**Longest Arithmetic Sequence Tree Path - Google Top Interview Questions**

### Problem Statement :

You are given a binary tree root. Return the length of the longest path starting from a node that goes top to bottom where its values form an arithmetic sequence. An arithmetic sequence is a sequence of numbers where the difference between each consecutive two numbers is the same. For example, [2, 4, 6, 8] is an arithmetic sequence as is [1, 4, 7, 10]. A sequence of length two or fewer is considered an arithmetic sequence. Constraints 0 ≤ n ≤ 100,000 where n is the number of nodes in root Example 1 Input root = [1, [4, [7, [0, null, null], null], null], null] Output 3

### Solution :

` ````
Solution in C++ :
int maxS = 0;
void dfs(Tree* root, int diff, int l) {
maxS = max(maxS, l);
if (!root) {
return;
}
if (root->left) {
if (root->left->val - root->val == diff) {
dfs(root->left, diff, l + 1);
} else {
dfs(root->left, root->left->val - root->val, 2);
}
}
if (root->right) {
if (root->right->val - root->val == diff) {
dfs(root->right, diff, l + 1);
} else {
dfs(root->right, root->right->val - root->val, 2);
}
}
}
int solve(Tree* root) {
if (root) {
maxS = 1;
} else {
return 0;
}
dfs(root, 0, 1);
return maxS;
}
```

` ````
Solution in Java :
import java.util.*;
/**
* public class Tree {
* int val;
* Tree left;
* Tree right;
* }
*/
class Solution {
int ans;
public int solve(Tree root) {
if (root == null) {
return 0;
}
ans = 1;
sol(root);
return ans;
}
HashMap<Integer, Integer> sol(Tree root) {
if (root == null) {
return new HashMap<>();
}
HashMap<Integer, Integer> l = sol(root.left);
HashMap<Integer, Integer> r = sol(root.right);
HashMap<Integer, Integer> mp = new HashMap<>();
if (root.left != null) {
int ldiff = root.val - root.left.val;
int x = l.getOrDefault(ldiff, 1);
int y = mp.getOrDefault(ldiff, 1);
mp.put(ldiff, Math.max(x + 1, y));
ans = Math.max(ans, mp.get(ldiff));
}
if (root.right != null) {
int rdiff = root.val - root.right.val;
int x = r.getOrDefault(rdiff, 1);
int y = mp.getOrDefault(rdiff, 1);
mp.put(rdiff, Math.max(x + 1, y));
ans = Math.max(ans, mp.get(rdiff));
}
return mp;
}
}
```

` ````
Solution in Python :
class Solution:
# global ans to use same solve function for recursion 😅
ans = 0
# diff is diffrence of cur value with prev to check airth seq
# ltill is longest airth seq ending before cur node
def solve(self, cur, ltill=0, diff=None):
# Intialize a global ans ans is max of prev longest airthmetic seq and cur longest
self.ans = max(self.ans, ltill)
# Check if ther is left child
if cur.left:
# compute diff with left child
ldiff = cur.left.val - cur.val
self.solve(
cur.left,
# if diff with previous child is diffrent
# from diff of cur from par
# or it's root new airthmetic sequence
# start from here so ltill is 1
# else extend prev max length ltill by 1
1 if diff == None or ldiff != diff else ltill + 1,
ldiff,
)
# same for right
if cur.right:
rdiff = cur.right.val - cur.val
self.solve(cur.right, 1 if diff == None or rdiff != diff else ltill + 1, rdiff)
# we start count from 0 so +1 solve single legth seq also
return self.ans + 1
```

## View More Similar Problems

## Unique Colors

You are given an unrooted tree of n nodes numbered from 1 to n . Each node i has a color, ci. Let d( i , j ) be the number of different colors in the path between node i and node j. For each node i, calculate the value of sum, defined as follows: Your task is to print the value of sumi for each node 1 <= i <= n. Input Format The first line contains a single integer, n, denoti

View Solution →## Fibonacci Numbers Tree

Shashank loves trees and math. He has a rooted tree, T , consisting of N nodes uniquely labeled with integers in the inclusive range [1 , N ]. The node labeled as 1 is the root node of tree , and each node in is associated with some positive integer value (all values are initially ). Let's define Fk as the Kth Fibonacci number. Shashank wants to perform 22 types of operations over his tree, T

View Solution →## Pair Sums

Given an array, we define its value to be the value obtained by following these instructions: Write down all pairs of numbers from this array. Compute the product of each pair. Find the sum of all the products. For example, for a given array, for a given array [7,2 ,-1 ,2 ] Note that ( 7 , 2 ) is listed twice, one for each occurrence of 2. Given an array of integers, find the largest v

View Solution →## Lazy White Falcon

White Falcon just solved the data structure problem below using heavy-light decomposition. Can you help her find a new solution that doesn't require implementing any fancy techniques? There are 2 types of query operations that can be performed on a tree: 1 u x: Assign x as the value of node u. 2 u v: Print the sum of the node values in the unique path from node u to node v. Given a tree wi

View Solution →## Ticket to Ride

Simon received the board game Ticket to Ride as a birthday present. After playing it with his friends, he decides to come up with a strategy for the game. There are n cities on the map and n - 1 road plans. Each road plan consists of the following: Two cities which can be directly connected by a road. The length of the proposed road. The entire road plan is designed in such a way that if o

View Solution →## Heavy Light White Falcon

Our lazy white falcon finally decided to learn heavy-light decomposition. Her teacher gave an assignment for her to practice this new technique. Please help her by solving this problem. You are given a tree with N nodes and each node's value is initially 0. The problem asks you to operate the following two types of queries: "1 u x" assign x to the value of the node . "2 u v" print the maxim

View Solution →