Consider a map of city streets, in the form of a grid.
You'd like to know if it's possible to make your way to the exit, under the following rules:
• You begin from the left side of the square in the top-left corner;
• The exit is on the right side of the square in the bottom-right corner;
• You must travel along a connected path between squares.
You're given directions, a matrix of integers representing the grid of streets, where each integer corresponds to a different type of road square:
• 0 stands for 
• 1 stands for 
• 2 stands for 
• 3 stands for 
• 4 stands for 
• 5 stands for 
Your task is to return true if it's possible to reach the exit, and false otherwise.
Example
• For directions = [[0, 2, 1], [5, 4, 0]], the output should be solution(directions) = true.
The map looks as follows:
It's possible to enter the top-left square from the left, travel along a connected path, and exit the right side of the bottom-right square. So the answer is true.
• For directions = [[0, 2, 1], [5, 4, 1]], the output should be solution(directions) = false.
The map looks as follows:
It's possible to enter the top-left square from the left, but there's no connected path that leads to the bottom-right square. So the answer is false.
• For directions = [[0, 2, 1], [5, 4, 2]], the output should be solution(directions) = false.
The map looks as follows:
The path leading to the bottom-right square exists, but it doesn't exit to the right.
• For directions = [[1], [4]], the output should be solution(directions) = false.
The map looks as follows:
It's possible to travel along the path to the exit, but the entrance isn't in the right place.
Input/Output
• [execution time limit] 3 seconds (java)
• [input] array.array.integer directions
The map of streets, represented as the rectangular matrix of integers.
Guaranteed constraints:
1 ≤ directions.length ≤ 100,
1 ≤ directions[0].length ≤ 100,
directions[i].length = directions[0].length,
0 ≤ directions[i][j] ≤ 5.
• [output] boolean
true if it's possible to reach the right side of the bottom right corner along a connected path from the left side of the top left corner, and false otherwise.