Analysis of sum from root to leaf node

Analysis of sum from root to leaf node in a tree

Problem statement:
Find minimum sum for each path from root node to leaf node in a tree. 
        0
     / |   \
    5  3    6
    /  /\   /\
   4  2  0  1 5
      /  /
     1  10
     \
      1
Julia's analysis: January 13, 2018 
Go over all the paths
0->5->4   9
0->3->2->1->1  7
0->3->0->10   13
0->6->1  7
0->6->5  11
Find minimum value 
total 5 paths, not path itself, need minimum sales path -> Math.min(9, 7, 13, 7, 11) -> minimum 7 
DFS search: 
depth first search -> recursive
Template: 
if the node is null
return 0
base case
if there is no child
return node.value
// have multiple child
minPath = Int.Max
foreach child
   fidnMinPath
   update minPath
   
return node.value + minPath   
recurrence formula
Write code