest {
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@Test
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public void testMaze() {
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// First create a 2 dimensions array to mimic a maze map
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int[][] map = new int[8][7];
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int[][] map2 = new int[8][7];
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// We use 1 to indicate wall
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// Set the ceiling and floor to 1
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for (int i = 0; i < 7; i++) {
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map[0][i] = 1;
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map[7][i] = 1;
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}
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// Then we set the left and right wall to 1
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for (int i = 0; i < 8; i++) {
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map[i][0] = 1;
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map[i][6] = 1;
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}
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// Now we have created a maze with its wall initialized
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// Here we set the obstacle
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map[3][1] = 1;
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map[3][2] = 1;
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//clone another map for setWay2 method
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for (int i = 0; i < map.length;i++) {
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for (int j = 0; j < map[i].length;j++) {
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map2[i][j]=map[i][j];
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}
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}
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MazeRecursion.setWay(map, 1, 1);
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MazeRecursion.setWay2(map2, 1, 1);
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int expectedMap[][] = new int[][]{
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{1,1,1,1,1,1,1},
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{1,2,0,0,0,0,1},
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{1,2,2,2,0,0,1},
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{1,1,1,2,0,0,1},
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{1,0,0,2,0,0,1},
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{1,0,0,2,0,0,1},
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{1,0,0,2,2,2,1},
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{1,1,1,1,1,1,1}
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};
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int expectedMap2[][] = new int[][]{
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{1,1,1,1,1,1,1},
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{1,2,2,2,2,2,1},
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{1,0,0,0,0,2,1},
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{1,1,1,0,0,2,1},
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{1,0,0,0,0,2,1},
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{1,0,0,0,0,2,1},
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{1,0,0,0,0,2,1},
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{1,1,1,1,1,1,1}
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};
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assertArrayEquals(map, expectedMap);
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assertArrayEquals(map2, expectedMap2);
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}
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}
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