**Utopian Tree**

### Problem Statement :

The Utopian Tree goes through 2 cycles of growth every year. Each spring, it doubles in height. Each summer, its height increases by 1 meter. A Utopian Tree sapling with a height of 1 meter is planted at the onset of spring. How tall will the tree be after growth cycles? For example, if the number of growth cycles is n = 5, the calculations are as follows: Period Height 0 1 1 2 2 3 3 6 4 7 5 14 Function Description Complete the utopianTree function in the editor below. utopianTree has the following parameter(s): int n: the number of growth cycles to simulate Returns int: the height of the tree after the given number of cycles Input Format The first line contains an integer, t, the number of test cases. t subsequent lines each contain an integer, n, the number of cycles for that test case. Constraints 1 <= t <= 10 0 <= n <= 60

### Solution :

` ````
Solution in C :
python 3 :
#!/usr/bin/env python
import sys
if __name__ == '__main__':
T = int(sys.stdin.readline())
for _ in range(T):
N = int(sys.stdin.readline())
height = 1
for i in range(N):
if i % 2 == 0:
height *= 2
else:
height += 1
print(height)
Java :
import java.util.Scanner;
import java.util.Vector;
public class Solution {
public static void main(String[] args) {
Scanner stdin = new Scanner(System.in);
int numCases = stdin.nextInt();
Vector<Long> cache = new Vector<>();
cache.add(1L);
for (int i = 0; i < numCases; i++) {
int numCycles = stdin.nextInt();
while(cache.size() <= numCycles) {
if (cache.size() % 2 == 0) {
cache.add(cache.lastElement() + 1);
} else {
cache.add(cache.lastElement() * 2);
}
}
System.out.println(cache.get(numCycles));
}
}
}
C ++ :
#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
int main() {
int T;
cin >> T;
for(int t = 0; t<T; t++){
int N;
cin >> N;
int ht = 1;
for(int i=0;i<N;i++){
if(i%2==0) ht*=2;
else ht++;
}
cout << ht << endl;
}
return 0;
}
C :
#include <stdio.h>
#include <string.h>
#include <math.h>
#include <stdlib.h>
int main() {
/* Enter your code here. Read input from STDIN. Print output to STDOUT */
int t,i,n;
scanf("%d",&t);
while(t>0)
{
int h=1;
scanf("%d",&n);
for(i=1;i<=n;i++)
{
if(i%2==1)
h=2*h;
else
h=h+1;
}
printf("%d\n",h);
t=t-1;
}
return 0;
}
```

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