Calculate Money in Bank

2 min readUpdated 20 May 2025

Problem Statement

Hercy, with a goal to purchase his first car, decides to save daily in a unique pattern using the bank. He starts his savings plan with $1 on the first day, which is a Monday. For each subsequent day until Sunday, he increments his daily contribution by $1. The uniqueness of his plan emerges every Monday, as he deposits $1 more than what he deposited the previous Monday. To determine how much money Hercy will have saved by any given day n, one needs to calculate the total accumulative deposit by the end of that day.

Examples

Example 1

Input:

EXAMPLE_ENTITY

n = 4

Output:

EXAMPLE_ENTITY

Explanation:

EXAMPLE_ENTITY

 After the 4th day, the total is 1 + 2 + 3 + 4 = 10.

Example 2

Input:

EXAMPLE_ENTITY

n = 10

Output:

EXAMPLE_ENTITY

Explanation:

EXAMPLE_ENTITY

 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:

EXAMPLE_ENTITY

n = 20

Output:

EXAMPLE_ENTITY

Explanation:

EXAMPLE_ENTITY

 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

Approach and Intuition

Understanding the deposit increments:
- Hercy increases his deposit by $1 daily from Tuesday to Sunday.
- Every Monday, the deposit amount is reset to $1 more than what was deposited on the previous Monday.
How to compute total savings:
- Identify the complete weeks within the given number of days n (since each week clearly contributes a known sum that increases each week).
- Calculate contributions for any remaining days after the last complete week.
- Add the outputs from the above two calculations to get the total saved amount.

By carefully summing up the contributions made during complete weeks and any additional days, we can efficiently compute the total savings Hercy has accrued by the nth day.

Solutions

CPP
class Solution {
public:
    int calculateTotalMoney(int days) {
        int fullWeeks = days / 7;
        int firstWeekMoney = 28;
        int lastWeekMoney = firstWeekMoney + (fullWeeks - 1) * 7;
        int totalFullWeekMoney = fullWeeks * (firstWeekMoney + lastWeekMoney) / 2;
            
        int moneyCounter = 1 + fullWeeks;
        int remainingDaysMoney = 0;
        for (int currentDay = 0; currentDay < days % 7; currentDay++) {
            remainingDaysMoney += moneyCounter + currentDay;
        }
            
        return totalFullWeekMoney + remainingDaysMoney;
    }
};
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Calculate the total amount of money saved over a given number of days based on a unique saving pattern where the amount saved starts at $1 and increases each day for a week, then resets the next week.

The solution provided in C++ efficiently calculates the total savings for any number of days using the following steps:

Determine the number of complete weeks (fullWeeks) within the given number of days by integer division (days / 7).
Calculate the total money saved in the first week, which is a fixed value (firstWeekMoney = 28).
Determine the total money saved in the last complete week of the period. This value is dynamic, based on the number of complete weeks, calculated as lastWeekMoney = firstWeekMoney + (fullWeeks - 1) * 7.
Compute the total money saved across all complete weeks (totalFullWeekMoney). This uses the arithmetic series sum formula, applied to the savings from complete weeks: totalFullWeekMoney = fullWeeks * (firstWeekMoney + lastWeekMoney) / 2.
Determine any additional saving for the remaining days if the total number of days doesn't constitute complete weeks. This is done by:
- Computing the starting amount for the remaining days (moneyCounter = 1 + fullWeeks).
- Initializing remainingDaysMoney to store the total savings for these additional days.
- Iterating over each remaining day to add the corresponding day's money to remainingDaysMoney.
Sum the calculated values for complete weeks and the remaining days to obtain the total saved money (return totalFullWeekMoney + remainingDaysMoney).

This approach uses mathematical operations to minimize iterations, making it efficient for a larger number of days, and elegantly handles both complete weeks and extra days without repeated manual calculation.

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Calculate Money in Bank

2 min readUpdated 20 May 2025

Problem Statement

Examples

Example 1

Input:

EXAMPLE_ENTITY

n = 4

Output:

EXAMPLE_ENTITY

Explanation:

EXAMPLE_ENTITY

 After the 4th day, the total is 1 + 2 + 3 + 4 = 10.

Example 2

Input:

EXAMPLE_ENTITY

n = 10

Output:

EXAMPLE_ENTITY

Explanation:

EXAMPLE_ENTITY

 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:

EXAMPLE_ENTITY

n = 20

Output:

EXAMPLE_ENTITY

Explanation:

EXAMPLE_ENTITY

 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

Approach and Intuition

Understanding the deposit increments:
- Hercy increases his deposit by $1 daily from Tuesday to Sunday.
- Every Monday, the deposit amount is reset to $1 more than what was deposited on the previous Monday.
How to compute total savings:
- Identify the complete weeks within the given number of days n (since each week clearly contributes a known sum that increases each week).
- Calculate contributions for any remaining days after the last complete week.
- Add the outputs from the above two calculations to get the total saved amount.

By carefully summing up the contributions made during complete weeks and any additional days, we can efficiently compute the total savings Hercy has accrued by the nth day.

Solutions

CPP
class Solution {
public:
    int calculateTotalMoney(int days) {
        int fullWeeks = days / 7;
        int firstWeekMoney = 28;
        int lastWeekMoney = firstWeekMoney + (fullWeeks - 1) * 7;
        int totalFullWeekMoney = fullWeeks * (firstWeekMoney + lastWeekMoney) / 2;
            
        int moneyCounter = 1 + fullWeeks;
        int remainingDaysMoney = 0;
        for (int currentDay = 0; currentDay < days % 7; currentDay++) {
            remainingDaysMoney += moneyCounter + currentDay;
        }
            
        return totalFullWeekMoney + remainingDaysMoney;
    }
};
Powered by Vultr AgentBeta

The solution provided in C++ efficiently calculates the total savings for any number of days using the following steps:

Determine the number of complete weeks (fullWeeks) within the given number of days by integer division (days / 7).
Calculate the total money saved in the first week, which is a fixed value (firstWeekMoney = 28).
Determine the total money saved in the last complete week of the period. This value is dynamic, based on the number of complete weeks, calculated as lastWeekMoney = firstWeekMoney + (fullWeeks - 1) * 7.
Compute the total money saved across all complete weeks (totalFullWeekMoney). This uses the arithmetic series sum formula, applied to the savings from complete weeks: totalFullWeekMoney = fullWeeks * (firstWeekMoney + lastWeekMoney) / 2.
Determine any additional saving for the remaining days if the total number of days doesn't constitute complete weeks. This is done by:
- Computing the starting amount for the remaining days (moneyCounter = 1 + fullWeeks).
- Initializing remainingDaysMoney to store the total savings for these additional days.
- Iterating over each remaining day to add the corresponding day's money to remainingDaysMoney.
Sum the calculated values for complete weeks and the remaining days to obtain the total saved money (return totalFullWeekMoney + remainingDaysMoney).

More to Explore

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Tech Talk: Implementing Fine-Grained Access Control with Vultr IAM

Tech Talk: Getting Started with Vultr IAM

Tech Talk: Simplifying Zero-Trust Networking with NetBird on Vultr Marketplace

0 Comments

Start the conversation

Be the first to comment and share your perspective with the community.