Last updated on October 5th, 2024 at 05:50 pm

Here, We see Out of Boundary Paths LeetCode Solution. This Leetcode problem is done in many programming languages like C++, Java, JavaScript, Python, etc. with different approaches.

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Out of Boundary Paths LeetCode Solution

Problem Statement

There is an m x n grid with a ball. The ball is initially at the position [startRow, startColumn]. You are allowed to move the ball to one of the four adjacent cells in the grid (possibly out of the grid crossing the grid boundary). You can apply at most maxMove moves to the ball.

Given the five integers m, n, maxMove, startRow, startColumn, return the number of paths to move the ball out of the grid boundary. Since the answer can be very large, return it modulo 109 + 7.

Example 1:

Input: m = 2, n = 2, maxMove = 2, startRow = 0, startColumn = 0
Output: 6

Example 2:

Input: m = 1, n = 3, maxMove = 3, startRow = 0, startColumn = 1
Output: 12

1. Out of Boundary Paths LeetCode Solution C++

class Solution {
public:
    int findPaths(int m, int n, int maxMove, int startRow, int startColumn) {
        const int M = 1000000000 + 7;
        vector<vector<int>> dp(m, vector<int>(n, 0));
        dp[startRow][startColumn] = 1;
        int count = 0;
        for (int moves = 1; moves <= maxMove; moves++) {
            vector<vector<int>> temp(m, vector<int>(n, 0));
            for (int i = 0; i < m; i++) {
                for (int j = 0; j < n; j++) {
                    if (i == m - 1) count = (count + dp[i][j]) % M;
                    if (j == n - 1) count = (count + dp[i][j]) % M;
                    if (i == 0) count = (count + dp[i][j]) % M;
                    if (j == 0) count = (count + dp[i][j]) % M;
                    temp[i][j] = (
                        ((i > 0 ? dp[i - 1][j] : 0) + (i < m - 1 ? dp[i + 1][j] : 0)) % M +
                        ((j > 0 ? dp[i][j - 1] : 0) + (j < n - 1 ? dp[i][j + 1] : 0)) % M
                    ) % M;
                }
            }
            dp = temp;
        }
        return count;
    }
};

2. Out of Boundary Paths LeetCode Solution Java

class Solution {
    public int findPaths(int m, int n, int maxMove, int startRow, int startColumn) {
        final int M = 1000000000 + 7;
        int[][] dp = new int[m][n];
        dp[startRow][startColumn] = 1;
        int count = 0;
        for (int moves = 1; moves <= maxMove; moves++) {
            int[][] temp = new int[m][n];
            for (int i = 0; i < m; i++) {
                for (int j = 0; j < n; j++) {
                    if (i == m - 1) count = (count + dp[i][j]) % M;
                    if (j == n - 1) count = (count + dp[i][j]) % M;
                    if (i == 0) count = (count + dp[i][j]) % M;
                    if (j == 0) count = (count + dp[i][j]) % M;
                    temp[i][j] = (
                            ((i > 0 ? dp[i - 1][j] : 0) + (i < m - 1 ? dp[i + 1][j] : 0)) % M +
                            ((j > 0 ? dp[i][j - 1] : 0) + (j < n - 1 ? dp[i][j + 1] : 0)) % M
                    ) % M;
                }
            }
            dp = temp;
        }
        return count;        
    }
}

3. Out of Boundary Paths LeetCode Solution JavaScript

var findPaths = function(m, n, maxMove, startRow, startColumn) {
    const M = 1000000000 + 7;
    let dp = new Array(m).fill(0).map(() => new Array(n).fill(0));
    dp[startRow][startColumn] = 1;
    let count = 0;
    for (let moves = 1; moves <= maxMove; moves++) {
        let temp = new Array(m).fill(0).map(() => new Array(n).fill(0));
        for (let i = 0; i < m; i++) {
            for (let j = 0; j < n; j++) {
                if (i === m - 1) count = (count + dp[i][j]) % M;
                if (j === n - 1) count = (count + dp[i][j]) % M;
                if (i === 0) count = (count + dp[i][j]) % M;
                if (j === 0) count = (count + dp[i][j]) % M;
                temp[i][j] = (
                    ((i > 0 ? dp[i - 1][j] : 0) + (i < m - 1 ? dp[i + 1][j] : 0)) % M +
                    ((j > 0 ? dp[i][j - 1] : 0) + (j < n - 1 ? dp[i][j + 1] : 0)) % M
                ) % M;
            }
        }
        dp = temp;
    }
    return count;    
};

4. Out of Boundary Paths LeetCode Solution Python

class Solution(object):
    def findPaths(self, m, n, maxMove, startRow, startColumn):
        M = 1000000000 + 7
        dp = [[0] * n for _ in range(m)]
        dp[startRow][startColumn] = 1
        count = 0
        for moves in range(1, maxMove + 1):
            temp = [[0] * n for _ in range(m)]
            for i in range(m):
                for j in range(n):
                    if i == m - 1:
                        count = (count + dp[i][j]) % M
                    if j == n - 1:
                        count = (count + dp[i][j]) % M
                    if i == 0:
                        count = (count + dp[i][j]) % M
                    if j == 0:
                        count = (count + dp[i][j]) % M
                    temp[i][j] = (
                        ((dp[i - 1][j] if i > 0 else 0) + (dp[i + 1][j] if i < m - 1 else 0)) % M +
                        ((dp[i][j - 1] if j > 0 else 0) + (dp[i][j + 1] if j < n - 1 else 0)) % M
                    ) % M
            dp = temp
        return count