根据给定条件计算N天后的分数总和

给定代表天数的整数N，任务是根据以下条件找到N天后的分数总和：

• 在第一个星期一，分数设置为1 。
• 在每个星期一，分数比上一个星期一的分数大1 。
• 每隔一天，分数变得比前一天的分数大1 。

例子：

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

天真的方法：解决问题的最简单方法是遍历[1，N]范围，并继续每天添加分数。最后，打印获得的所有分数的总和。

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
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.

输出：

30

时间复杂度： O(N)
辅助空间： O(1)

高效的方法：可以基于以下观察来优化上述方法：

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)                                                                                                                  

因此，总得分为[F / 2 *(49 + 7 * F)] + [D / 2 *(2 * F + D + 1)] 。

下面是上述方法的实现：

C++

// C++ program for the above approach
#include 
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

输出：

30

时间复杂度： O(1)
辅助空间： O(1)