# The algorithm problem - Backtracing pattern in JavaScript

JavascriptFront End TechnologyObject Oriented ProgrammingWeb Development

Consider the following backtracing problem: On a 2−dimensional grid, there are 4 types of squares −

• 1 represents the starting square. There is exactly one starting square.

• 2 represents the ending square. There is exactly one ending square.

• 0 represents empty squares we can walk over.

• −1 represents obstacles that we cannot walk over.

We are required to write a function that returns the number of 4−directional walks from the starting square to the ending square, that walk over every non−obstacle square exactly once.

## Example

const arr = [
[1,0,0,0],
[0,0,0,0],
[0,0,2,-1]
];
const uniquePaths = (arr, count = 0) => {
const dy = [1,−1,0,0], dx = [0,0,1,−1];
const m = arr.length, n = arr[0].length;
const totalZeroes = arr.map(row => row.filter(num => num ===
0).length).reduce((totalZeroes,nextRowZeroes) => totalZeroes +
nextRowZeroes, 0);
const depthFirstSearch = (i, j, covered) => {
if (arr[i][j] === 2){
if (covered === totalZeroes + 1) count++;
return;
};
for (let k = 0; k < 4; k++)
if (i+dy[k] >= 0 && i+dy[k] < m && j+dx[k] >= 0 && j+dx[k] < n
&& arr[i+dy[k]][j+dx[k]] !== −1 ){
arr[i][j] = −1;
depthFirstSearch(i+dy[k],j+dx[k],covered+1);
arr[i][j] = 0;
}
return;
};
for (let row = 0; row < m; row++)
for (let col = 0; col < n; col++)
if (arr[row][col] === 1){
arr[row][col] = −1;
depthFirstSearch(row,col,0);
break;
}
return count;
};
console.log(uniquePaths(arr));

## Explanation

• We set up variables to facilitate four directional iteration when traversing grid, count zeroes in matrix to allow for checking coverage when base condition of recursion reached

• Then we set up the DFS (Depth First Search) backtrack function to mark grid with −1 on the active path and to check path length when the finish cell is reached

• And lastly, we launch the DFS from the start cell to count all full paths and return the count

## Output

And the output in the console will be −

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Published on 21-Nov-2020 09:26:17