Longest Increasing Path in a Matrix

Given an integer matrix, find the length of the longest increasing path.

From each cell, you can either move to four directions: left, right, up or down. You may NOT move diagonally or move outside of the boundary (i.e. wrap-around is not allowed).

Example 1:

nums = [
  [9,9,4],
  [6,6,8],
  [2,1,1]
]

Return 4
The longest increasing path is [1, 2, 6, 9].

Example 2:

nums = [
  [3,4,5],
  [3,2,6],
  [2,2,1]
]

Return 4
The longest increasing path is [3, 4, 5, 6]. Moving diagonally is not allowed.

Analyse: backtracking. 

Time Limit Exceeded Version.

class Solution {
public:
    int longestIncreasingPath(vector<vector<int>>& matrix) {
        int result;
        if(matrix.empty() || matrix[0].empty()) return result;
        
        int depth = 0;
        vector<vector<bool> > visited(matrix.size(), vector<bool>(matrix[0].size(), false));
        for(int i = 0; i < matrix.size(); i++){
            for(int j = 0; j < matrix[i].size(); j++){
                helper(matrix, visited, i, j, result, depth, INT_MIN);
            }
        }
        return result;
    }
    
    void helper(vector<vector<int> >& matrix, vector<vector<bool> > visited, int i, int j, int& result, int depth, int former){
        if(i >= matrix.size() || i < 0 || j >= matrix[i].size() || j < 0 || matrix[i][j] <= former || visited[i][j])
            return;
            
        visited[i][j] = true;
        depth++;
        result = max(result, depth);
        former = matrix[i][j];
        helper(matrix, visited, i + 1, j, result, depth, former);
        helper(matrix, visited, i - 1, j, result, depth, former);
        helper(matrix, visited, i, j + 1, result, depth, former);
        helper(matrix, visited, i, j - 1, result, depth, former);
        visited[i][j] = false;
    }
};