[LeetCode] 1716. Calculate Money in Leetcode Bank

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

计算力扣银行的钱。

Hercy 想要为购买第一辆车存钱。他 每天 都往力扣银行里存钱。
最开始，他在周一的时候存入 1 块钱。从周二到周日，他每天都比前一天多存入 1 块钱。在接下来每一个周一，他都会比前一个周一多存入 1 块钱。
给你 n ，请你返回在第 n 天结束的时候他在力扣银行总共存了多少块钱。

思路

这是一道数学题。因为存钱是按照星期来存的，所以我们一开始用 n 除以 7，看看一共有几个星期；如果有余数，则再进行计算。对于一整个星期，计算方式就是等差数列。

复杂度

时间O(round)
空间O(1)

代码

Java实现

class Solution {
    public int totalMoney(int n) {
        int res = 0;
        int round = n / 7;
        int remainder = n % 7;
        int start = 1;
        int end = 7;
        for (int i = 0; i < round; i++) {
            res += helper(start++, end++);
        }

        // last round
        start = 1 + round;
        end = remainder + round;
        for (int i = start; i <= end; i++) {
            res += i;
        }
        return res;
    }

    // first item, last item, round
    private int helper(int start, int end) {
        return (start + end) * (end - start + 1) / 2;
    }
}