1716. Calculate Money in Leetcode Bank
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.
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
Solutions
Solution: Math
- Time complexity: O(1)
- Space complexity: O(1)
JavaScript
js
/**
* @param {number} n
* @return {number}
*/
const totalMoney = function (n) {
const weeks = Math.floor(n / 7);
const trapezoid = (a, b) => ((a + b) * (b - a + 1)) / 2;
const firstWeek = trapezoid(1, 7);
const totalFullWeek = trapezoid(0, weeks - 1) * 7 + firstWeek * weeks;
const days = n % 7;
const remainingDays = trapezoid(1, days) + weeks * days;
return totalFullWeek + remainingDays;
};