Problem:

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.

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

Problem Analysis:

• This question is an Arithmetic Progression problem, we need to be familiar with the Arithmetic Progression Formula List and apply it accordingly.

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

Solutions:

class Solution:
    def totalMoney(self, n: int) -> int:
        # w1 = 1+2+3+4+5+6+7 = 28
        # w2 = ... = 28 + 7
        # ap formula 1: Sn = n/2[2a + (n – 1)d]
        # ap formula 2: Sn = n/2[first term + last term]
        w = n // 7 # weeks
        rd = n % 7 # remaining days
        return w * 28 + 7 * (w - 1) * w // 2 + (w + 1 + w + rd) * rd // 2

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