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# Cracking the Code CodeChef Solution

## Cracking the Code CodeChef Solution in C++14

``````#include <bits/stdc++.h>
#define pb push_back
#define sz(a) (int)a.size()
#define x 1.0*sqrt(2)
#define y 1.0*sqrt(3)
using namespace std;
typedef long long ll;
int main()
{
ios_base::sync_with_stdio(0); cin.tie(NULL);
ll i , k , s; cin >> i >> k >> s;
double ai , bi; cin >> ai >> bi;
if((i&1) != (k&1)){
double s = ai+bi;
double r = ai-bi;
ai = x*s - x*y*r;
bi = x*r + x*y*s;
i++;
}
cout << fixed << setprecision(2);
cout << 1.0 * (ai+bi) * pow(2 , 2*(k-i) - s) << endl;
return 0;
}``````

## Cracking the Code CodeChef Solution in PYTH 3

``````# cook your dish here
import math

def main():
#print("enter i, k, s")
IN = '11 6 5'
z = IN.split()
z = input().split()
i = int(z[0])
k = int(z[1])
s = int(z[2])

#print("enter a_i and b_i")
IN = '4 5'
z = IN.split()
z = input().split()
a_i = int(z[0])
b_i = int(z[1])

#print ( "i = %d   k = %d   s = %d " % (i, k, s)  )
#print ( "a_i = %d   b_i = %d" % (a_i, b_i)  )

x = math.sqrt(2)
y = math.sqrt(3)
#print(x,y)

# Obtaining the k-th element when k >= i
if(i<=k):
diff = k-i
#if both k and i are odd or even
if(k-i)%2==0:
#print("#1")
ans =  (a_i + b_i) * math.pow(2,2*(k-i)-s)
#diff = int(diff/2)
#ans =  (a_i + b_i) * math.pow(2,4*diff-s)

#if i and k are of different parities then obtaining first
# a_(i+1) and b_(i+1)
else:
#print("#2")
ans = (2*x*a_i + 2*x*y*b_i) * math.pow(2,2*(k-(i+1))-s )
diff = int(diff/2)
ans = (2*x*a_i + 2*x*y*b_i) * math.pow(2,4*diff - s)
#print("1: ", (2*x*a_i + 2*x*y*b_i))
#print("2: ", math.pow(2,4*diff - 2- s))
#print("2 sol: ", math.pow(2,4*int(diff)-s))
#print("diff: ",diff)

# Obtaining the k_th element when k < i
else:
diff = i-k
#if both k and i are odd or even
if(i-k)%2==0:
#print("#3")
ans =  (a_i + b_i) / math.pow(2,2*(i-k)+s)
#diff =  int(diff/2)
#ans =  (a_i + b_i) / math.pow(2,4*diff+s)

#if i and k are of different parities then obtaining first
# a_(i+1) and b_(i+1)
else:
#print("#4")
ans = (2*x*a_i + 2*x*y*b_i) / math.pow(2,2*(i+1-k)+s)
diff = int(diff/2)
ans = (2*x*a_i + 2*x*y*b_i) / math.pow(2,4*diff + 4 + s)

print(ans)

main()``````

## Cracking the Code CodeChef Solution in C

``````#include <stdio.h>
#include <math.h>
int main()
{
long long int i,k,s;
double ans,a_i,b_i;
scanf("%lld%lld%lld",&i,&k,&s);
scanf("%lf%lf",&a_i,&b_i);
if((k-i)%2==0)
{
ans=a_i+b_i;
printf("%lf\n",ans*pow(2.0,(2*(k-i))-s));
}
else
{
ans = sqrt(2)*pow(2.0,(2*(k-i)-1-s))*(a_i+(sqrt(3)*b_i));
printf("%lf\n",ans);
}
return 0;
}
``````

