​EscapeRooms

Problem Statement:
The EscapeRooms game consists of a grid ‘play’ representing a house of m * n size (m rows and n columns) where each cell represents a room. The grid is randomly generated with values 0 and -1. Now, you need to find out the total number of different possible paths to travel from the top left to the bottom right of this grid. Avoid backtracking – you can only move one step right or one step down.

There are certain rules to play this game:
1. To reach a cell with coordinates (m-1,n-1) a player can only start from the top left (0, 0) of the grid.
2. The player can only move one step right or one step down of the grid. This means that if he is currently at [0, 1] cell, he can move to either [0, 2] or [1, 1] room only 

3. There are few random cells in the grid with value -1 representing rooms that are locked via which no player can pass and remaining cells have value 0.
The number of locked rooms is indicated by a positive integer p and their positions are provided in a positive integer array numbers of size p * 2 such that the positions are to be read in pair. The locked rooms will have value -1.
figure,  
p=2,
numbers[4] = {1, 0, 2, 1}
which means in the grid play[3][3], 2 rooms are locked and their positions are play[1][0] and play[2][1] wherein first pair of the array numbers is [1,0] and 2nd pair is [2,1].

We need to count the number of paths a player can take to travel from [0,0] to [m-1, n-1].

public class EscapeRooms {

public static void main(String[] args) {
/*
* Case 1;
*/
int m = 5;
int n = 4;
int p = 4;
int[] numbers = {1,1,2,2,3,0,4,2};
// Ans : 3
/*
* Case 2
int m = 4;
int n = 3;
int p = 2;
int[] numbers = {2,0,2,2};
// Ans : 2
*/
/*
* Case 3
int m = 10;
int n = 5;
int p = 5;
int[] numbers = {2, 4, 3, 1, 6, 2, 8, 1, 9, 3};
// Ans : 179
*/
/*
* Case 4
int m = 2;
int n = 2;
int p = 1;
int[] numbers = {0, 1};
// Ans : 1
*/
long start = System.currentTimeMillis();
System.out.println(findPaths(m, n, p, numbers));
System.out.println("Time taken : " + (System.currentTimeMillis() - start) + " ms");
}

public static int findPaths(int m, int n, int p, int[] numbers) {

int[][] rooms = new int[m][n];
int i = 0;
while(p > 0) {
rooms[numbers[i]][numbers[i+1]] = -1;
i = i+2;
p--;
}

int count = totalPaths(m-1, n-1, rooms);
return count;
}

public static int totalPaths(int m, int n, int[][] rooms) {

int no = 0;
if(m == 0 && n == 0) {
return 1;
}
if(m == 0 && n > 0 && rooms[m][n] == 0) {
no = totalPaths(m, n-1, rooms);
} else if(m > 0 && n == 0 && rooms[m][n] == 0) {
no = totalPaths(m-1, n, rooms);
} else if(rooms[m][n] == 0){
int no1 = totalPaths(m-1, n, rooms);
int no2 = totalPaths(m, n-1, rooms);
no = no1 + no2;
}
if(rooms[m][n] == 0)
rooms[m][n] = no;
else if(rooms[m][n] > 0)
no = rooms[m][n];
return no;
}

}