Calculate sum of scores after N days based on given conditions

Given an integer N, representing the number of days, the task is to find the sum of scores after N days based on the following conditions:

• On the first Monday, score is set to 1.
• On every Monday, the score becomes 1 greater than the score on the previous Monday.
• On every other day, the score becomes equal to 1 greater than the score on the previous day.

Examples:

Input: N=4
Output: 10
Explanation: 
Scores on each day of the four days are as follows: 
Monday: 1
Tuesday: 2
Wednesday: 3
Thursday: 4
Total sum of scores = 1 + 2 + 3 + 4 = 10

Input: N=8
Output: 30
Explanation:
Scores on each day of the 8 days are as follows:
Monday: 1
Tuesday: 2
Wednesday: 3
Thursday: 4
Friday: 5
Saturday: 6
Sunday: 7
Monday: 2
Total sum of scores = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 2 = 30

Naive Approach: The simplest approach to solve the problem is to iterate over the range [1, N] and keep on adding the score on each day. Finally, print the sum of all the scores obtained.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to c sum of calculate
// sum of scores after n days
void findScoreSum(int n)
{
    // Store the required sum
    int total = 0;

    // Store the score on previous
    // monday and current day respectively
    int prev_monday = 0, curr_day = 0;

    // Iterate over the range [1, n]
    for (int day = 1; day <= n; day++) {

        // If the current day is monday
        if (day % 7 == 1) {

            // Increment score of
            // prev_monday by 1
            prev_monday++;

            // Update score of current day
            curr_day = prev_monday;
        }

        // Add score of current day and
        // increment score for next day
        total += curr_day++;
    }

    // Print the result
    cout << total;
}

// Driver Code
int main()
{
    int N = 8;
    findScoreSum(N);

    return 0;
}

Java

// Java Program to implement
// the above approach
import java.io.*;
class GFG
{

  // Function to c sum of calculate
  // sum of scores after n days
  static void findScoreSum(int n)
  {

    // Store the required sum
    int total = 0;

    // Store the score on previous
    // monday and current day respectively
    int prev_monday = 0, curr_day = 0;

    // Iterate over the range [1, n]
    for (int day = 1; day <= n; day++)
    {

      // If the current day is monday
      if (day % 7 == 1)
      {

        // Increment score of
        // prev_monday by 1
        prev_monday++;

        // Update score of current day
        curr_day = prev_monday;
      }

      // Add score of current day and
      // increment score for next day
      total += curr_day++;
    }

    // Print the result
    System.out.println(total);
  }

  // Driver Code
  public static void main (String[] args)
  {
    int N = 8;
    findScoreSum(N);
  }
}

// This code is contributed by avanitrachhadiya2155

Python3

# Python3 program for the above approach

# Function to c sum of calculate
# sum of scores after n days
def findScoreSum(n):

    # Store the required sum
    total = 0

    # Store the score on previous
    # monday and current day respectively
    prev_monday, curr_day = 0, 0

    # Iterate over the range [1, n]
    for day in range(1, n + 1):

        # If the current day is monday
        if (day % 7 == 1):

            # Increment score of
            # prev_monday by 1
            prev_monday += 1

            # Update score of current day
            curr_day = prev_monday

        # Add score of current day and
        # increment score for next day
        total += curr_day
        curr_day += 1

    # Print the result
    print(total)

# Driver Code
if __name__ == '__main__':

    N = 8

    findScoreSum(N)

# This code is contributed by mohit kumar 29

C#

// C# Program to implement
// the above approach
using System;

class GFG
{

// Function to c sum of calculate
// sum of scores after n days
static void findScoreSum(int n)
{
    // Store the required sum
    int total = 0;

    // Store the score on previous
    // monday and current day respectively
    int prev_monday = 0, curr_day = 0;

    // Iterate over the range [1, n]
    for (int day = 1; day <= n; day++) {

        // If the current day is monday
        if (day % 7 == 1) {

            // Increment score of
            // prev_monday by 1
            prev_monday++;

            // Update score of current day
            curr_day = prev_monday;
        }

        // Add score of current day and
        // increment score for next day
        total += curr_day++;
    }

    // Print the result
    Console.Write(total);
}

// Driver Code
public static void Main(String[] args)
{
    int N = 8;
    findScoreSum(N);
}
}

// This code is contributed by code_hunt.

Javascript

<script>

// Javascript Program to implement
// the above approach

// Function to c sum of calculate
// sum of scores after n days
function findScoreSum(n)
{

    // Store the required sum
    let total = 0;

    // Store the score on previous
    // monday and current day respectively
    let prev_monday = 0, curr_day = 0;

    // Iterate over the range [1, n]
    for(let day = 1; day <= n; day++)
    {

        // If the current day is monday
        if (day % 7 == 1)
        {

            // Increment score of
            // prev_monday by 1
            prev_monday++;

            // Update score of current day
            curr_day = prev_monday;
        }

        // Add score of current day and
        // increment score for next day
        total += curr_day++;
    }

    // Print the result
    document.write(total);
}

// Driver code
let N = 8;

findScoreSum(N);

// This code is contributed by target_2

</script>

Output:

30

Time Complexity: O(N)
Auxiliary Space: O(1)

