Count of total Heads and Tails after N flips in a coin

Given character C and an integer N representing N number of coins in C position where C can be either head or tail. We can flip the coins N times, wherein the ith round the player will flip the face of all the coins whose number is less than or equal to i. The task is to determine the total number of head and tail after flipping N possible times.

Examples:

Input: C = ‘H’, N = 5 
Output: Head = 2, Tail = 3 
Explanation:
H means initially all the coins are facing in head direction, N means the total number of coins. 
So initially for i = 0, we have: H H H H H 
After the first round that is i = 1: T H H H H 
After the second round that is i = 2: H T H H H 
After the third round that is i = 3: T H T H H 
After the fourth round that is i = 4: H T H T H 
After the fifth round that is i = 5: T H T H T 
Hence the total count of the head is 2 and tail is 3.

Input: C = ‘T’, N = 7 
Output: Head = 4, Tail = 3 
Explanation:
After all the possible flips the head and tail count is 4 and 3. 

Approach: 
To solve the problem mentioned above we have to follow the steps given below:  

• In the question above if we observe then there is a pattern that if initially, all the coins are facing towards head direction then the total number of heads after N rounds will be the floor value of (n / 2) and tails will be the cell value of (n / 2).
• Otherwise, if all the coins are facing towards tail direction then a total number of tails after N rounds will be a floor value of (n / 2) and heads will be ceil value of (n / 2).

Below is the implementation: 

C++

// C++ program to count total heads
// and tails after N flips in a coin
#include<bits/stdc++.h>
using namespace std;

// Function to find count of head and tail
pair<int, int> count_ht(char s, int N)
{

    // Check if initially all the
    // coins are facing towards head
    pair<int, int>p;
    if(s == 'H')
    {
        p.first = floor(N / 2.0);
        p.second = ceil(N / 2.0);
    }

    // Check if initially all the coins
    // are facing towards tail
    else if(s == 'T')
    {
        p.first = ceil(N / 2.0);
        p.second = floor(N / 2.0);
    }

    return p;
}

// Driver code
int main()
{
    char C = 'H';
    int N = 5;

    pair<int, int> p = count_ht(C, N);

    cout << "Head = " << (p.first) << "\n";
    cout << "Tail = " << (p.second) << "\n";
}

// This code is contributed by virusbuddah_

Java

// Java program to count
// total heads and tails
// after N flips in a coin
import javafx.util.Pair;
public class Main
{
// Function to find count of head and tail
public static Pair <Integer,
                    Integer> count_ht(char s,
                                      int N)
{
  // Check if initially all the
  // coins are facing towards head
  Pair <Integer,
        Integer> p = new Pair <Integer,
                               Integer> (0, 0);
  if(s == 'H')
  {
     p = new Pair <Integer,
                   Integer> ((int)Math.floor(N / 2.0),
                             (int)Math.ceil(N / 2.0));
  }

  // Check if initially all the coins
  // are facing towards tail
  else if(s == 'T')
  {
     p = new Pair <Integer,
                   Integer> ((int)Math.ceil(N / 2.0),
                             (int)Math.floor(N / 2.0));
  }
  return p;
}

public static void main(String[] args)
{
  char C = 'H';
  int N = 5;
  Pair <Integer,
        Integer> p = count_ht(C, N);
  System.out.println("Head = " + p.getKey());
  System.out.println("Tail = " + p.getValue());
}
}

// This code is contributed by divyeshrabadiya07

Python3

# Python3 program to Count total heads
# and tails after N flips in a coin

# Function to find count of head and tail
import math
def count_ht( s, N ):

    # Check if initially all the
    # coins are facing towards head
    if s == "H":
        h = math.floor( N / 2 )
        t = math.ceil( N / 2 )

    # Check if initially all the coins
    # are facing towards tail
    elif s == "T":
        h = math.ceil( N / 2 )
        t = math.floor( N / 2 )

    return [h, t]

# Driver Code
if __name__ == "__main__":
    C = "H"
    N = 5
    l = count_ht(C, n)
    print("Head = ", l[0])
    print("Tail = ", l[1])

C#

// C# program to count total heads
// and tails after N flips in a coin
using System;

class GFG{

// Function to find count of head and tail
public static Tuple<int, int> count_ht(char s,
                                       int N)
{

    // Check if initially all the
    // coins are facing towards head
    Tuple<int, int> p = Tuple.Create(0, 0);

    if (s == 'H')
    {
        p = Tuple.Create((int)Math.Floor(N / 2.0),
                         (int)Math.Ceiling(N / 2.0));
    }

    // Check if initially all the coins
    // are facing towards tail
    else if (s == 'T')
    {
        p = Tuple.Create((int)Math.Ceiling(N / 2.0),
                         (int)Math.Floor(N / 2.0));
    }
    return p;
}

// Driver Code
static void Main()
{
    char C = 'H';
    int N = 5;
    Tuple<int, int> p = count_ht(C, N);

    Console.WriteLine("Head = " + p.Item1);
    Console.WriteLine("Tail = " + p.Item2);
}
}

// This code is contributed by divyesh072019

Javascript

<script>

// JavaScript program to count total heads
// and tails after N flips in a coin

// Function to find count of head and tail
function count_ht(s, N)
{

    // Check if initially all the
    // coins are facing towards head
    var p = [0,0];
    if(s == 'H')
    {
        p[0] = Math.floor(N / 2.0);
        p[1] = Math.ceil(N / 2.0);
    }

    // Check if initially all the coins
    // are facing towards tail
    else if(s == 'T')
    {
        p[0] = Math.ceil(N / 2.0);
        p[1] = Math.floor(N / 2.0);
    }

    return p;
}

// Driver code
var C = 'H';
var N = 5;

var p = count_ht(C, N);

document.write( "Head = " + (p[0]) + "<br>");
document.write( "Tail = " + (p[1]) + "<br>");

</script>

Output:

Head =  2
Tail =  3

Time complexity: O(1)
Auxiliary space: O(1)