algoadvance

LeetCode problem 1716. Calculate Money in Leetcode Bank requires you to calculate the amount of money in the Leetcode bank after n days. The rules for the bank deposits are as follows:

• You start with $1 on Monday.
• Every day of the week, you deposit one more dollar than the previous day (i.e., $2 on Tuesday, $3 on Wednesday, and so on until $7 on Sunday).
• Every Monday, you start with one more dollar than the previous Monday (i.e., $(7 + 1) for the second week, $(7 + 2) for the third week, etc.).

The goal is to return the total amount of money in the bank after n days.

Clarifying Questions

1. Q: What are the constraints on n? A: 1 <= n <= 1000

2. Q: Are there any special cases to consider, such as n being a small number (like 1 or 7)? A: Yes, handling small numbers should conform to the general rules applied for the problem.

Strategy

1. Weekly Calculation:
   • Each week starts a new sequence, with the first Monday of week i having a deposit of $i.
   • The sequence for any week continues by incrementing the deposit amount by $1 each subsequent day until Sunday.
2. Summing the Weeks:
   • Complete weeks are easy to calculate since they repeat periodically.
   • For remaining days in a partial week, simply continue the sequence from where the last full week left off.

Code

def totalMoney(n: int) -> int:
    # Full weeks
    full_weeks = n // 7
    # Remaining days after full weeks
    remaining_days = n % 7
    
    # Calculate money from complete weeks
    total_money = 0
    
    for week in range(full_weeks):
        # For week i (0-indexed), the deposits start from 1+week till 7+week
        total_money += sum(range(1 + week, 8 + week))
    
    # Calculate money from the remaining days
    start_day = 1 + full_weeks  # the day number in sequence after full_weeks weeks
    for day in range(remaining_days):
        total_money += start_day + day
    
    return total_money

# Example usage:
print(totalMoney(10))  # Expected output: 37

Time Complexity

The time complexity of the solution is O(1) because the number of weeks (n / 7) is limited by the constraints, making the loop iterations constant time. Calculating the sums of each week and the remaining days is done with a finite number of operations independent of the input size n. Hence, the code performs efficiently even at the upper limit of constraints (i.e., n = 1000).

Try our interview co-pilot at AlgoAdvance.com

• Got blindsided by a question you didn’t expect?

• Spend too much time studying?

• Or simply don’t have the time to go over all 3000 questions?