Efficient Approach: The above approach can be optimized based on the following observations: 

Let the number of full weeks be F and the remaining days be D.
Sum of scores after N days = Sum of scores in the first F weeks + Sum of scores in the remaining D days 

Sum of scores in the first F weeks:
Sum of scores in the first week = 1 + 2 + 3 + … + 7
Sum of scores in the second week = 2 + 3 + 4 + … + 8 = 7*1 + (1 + 2 + 3 + … + 7)
Sum of scores in the third week = 3 + 4 + 5 + … + 9 = 7*2 + (1 + 2 + 3 + … + 7)
…
Sum of scores in F^th week = 7*(F – 1) + (1 + 2 + 3 + … + 7)
Total sum of scores in the first F weeks = F * (1 + 2 + 3 + … + 7) + 7(1 + 2 + … + (F – 1)) 
                                                             = F * ((7 * 8) / 2) + 7 * (F * (F – 1) / 2)    
                                                             = F / 2 * (49 + 7 * F)

Sum of scores for the remaining D days:
Sum of scores in the remaining D days = (F + 1) + (F + 2) + … + (F + D)
                                                             = F * D + D * (D + 1) / 2
                                                             = D / 2 * (2 * F + D + 1)                                                                                                                  

So, the total sum of scores is [F/2 * (49 + 7*F)] + [D/2 * (2*F + D+1)].

Below is the implementation of the above approach: 

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

// Function to calculate sum
// of scores after n days
void findScoreSum(int n)
{
    // Store the number
    // of full weeks
    int F = n / 7;

    // Stores the remaining
    // days in the last week
    int D = n % 7;

    // Store the sum of scores
    // in the first F full weeks
    int fullWeekScore
        = (49 + 7 * F) * F / 2;

    // Store the sum of scores
    // in the last week
    int lastNonFullWeekScore
        = (2 * F + D + 1) * D / 2;

    // Print the result
    cout << fullWeekScore + lastNonFullWeekScore;
}

// Driver Code
int main()
{
    int N = 8;
    findScoreSum(N);

    return 0;
}

Java

// Java program for the above approach
import java.io.*;
import java.lang.*;
import java.util.*;

class GFG {

  // Function to calculate sum
  // of scores after n days
  static void findScoreSum(int n)
  {
    // Store the number
    // of full weeks
    int F = n / 7;

    // Stores the remaining
    // days in the last week
    int D = n % 7;

    // Store the sum of scores
    // in the first F full weeks
    int fullWeekScore = (49 + 7 * F) * F / 2;

    // Store the sum of scores
    // in the last week
    int lastNonFullWeekScore = (2 * F + D + 1) * D / 2;

    // Print the result
    System.out.println(fullWeekScore
                       + lastNonFullWeekScore);
  }

  // Driver Code
  public static void main(String[] args)
  {
    int N = 8;
    findScoreSum(N);
  }
}

// This code is contributed by Kingash.

Python3

# Python3 program for the above approach

# Function to calculate sum
# of scores after n days
def findScoreSum(n):
    # Store the number
    # of full weeks
    F = n // 7

    # Stores the remaining
    # days in the last week
    D = n % 7

    # Store the sum of scores
    # in the first F full weeks
    fullWeekScore = (49 + 7 * F) * F // 2

    # Store the sum of scores
    # in the last week
    lastNonFullWeekScore = (2 * F + D + 1) * D // 2

    # Print the result
    print(fullWeekScore + lastNonFullWeekScore)

# Driver Code
if __name__ == '__main__':
    N = 8
    findScoreSum(N)

    # This code is contributed by SURENDRA_GANGWAR.

C#

// C# program for the above approach
using System;

class GFG{

// Function to calculate sum
// of scores after n days
static void findScoreSum(int n)
{

    // Store the number
    // of full weeks
    int F = n / 7;

    // Stores the remaining
    // days in the last week
    int D = n % 7;

    // Store the sum of scores
    // in the first F full weeks
    int fullWeekScore = (49 + 7 * F) * F / 2;

    // Store the sum of scores
    // in the last week
    int lastNonFullWeekScore = (2 * F + D + 1) * D / 2;

    // Print the result
    Console.WriteLine(fullWeekScore +
                      lastNonFullWeekScore);
}

// Driver Code
static public void Main()
{
    int N = 8;

    findScoreSum(N);
}
}

// This code is contributed by rag2127

Javascript

<script>

// JavaScript program to implement
// the above approach

  // Function to calculate sum
  // of scores after n days
  function findScoreSum(n)
  {
    // Store the number
    // of full weeks
    let F = n / 7;

    // Stores the remaining
    // days in the last week
    let D = n % 7;

    // Store the sum of scores
    // in the first F full weeks
    let fullWeekScore = (49 + 7 * F) * F / 2;

    // Store the sum of scores
    // in the last week
    let lastNonFullWeekScore = (2 * F + D + 1) * D / 2;

    // Print the result
    document.write(Math.floor(fullWeekScore
                       + lastNonFullWeekScore));
  }

// Driver code
    let N = 8;
    findScoreSum(N);

// This code is contributed by susmitakundugoaldanga.
</script>

Output:

30

Time Complexity: O(1)
Auxiliary Space: O(1)