Skiing in Singapore

Try to solve the problem at http://geeks.redmart.com/2015/01/07/skiing-in-singapore-a-coding-diversion/

1. Transform txt file to array

Sample data from source

[
  ["4", "8", "7", "3"],
  ["2", "5", "9", "3"],
  ["6", "3", "2", "5"],
  ["4", "4", "1", "6"]
]

2. Find the in-out directions of every node and store back to array

The result is the the length and the different between first and last node values, so I don't have to care about the value along the path if it is not the first node.

[
  ["←,↓,?,?",  "8",         "↑→,→,?,?",  "→,,1,3"],
  ["↓←↑,,1,2", "↓←,↓←,?,?", "9",         "↑→,,1,3"],
  ["6",        "↓↑→,→,?,?", "↓←→,↓,?,?", "↑,↑←,?,?"],
  ["↓,,1,4",   "4",         "↓←→,,1,1",  "6"]
]

I store the new value in format {a, b, c, d}

• a -> possible coming directions
• b -> possible going directions
• c -> number of nodes to last node
• d -> last node value

Only last node will have c and d value at this stage, ? indicate that currently is unknown

3. Start from the number

Node that does not have the way to go higher will be the starting point. After started with "8" the array will looks like this

[
  ["←,↓,2,2",  "8",         "↑→,→,2,3",  "→,,1,3"],
  ["↓←↑,,1,2", "↓←,↓←,4,1", "9",         "↑→,,1,3"],
  ["6",        "↓↑→,→,3,1", "↓←→,↓,2,1", "↑,↑←,?,?"],
  ["↓,,1,4",   "4",         "↓←→,,1,1",  "6"]
]

Next time when run "9" it will not run all the previous paths again, just use the stored values.

4. Compare every number paths

The final array is

[
  ["←,↓,2,2",  "8",         "↑→,→,2,3",  "→,,1,3"],
  ["↓←↑,,1,2", "↓←,↓←,4,1", "9",         "↑→,,1,3"],
  ["6",        "↓↑→,→,3,1", "↓←→,↓,2,1", "↑,↑←,3,1"],
  ["↓,,1,4",   "4",         "↓←→,,1,1",  "6"]
]

Take a look at "9" the most longest length is "↓←,↓←,4,1" so the result is

length: 4 + 1 = 5 // plus 1 for 9 itself
size: 9 - 1 = 8