# Candy Race Taking Square Candies - Microsoft Top Interview Questions

### Problem Statement :

```You are given an integer n representing the number of candies. You are playing a game against a friend and in each round a player can take some positive, square number. A player that can't make a move loses.

Given that you go first and everyone plays optimally, return whether you will win.

Constraints

1 ≤ n ≤ 100,000

Example 1

Input

n = 11

Output

True

Explanation

First you can take 9 candies, leaving 2 candies. Then, your friend can only take 1 candy, leaving 1
candy. Then you can take the last candy. Since your friend can't make any more moves, you win.```

### Solution :

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

bool solve(int n) {
vector<int> dp(n + 1);
dp[0] = 0;
for (int i = 1; i <= n; i++) {
for (int j = 1; j * j <= i; j++) {
if (dp[i - j * j] == 0) dp[i] = true;
}
}
return dp[n];
}```
```

```                        ```Solution in Python :

class Solution:
def solve(self, n):
@lru_cache(None)
def can_win(candies):
if candies <= 0:
return False
res = False
for candy in range(int(sqrt(candies)), 0, -1):
if candy * candy > candies:
break
res = res | (not can_win(candies - candy * candy))
if res:
return res
return res

return can_win(n)```
```

## 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

## Array Pairs

Consider an array of n integers, A = [ a1, a2, . . . . an] . Find and print the total number of (i , j) pairs such that ai * aj <= max(ai, ai+1, . . . aj) where i < j. Input Format The first line contains an integer, n , denoting the number of elements in the array. The second line consists of n space-separated integers describing the respective values of a1, a2 , . . . an .

## Self Balancing Tree

An AVL tree (Georgy Adelson-Velsky and Landis' tree, named after the inventors) is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. We define balance factor for each node as : balanceFactor = height(left subtree) - height(righ

## Array and simple queries

Given two numbers N and M. N indicates the number of elements in the array A[](1-indexed) and M indicates number of queries. You need to perform two types of queries on the array A[] . You are given queries. Queries can be of two types, type 1 and type 2. Type 1 queries are represented as 1 i j : Modify the given array by removing elements from i to j and adding them to the front. Ty