# Sum of Two Numbers in BSTs - Amazon Top Interview Questions

### Problem Statement :

```You are given two binary search trees a and b and an integer target. Return whether there's a number in a and a number in b such that their sum equals to target

Constraints

n ≤ 100,000 where n is the number of nodes in a
m ≤ 100,000 where m is the number of nodes in b

Example 1

Input

a = [5, [3, null, null], [7, null, null]]
b = [4, [2, null, null], [8, null, null]]

target = 9

Output

True

Explanation

We can pick 7 from a and 2 from b.

Example 2

Input

a = [5, [3, null, null], [7, null, null]]
b = [4, [2, null, null], [8, null, null]]

target = 4

Output

False```

### Solution :

```                        ```Solution in C++ :

bool solve(Tree* a, Tree* b, int target) {
vector<Tree*> aStk;
vector<Tree*> bStk;

while ((a || !aStk.empty()) && (b || !bStk.empty())) {
while (a) {
aStk.push_back(a);
a = a->left;
}

while (b) {
bStk.push_back(b);
b = b->right;
}

int sm = aStk.back()->val + bStk.back()->val;
if (sm == target) return true;

if (sm < target) {
// need to increase sm
a = aStk.back();
aStk.pop_back();
a = a->right;
} else {
b = bStk.back();
bStk.pop_back();
b = b->left;
}
}

return false;
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, a, b, target):

d = set()

# iterate through a and save values
s = []
root = a
while True:
while root:
s.append(root)
root = root.left

if not s:
break

# add target - val to our set
node = s.pop()

root = node.right

# iterate through b and see if a value exists in our set
s = []
root = b
while True:
while root:
s.append(root)
root = root.left

if not s:
break

node = s.pop()
if node.val in d:
return True

root = node.right

return False```
```

## Kitty's Calculations on a Tree

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## Is This a Binary Search Tree?

For the purposes of this challenge, we define a binary tree to be a binary search tree with the following ordering requirements: The data value of every node in a node's left subtree is less than the data value of that node. The data value of every node in a node's right subtree is greater than the data value of that node. Given the root node of a binary tree, can you determine if it's also a

## Square-Ten Tree

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## Balanced Forest

Greg has a tree of nodes containing integer data. He wants to insert a node with some non-zero integer value somewhere into the tree. His goal is to be able to cut two edges and have the values of each of the three new trees sum to the same amount. This is called a balanced forest. Being frugal, the data value he inserts should be minimal. Determine the minimal amount that a new node can have to a

## Jenny's Subtrees

Jenny loves experimenting with trees. Her favorite tree has n nodes connected by n - 1 edges, and each edge is ` unit in length. She wants to cut a subtree (i.e., a connected part of the original tree) of radius r from this tree by performing the following two steps: 1. Choose a node, x , from the tree. 2. Cut a subtree consisting of all nodes which are not further than r units from node x .

## Tree Coordinates

We consider metric space to be a pair, , where is a set and such that the following conditions hold: where is the distance between points and . Let's define the product of two metric spaces, , to be such that: , where , . So, it follows logically that is also a metric space. We then define squared metric space, , to be the product of a metric space multiplied with itself: . For