666. Path Sum IV

If the depth of a tree is smaller than 5, then this tree can be represented by a list of three-digits integers.

For each integer in this list:

1. The hundreds digit represents the depth D of this node, 1 <= D <= 4.
2. The tens digit represents the position P of this node in the level it belongs to, 1 <= P <= 8. The position is the same as that in a full binary tree.
3. The units digit represents the value V of this node, 0 <= V <= 9.

Given a list of ascending three-digits integers representing a binary with the depth smaller than 5. You need to return the sum of all paths from the root towards the leaves.

Example 1:

Input: [113, 215, 221]
Output: 12
Explanation: 
The tree that the list represents is:
    3
   / 
  5   1

The path sum is (3 + 5) + (3 + 1) = 12.

Example 2:

Input: [113, 221]
Output: 4
Explanation: 
The tree that the list represents is: 
    3
     
      1

The path sum is (3 + 1) = 4.

先转换为树，可以用hashmap表示树，ref: https://leetcode.com/problems/path-sum-iv/discuss/106892/Java-solution-Represent-tree-using-HashMap

time: O(n), space: O(n)

class Solution {
    int sum = 0;
    Map<Integer, Integer> tree;
    
    public int pathSum(int[] nums) {
        if(nums == null || nums.length == 0) {
            return 0;
        }
        tree = new HashMap<>();
        for(int n : nums) {
            int k = n / 10;
            int v = n % 10;
            tree.put(k, v);
        }
        
        dfs(nums[0] / 10, 0);
        return sum;
    }
    
    public void dfs(int root, int preSum) {
        int depth = root / 10;
        int pos = root % 10;
        
        int left = (depth + 1) * 10 + pos * 2 - 1;
        int right = (depth + 1) * 10 + pos * 2;
        
        int curSum = preSum + tree.get(root);
        
        if(!tree.containsKey(left) && !tree.containsKey(right)) {
            sum += curSum;
            return;
        }
        if(tree.containsKey(left)) {
            dfs(left, curSum);
        }
        if(tree.containsKey(right)) {
            dfs(right, curSum);
        }
    }
}