Cracking the Coding Interview, 4 Edition - 150 Programming Interview Questions and Solutions

Solutions to Chapter 4 | Trees and Graphs
4.8 You are given a binary tree in which each node contains a value. Design an algorithm
to print all paths which sum up to that value. Note that it can be any path in the tree
- it does not have to start at the root.
SOLUTION
pg 54
Let’s approach this problem by simplifying it. What if the path had to start at the root? In that
case, we would have a much easier problem:
Start from the root and branch left and right, computing the sum thus far on each path.
When we find the sum, we print the current path. Note that we don’t stop just because
we found the sum. Why? Because we could have the following path (assume we are
looking for the sum 5): 2 + 3 + –4 + 3 + 1 + 2. If we stopped once we hit 2 + 3, we’d miss
several paths (2 + 3 + -4 + 3 + 1 and 3 + -4 + 3 + 1 + 2). So, we keep going along every
possible path.
Now, what if the path can start anywhere? In that case, we make a small modification. On
every node, we look “up” to see if we’ve found the sum. That is—rather than asking “does
this node start a path with the sum?,” we ask “does this node complete a path with the sum?”
1 void findSum(TreeNode head, int sum, ArrayList buffer,
2 int level) {
3 if (head == null) return;
4 int tmp = sum;
5 buffer.add(head.data);
6 for (int i = level;i >- 1; i--){
7 tmp -= buffer.get(i);
8 if (tmp == 0) print(buffer, i, level);
9 }
10 ArrayList c1 = (ArrayList) buffer.clone();
11 ArrayList c2 = (ArrayList) buffer.clone();
12 findSum(head.left, sum, c1, level + 1);
13 findSum(head.right, sum, c2, level + 1);
14 }
15
16 void print(ArrayList buffer, int level, int i2) {
17 for (int i = level; i