## Cracking the Code CodeChef Solution in JAVA

``````/* package codechef; // don't place package name! */

import java.io.PrintWriter;
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.BigInteger;
import java.text.DecimalFormat;
class Main
{
static class Chef implements Comparable<Chef> {
int age;
int rating;
Chef(int age,int rating) {
this.age = age;
this.rating = rating;
}
@Override
public int compareTo(Chef p) {
return this.age-p.age;
}
}
/*
class Pair
{
int f,s;
Pair( int f, int s)
{
this.f=f;
this.s=s;
}
}*/
static class Dish{

int id;
int time;

Dish(int a, int b){
this.id = a;
this.time = b;
}
}

static class compare implements Comparator<Dish>{
public int compare(Dish a, Dish b){
if(a.time!=b.time)return a.time - b.time;
else return a.id - b.id;
}
}

static class Pair {
char prefix;
int suffixId;
Pair(char prefix, int suffixId) {
this.prefix = prefix;
this.suffixId = suffixId;
}

@Override
public int hashCode() {
final int prime = 199;
int hash = 0;
hash = prime * prefix + hash;
hash = prime * suffixId + hash;
return hash;
}

@Override
public boolean equals(Object obj) {
if(obj instanceof Pair) {
Pair p2 = (Pair) obj;
return this.prefix == p2.prefix && this.suffixId == p2.suffixId;
}
return false;
}
}
static class Circle{
long x;
long y;
long r;

public Circle(long x, long y, long r) {
this.x = x;
this.y = y;
this.r = r;
}
}

static class Distance{
long shortest;
long largest;

}
/*static class pair implements Comparable<pair>
{
long x;
int y;
pair(long x,int y)
{
this.x=x;
this.y=y;
}
public int compareTo(pair o)
{
return (int)(x-o.x);
}

}
static	class Pair
{
long x,y;
Pair(long x, long y)
{
this.x = x;
this.y = y;
}
}
static class PairComparator implements Comparator<Pair>
{
public long compare(Pair a, Pair b)
{
//if(a.x==b.x)
return a.y-b.y;
//	return a.x-b.x;
}
}
static class Point {
public double x, y;

private static final int MAX = (int) 1e6 + 1;

public Point(double x, double y) {
this.x = x;
this.y = y;
}

public int hashCode() {
return (int)x * MAX + (int)y;
}

public boolean equals(Object ob) {
if(ob instanceof Point) {
Point other = (Point) ob;
return other.x == x && other.y == y;
}

return false;
}

public String toString() {
return "(" + x + ", " + y + ")";
}
}*/
/*	static int days4=0;
static int all;
static long phi[]=new long[1000001];
static long ans[]=new long[1000001];
//static int tree[],sum[];
//public static long mod = 1000000007;	public static long [][] tempMatrix;
public static long max = (long) Math.pow(10, 9) + 7;
static StringBuilder res = new StringBuilder();
//static Node tree[];
//static int a[];
//	static long mod = 998244353;
public static int rootColor=0;
static int MX = (1<<18);
//	 static boolean primes[]=new boolean[10000001];*/

static double pi = 3.1415926535;
private static final int MAXN = 5000;
/*    private static final int MOD = 1000_000_007;
private static Modular modular_nCr = new Modular(MOD);
private static Modular modular = new Modular(MOD);
private static final long[][] nCr = new long[MAXN+5][MAXN+5];
static int[] maxval = new int[1000000];
static int[] minval = new int[1000000];
private static long bruteAns = 1;
static double eps = 1e-7;
static {
nCr[0][0]=1;
for(int i=0;i<=MAXN;i++)
nCr[i][0]=1;
for(int i=1;i<=MAXN;i++){
for(int j=1;j<=i;j++){
nCr[i][j]=(nCr[i-1][j-1]+nCr[i-1][j])%MOD;
}
}
}*/
/*
static { nCr[0][0] = 1;
for (int i = 1; i < MAXN; i++) {
nCr[i][0] = 1;
for (int j = 1; j <= i; j++) {
nCr[i][j] = modular_nCr.add(nCr[i - 1][j - 1], nCr[i - 1][j]);
} }
}

static int arr[] , dp[][][];
//		static int n ;
static int final_sum=0;
static int mod=1000000007;
static ArrayList<Integer> graph[];
static boolean vis[];
static int seive[]=new int[1000001];
static int primes[] = {2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97};
static int[] calcPower() {
