LEL.js

var longestIncreasingPath = function(matrix) {
    
    if (matrix.length === 0) return 0;
    if (matrix[0].length === 0) return 0;
    
    var m = matrix.length;
    var n = matrix[0].length;
    var max = -99999
    var memory = [];
    for (var p = 0; p < m; p++) {
       memory.push([]);
       for (var q = 0; q < n; q++) {
           memory[p].push(0); 
       }
    }
    
    for (var i = 0; i < m; i++) {
        for (var j = 0; j < n; j++) {
            var path = getLongestPath(matrix, i, j, -1, 0, memory);
            
            if (path > max) max = path;
        }
    }
    console.log(memory);
    return max;
};

var getLongestPath = function(matrix, m, n, number, length, memory) {
    var coords = [[0, -1], [0, 1], [1, 0], [-1, 0]];
    var max = -9999;
    
    if (m < 0 || m >= matrix.length) return 0;
    if (n < 0 || n >= matrix[0].length) return 0;
    if (number >= matrix[m][n]) return 0;
    if (memory[m][n]) return memory[m][n];
    
    for (var i = 0; i < coords.length; i++) {
        var path = getLongestPath(matrix, m + coords[i][0], n + coords[i][1], matrix[m][n], length, memory) + 1;
        if (path > max) max = path;
    }
    memory[m][n] = max;
    return max;
}