https://leetcode.com/problems/unique-paths-iii/submissions/

uniquePaths3.js

/**
 * @param {number[][]} grid
 * @return {number}
 */
var uniquePathsIII = function(grid) {
    
    const visited = new Array(grid.length).fill(0).map(() => new Array(grid[0].length).fill(0));
    let visitedCount = 0;
    const squaresToVisit = countNonObstacleSquares(grid);
    
    const traverse = (i, j) => {
        
        if(grid[i][j] === 2){ // we found the end
            if(visitedCount === squaresToVisit + 1) return 1;
            return 0;
        }
        
        const traversalResults = [
            [i, j+1], // move down
            [i, j-1], // move up
            [i+1, j], // move right
            [i-1, j] // move left
        ].filter(([y, x]) => {
            if(y < 0 || y >= grid.length) return false; // y/i out of bounds
            if(x < 0 || x >= grid[0].length) return false; // x/j out of bounds
            if(grid[y][x] === 1) return false // back at start
            if(grid[y][x] === -1) return false // cannot walk over
            if(visited[y][x] === 1) return false // already visited
            return true;
        })
        .map(([y, x]) => {
            visited[y][x] = 1; // mark as visited
            visitedCount++;
            const result = traverse(y, x);
            visited[y][x] = 0; // backtrack
            visitedCount--;
            return result;
        })
        .reduce((a, b) => a + b, 0);
        
        return traversalResults;
    };
    
    const [i, j] = findStart(grid);
    return traverse(i, j);
};

function countNonObstacleSquares(grid) {
    let count = 0;
    for(let i=0; i<grid.length; i++)  {
        for(let j=0; j<grid[i].length; j++){
            if(grid[i][j] === 0) count++;
        }
    }
    return count;
}

function findStart(grid) {
    for(let i=0; i<grid.length; i++)  {
        for(let j=0; j<grid[i].length; j++){
            if(grid[i][j] === 1) return [i, j];
        }
    }
    throw new Error('Grid does not contain a start (1) square');
};