Problem

Solution

Intuition

The problem requires us to add up the total amount in the bank that a person deposits given the depositing amounts of starting with depositing a dollar and then increasing the deposit amount by one dollar every day, until a full week has passed after which we deposit one more than we did at the start of the previous week. This just boils down into a math solution where we are adding consecutive numbers.

Approach

1. We first calculate the number of full weeks that has passed, weeks_completed by using trunacting division.
2. Then we add a full weeks amount per week that has passed along with an additional 7 dollars per week per additional week past the first week. We calculate the consecutive sum of numbers from 0 to the total number of weeks completed and multiply by 7 for this value.
3. Then we find the number of extra_days that have passed using modulus and calculate the extra money to add by using the similar consecutive numbers addition trick keeping in mind the values are higher per week_completed.

Complexity

• Time complexity: $O(1)$. We perform constant time math operations for this solution.

• Space complexity: $O(1)$. We do not utilize any additional space.

Code

class Solution:
    def totalMoney(self, n: int) -> int:
        weeks_completed = n // 7
        res = weeks_completed * 28
        res += (7 * weeks_completed * (weeks_completed - 1)) // 2

        if (n % 7):
            extra_days = n % 7
            day_1 = weeks_completed + 1
            res += ((day_1 + day_1 + extra_days - 1) * (extra_days)) // 2

        return res