Number of Increasing Paths in a Grid - DFS w/ Memoization [JS]

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Description 

Solution: DFS w/ Recursion & Memoization

DFS from every cell to count the number of paths from each cell.
Memoize the results of each dfs(row, column).
This solution works because each path must be strictly increasing, insuring that we never revisit a cell.

Time Complexity: O(mn) 450ms
Space Complexity: O(mn) 86.7MB

var countPaths = function(grid) {
  let m = grid.length, n = grid[0].length, mod = 10 ** 9 + 7;
  let ans = 0, memo = Array(m).fill(0).map(() => Array(n).fill(-1));
  for (let i = 0; i < m; i++) {
    for (let j = 0; j < n; j++) {
      ans = (ans + dfs(i, j)) % mod;
    }
  }
  return ans;

  function dfs(i, j) {
    const directions = [[-1, 0], [0, 1], [1, 0], [0, -1]];
    if (memo[i][j] !== -1) return memo[i][j];
    let ans = 1;
    for (let [x, y] of directions) {
      let newX = i + x, newY = j + y;
      if (newX < 0 || newX >= m || newY < 0 || newY >= n || grid[newX][newY] <= grid[i][j]) continue;
      ans = (ans + dfs(newX, newY)) % mod;
    }
    return memo[i][j] = ans;
  }     
};

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Location: Auckland, New Zealand

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