Calculate Money in Leetcode Bank

Problem Description

Hercy wants to save money for his first car. He puts money in the Leetcode bank every day.

He starts by putting in $1 on Monday, the first day. Every day from Tuesday to Sunday, he will put in $1 more than the day before. On every subsequent Monday, he will put in $1 more than the previous Monday. Given n, return the total amount of money he will have in the Leetcode bank at the end of the nth day.

Examples

Example 1:

Input: n = 4
Output: 10
Explanation: After the 4th day, the total is 1 + 2 + 3 + 4 = 10.

Example 2:

Input: n = 10
Output: 37
Explanation: After the 10th day, the total is (1 + 2 + 3 + 4 + 5 + 6 + 7) + (2 + 3 + 4) = 37. Notice that on the 2nd Monday, Hercy only puts in $2.

Example 3:

Input: n = 20
Output: 96
Explanation: After the 20th day, the total is (1 + 2 + 3 + 4 + 5 + 6 + 7) + (2 + 3 + 4 + 5 + 6 + 7 + 8) + (3 + 4 + 5 + 6 + 7 + 8) = 96.

Constraints

• 1 <= n <= 1000

Solution for 1710. Calculate Money in Leetcode Bank

Intuition

Hercy contributes money to the Leetcode bank based on a specific pattern. He starts with $1 on the first day and increases his contribution by$1 each subsequent day. Additionally, on each Monday, he increases the contribution by $1 more than the previous Monday. To calculate the total amount after a certain number of days, we need to follow this contribution pattern.

Approach

1. Calculate the number of complete weeks (week_count = n / 7).
2. Calculate the total contribution from complete weeks using the arithmetic sum formula for each week: ((week_count * (week_count - 1)) / 2) * 7.
3. Calculate the total contribution from days beyond complete weeks using the arithmetic sum formula: (week_count * 28).
4. Calculate the contribution from the remaining days (less than a week) using the arithmetic sum formula for the remaining days: ((remaining_days * (remaining_days + 1)) / 2) + (week_count * remaining_days).
5. Sum up the contributions calculated in steps 2, 3, and 4 to get the total amount.

Code in Different Languages

Python

Written by @agarwalhimanshugaya

       class Solution(object):
 def totalMoney(self, n):
     week_count = n // 7
     remaining_days = n % 7
     
     total = ((week_count * (week_count - 1)) // 2) * 7 
     total += week_count * 28
     total += ((remaining_days * (remaining_days + 1)) // 2) + (week_count * remaining_days)
     
     return total
     

Java

Written by @agarwalhimanshugaya

       class Solution {
 public int totalMoney(int n) {
     int week_count = n / 7;
     int remaining_days = n % 7;
     
     int total = ((week_count * (week_count - 1)) / 2) * 7; // Contribution from complete weeks
     total += week_count * 28; // Contribution from complete weeks (additional on Mondays)
     total += ((remaining_days * (remaining_days + 1)) / 2) + (week_count * remaining_days); // Contribution from remaining days
     
     return total;
 }
}

C++

Written by @agarwalhimanshugaya

    class Solution {
public:
 int totalMoney(int n) {
     int week_count = n / 7;
     int remaining_days = n % 7;
     
     int total = ((week_count * (week_count - 1)) / 2) * 7; // Contribution from complete weeks
     total += week_count * 28; // Contribution from complete weeks (additional on Mondays)
     total += ((remaining_days * (remaining_days + 1)) / 2) + (week_count * remaining_days); // Contribution from remaining days
     
     return total;
 }
};

Complexity Analysis

• Time Complexity: $O(1)$
• Space Complexity: $O(1)$

References

• LeetCode Problem: Calculate Money in Leetcode Bank
• Solution Link: LeetCode Solution