int[] arr = new int[26];
for (int i = 0; i < 26; i++) {
arr[i] = (int) Math.pow(2, i);
}
return arr;
}
// static int p[] = new int[1000001], size[] = new int[1000001], n, m;
static int bits=32;
static class Trie
{
Trie tree[]=new Trie[2];
int val=0;
public Trie()
{
val=0;
tree[0]=null;tree[1]=null;
}
}
static Trie root;
static void insert(int xor)
{
Trie temp=root;
for(int i=bits-1;i>=0;i--)
{
int v = (xor & (1<<i)) >=1 ? 1 : 0;
if(temp.tree[v]==null)
temp.tree[v]=new Trie();
temp=temp.tree[v];
}
temp.val=xor;
}
static int query(int xor)
{
Trie temp=root;
for(int i=bits-1;i>=0;i--)
{
int v = (xor & (1<<i)) >=1 ? 1 : 0;
if(temp.tree[1-v]!=null)
temp=temp.tree[1-v];
else if(temp.tree[v]!=null)
temp=temp.tree[v];
}
return xor^temp.val;
}
public static int getBit(int n, int pos) {
return (n & (1 << pos)) == 0 ? 0 : 1;
}
private static int n, m, ci, cj;
private static char[][] g;
private static boolean[][] vs;
private static int[] v = new int[]{-1, 0, 1, 0};
private static int[] h = new int[]{0, 1, 0, -1};
private static char[] d = new char[]{'U', 'R', 'D', 'L'};

private static boolean v(int i, int j) {
return (i >= 0 && i < n && j >= 0 && j < m);
}

private static boolean pr(int i, int j) {
return g[i][j] == '*';
}
private static double dh, dl, dr, k;
static int zero = Integer.MAX_VALUE, one = Integer.MAX_VALUE;
static ArrayList<Long> leaf=new ArrayList<>();*/
static int mod=1000000007;
static int MX = 1000001;
static int pr[] = new int[MX];
static boolean cmp[] = new boolean[MX];
static int c = 0;
static void pre(){
for(int x = 2;x<MX;x++){
if(!cmp[x]){
pr[c++] = x;
for(int y = x+x; y<MX; y+=x){
cmp[y] = true;
}
}
}
}

//		static final int MAXN = (int) 1e6;
static int spf[] = new int[MAXN];
static ArrayList<Integer> primes = new ArrayList<>();
static   final int size = 1000001;
static	final long MOD = 1000000007L;
static	int n;
static	int m;
static	int a[] = new int[size];
static	int dp[] = new int[size];
//	static	int arr[] = new int[size];
static	int stops;
static int[] arr = new int[] {2,3,5,7,11,13,17,19,23,29};
public static List<Integer> g[];
public static long[] subLeaf;
public static long[] count;

public static void dfs(int node,int parent){
if(g[node].size()==1){
subLeaf[node]=1;
return;
}
long paths=0;
for(Integer i : g[node]){
if(i==parent){
continue;
}
dfs(i,node);
subLeaf[node]+=subLeaf[i];
count[node]+=(paths*subLeaf[i]);
paths+=subLeaf[i];
}
}

public static void main (String[] args) throws java.lang.Exception
{
PrintWriter pw=new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
StringBuilder sb = new StringBuilder();
FastScanner in=new FastScanner();
//	Scanner sc = new Scanner(System.in);
PrintWriter out=new PrintWriter(System.out);

HashMap<Character, Integer> h = new HashMap<Character, Integer>();
//	TreeMap<Integer, Integer> h1 = new TreeMap<Integer, Integer>();
//	HashMap<Integer, Integer> h2 = new HashMap<Integer, Integer>();
//	HashSet<Point> s = new HashSet<Point>();

//	HashSet<Double> s2 = new HashSet<Double>();
//	HashSet<Double> s3 = new HashSet<Double>();
//	HashSet<Character> h2 = new HashSet<Character>();
//long t= in.nextLong();
//	long t = in.nextLong();
//DecimalFormat df = new DecimalFormat("#,###,##0.000000");

/* boolean prime[]=new boolean[10000000];
int p[]=new int[10000000];
int k=1;
Arrays.fill(prime, true);
prime[0]=false;
prime[1]=false;for(int i=2;i<10000000;i++)
{
if(!prime[i])
{
p[i]=p[i-1];
continue;
}
p[i]=k; k++;
for(long j=(long)i*i;j<10000000;j+=i)
prime[(int)j]=false;
}
/*  int pri[]=new int[1000005];
int p=2;
List<Integer> list=new ArrayList<>();
while(p*p <=1000005)
{
if(pri[p]==0)
{
for(int i=p*2;i<=1000004;i=i+p)
{
pri[i]=1;
}
}
p++;
}
//System.out.println(list);*/
//		int t = in.nextInt();
//		while(t-->0)
//		{
long i,k,s;
i = in.nextLong();
k = in.nextLong();
