Add maze recursion algorithm (#3204)

src/main/java/com/thealgorithms/backtracking/MazeRecursion.java

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

src/test/java/com/thealgorithms/backtracking/MazeRecursionTest.java

@@ -0,0 +1,78 @@
+package com.thealgorithms.backtracking;
+
+import org.junit.jupiter.api.Test;
+import static org.junit.jupiter.api.Assertions.*;
+
+/**
+ * @author onglipwei
+ * @create 2022-08-03 5:17 AM
+ */
+public class MazeRecursionTest {
+
+    @Test
+    public void testMaze() {
+
+
+        // First create a 2 dimensions array to mimic a maze map
+        int[][] map = new int[8][7];
+        int[][] map2 = new int[8][7];
+
+        // We use 1 to indicate wall
+        // Set the ceiling and floor to 1
+        for (int i = 0; i < 7; i++) {
+            map[0][i] = 1;
+            map[7][i] = 1;
+        }
+
+        // Then we set the left and right wall to 1
+        for (int i = 0; i < 8; i++) {
+            map[i][0] = 1;
+            map[i][6] = 1;
+
+        }
+
+        // Now we have created a maze with its wall initialized
+
+        // Here we set the obstacle
+        map[3][1] = 1;
+        map[3][2] = 1;
+
+        //clone another map for setWay2 method
+        for (int i = 0; i < map.length;i++) {
+            for (int j = 0; j < map[i].length;j++) {
+                map2[i][j]=map[i][j];
+            }
+        }
+
+        MazeRecursion.setWay(map, 1, 1);
+        MazeRecursion.setWay2(map2, 1, 1);
+
+
+        int expectedMap[][] = new int[][]{
+                {1,1,1,1,1,1,1},
+                {1,2,0,0,0,0,1},
+                {1,2,2,2,0,0,1},
+                {1,1,1,2,0,0,1},
+                {1,0,0,2,0,0,1},
+                {1,0,0,2,0,0,1},
+                {1,0,0,2,2,2,1},
+                {1,1,1,1,1,1,1}
+        };
+
+        int expectedMap2[][] = new int[][]{
+                {1,1,1,1,1,1,1},
+                {1,2,2,2,2,2,1},
+                {1,0,0,0,0,2,1},
+                {1,1,1,0,0,2,1},
+                {1,0,0,0,0,2,1},
+                {1,0,0,0,0,2,1},
+                {1,0,0,0,0,2,1},
+                {1,1,1,1,1,1,1}
+        };
+
+        assertArrayEquals(map, expectedMap);
+        assertArrayEquals(map2, expectedMap2);
+
+    }
+
+}