```
class Solution(object):
def pathSum(self, nums):
"""
:type nums: List[int]
:rtype: int
"""
total, nodes_map = 0, {}
def num_to_tuple(num, i):
# The node 113 becomes a tuple of (0, 0, 3).
depth, pos, value = int(str(num)[0]) - 1, int(str(num)[1]) - 1, int(str(num)[2])
if depth not in nodes_map:
nodes_map[depth] = {}
nodes_map[depth][pos] = i
return (depth, pos, value)
# Convert numbers to tuples.
nodes = [num_to_tuple(num, i) for i, num in enumerate(nums)]
path_sums = [0] * len(nodes)
for index, node in enumerate(nodes):
depth, pos, value = node
path_sums[index] = value
# Look up the dictionary for the node's parent.
if depth - 1 in nodes_map and (pos // 2) in nodes_map[depth - 1]:
# If node has a parent, add the parent's value to the path sum.
path_sums[index] += path_sums[nodes_map[depth - 1][pos // 2]]
# Look up the dictionary for the node's children.
if not (depth + 1 in nodes_map and ((pos * 2) in nodes_map[depth + 1] or (pos * 2 + 1) in nodes_map[depth + 1])):
# If there are no children, it is a leaf. Add the path sum to the total.
total += path_sums[index]
return total
```