s = in.nextLong();

int ai, bi;
ai = in.nextInt();
bi = in.nextInt();

double a = ai, b = bi;
if ((k % 2 == 0 && i % 2 != 0) || (k % 2 != 0 && i % 2 == 0)) {
i++;
a = Math.sqrt(2.0) * ((ai + bi) - Math.sqrt(3.0) * (ai - bi));
b = Math.sqrt(2.0) * ((ai - bi) + Math.sqrt(3.0) * (ai + bi));

}

double result = (a + b) * Math.pow(2.0, 2 * (k - i) - s);
out.println(result);
//		}
out.close();
}

static boolean isSquare(int n)
{
if(Math.ceil((double)Math.sqrt(n))==Math.floor((double)Math.sqrt(n)))
return true;
return false;
}

public static long gcd(long a,long b,long n){
if(a==b){
return (power(a,n,mod)+power(b,n,mod))%mod;
}
long res=1l;
long num=a-b;
for(long i=1;i*i<=num;i++){
if(num%i==0){
long temp= (power(a,n,i)+ power(b,n,i))%i;
if(temp==0){
res=Math.max(res,i);
}
temp= (power(a,n,num/i) + power(b,n,num/i))%(num/i);
if(temp==0){
res=Math.max(res,num/i);
}
}
}
return res%mod;
}
public static long power(long a,long n,long d){
long res=1l;
while(n>0){
if(n%2==1){
res =((res%d)*(a%d))%d;
n--;
}else{
a=((a%d)*(a%d))%d;
n=n/2;
}
}
return res%mod;
}
/*	static long power(long x,long y) {
long res=1;
x%=m;
while(y>0) {
if(y%2!=0)
res=(res*x)%m;
y=y>>1;
x=(x*x)%m;
}
return res;
}
*/

static long gcd(long a, long b)
{
if(b==0)
return a;
else
return gcd(b, a%b);
}
static long  nextPower_2 (  long x, long y )
{

long  count  =  0 ;
while ( y < x )
{count ++ ;
y  =  y <<  1 ;
}
return  count ;
}
/*
static long power(long a, long b, long p)
{ 	long x = 1, y = a;
while (b > 0) {
if (b % 2 == 1) {
x = (x * y);
if (x >= p) x %= p;
}
y = (y * y); if (y >= p) y %= p;
b /= 2;}
return x;
}*/
public static class Modular {

private int MOD;

Modular(int MOD) {
this.MOD = MOD;
}

public long add(long a, long b) {
return (a + b) % MOD;
}

public long sub(long a, long b) {
return (a - b + MOD) % MOD;
}

public long mul(long a, long b) {
return (a * b) % MOD;
}

public long div(long a, long b) {
return mul(a, inverseEuler(b));
}	public long power(long a, long b) {
long x = 1, y = a;
while (b > 0) {
if (b % 2 == 1) {
x = (x * y);if (x >= MOD) x %= MOD;
}
y = (y * y);
if (y >= MOD) y %= MOD;
b /= 2;}
return x;
}

public long inverseEuler(long n) {
return power(n, MOD - 2);
}
}
byte[] buf = new byte[2048];
int index, total;
in = is;
}	int scan() throws IOException {
if (index >= total) {
index = 0;
if (total <= 0) { return -1;
}
}
return buf[index++];
}

String next() throws IOException {
int c;
for (c = scan(); c <= 32; c = scan()) ;
StringBuilder sb = new StringBuilder(); for (; c > 32; c = scan()) {
sb.append((char) c);}
return sb.toString();
}String nextLine() throws IOException {
int c;for (c = scan(); c <= 32; c = scan()) ;
StringBuilder sb = new StringBuilder();
for (; c != 10 && c != 13; c = scan()) {
sb.append((char) c);
} return sb.toString();
}char nextChar() throws IOException {
int c;
for (c = scan(); c <= 32; c = scan()) ;
return (char) c;
}	int nextInt() throws IOException {
int c, val = 0;
for (c = scan(); c <= 32; c = scan()) ;
boolean neg = c == '-';
if (c == '-' || c == '+') {
c = scan(); }
for (; c >= '0' && c <= '9'; c = scan()) {
val = (val << 3) + (val << 1) + (c & 15);
}
return neg ? -val : val;
}long nextLong() throws IOException {
int c;long val = 0;
for (c = scan(); c <= 32; c = scan()) ;
boolean neg = c == '-';
if (c == '-' || c == '+') {
c = scan();
}
for (; c >= '0' && c <= '9'; c = scan()) {
val = (val << 3) + (val << 1) + (c & 15);
}
return neg ? -val : val;
}
}

static class FastScanner{
StringTokenizer st;
String nextToken(){
while(st==null||!st.hasMoreElements())
return st.nextToken();
}
int nextInt(){return Integer.parseInt(nextToken());}
long nextLong(){return Long.parseLong(nextToken());}
double nextDouble(){return Double.parseDouble(nextToken());}
}
}``````

## Cracking the Code CodeChef Solution in PYTH

``````import math
c1=math.sqrt(2)-math.sqrt(6)
c2=math.sqrt(2)+math.sqrt(6)
z=raw_input().split()
i=int(z[0])
k=int(z[1])
s=int(z[2])
z=raw_input().split()
a_i=int(z[0])
b_i=int(z[1])
if(i<=k):
diff=k-i
if(diff%2==0):
diff=diff/2
ans=(a_i+b_i)*math.pow(2,4*diff-s)
else:
diff=diff/2
ans=(c1*(a_i-b_i)+c2*(a_i+b_i))*math.pow(2,4*diff-s)
else:
diff=i-k
if(diff%2==0):
diff=diff/2
ans=(a_i+b_i)/math.pow(2,4*diff+s)
else:
diff=diff/2
ans=(c1*(a_i-b_i)+c2*(a_i+b_i))/math.pow(2,4*diff+4+s)
print ans``````

## Cracking the Code CodeChef Solution in C#

``````using System;

namespace CodeChefPractice
{
// Prepared as a solution to Chef and Cracking the Code
// David Sturge (David_S)  31 May 2018.

class CrackingCode
{
public class Test
{
public static void Main()
{
int i = data1[0];
int k = data1[1];
int s = data1[2];
int a_i = data2[0];
int b_i = data2[1];

// The recurrence relations simplify to
// a[n+2] = 16 * a[n]  and b[n+2] = 16 * b[n]
// We need to be careful to avoid underflow or overflow,
// by incorporating 2^s into 'inv_power_of_2'.
int inv_power_of_2 = s;
if (k > i) {
inv_power_of_2 -= 4 * ( ( k - i ) / 2 );
} else if (k < i) {
inv_power_of_2 += 4 * ( ( i - k + 1 ) / 2 );
}
double fac = Math.Pow(0.5, inv_power_of_2);
double a_k = fac * a_i;
double b_k = fac * b_i;

if (( k - i ) % 2 != 0) {
// Extra evaluation for odd one
double sum = a_k + b_k;
double dif = a_k - b_k;
double x = Math.Sqrt(2.0);
double xy = Math.Sqrt(6.0);
a_k = x * sum - xy * dif;
b_k = x * dif + xy * sum;
}
// The result (factor 2^s incorporated already)
double q = a_k + b_k;
Console.WriteLine(q);

}

private static int[] DecodeString(int num, String s)
// Decode num integers from line of input
{
int[] output = new int[num];
int start_i = 0;
int len = s.Length;
while (num_read < num && start_i < len) {
int next_i;
output[num_read++] = StringToInt(s, start_i, out next_i);
start_i = next_i + 1;
}
return output;
}

private static int StringToInt(String s, int index, out int space_i)
// Convert string from index up to next space or end to integer.
// Return space_i = index of next space encountered, or off end of string.
{
bool minus = s[index] == '-';
if (minus)
++index;
const char zero = '0';
int n = s[index] - zero;
int len = s.Length;
while (++index < len) {
if (s[index] < zero)
break;
n = n * 10 + ( s[index] - zero );
}
space_i = index;
return (minus) ? -n : n;
}
}
}
}``````
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