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✨feat: Add 1713
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‎Index/数学.md‎

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| [1518. 换酒问题](https://leetcode-cn.com/problems/water-bottles/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/water-bottles/solution/gong-shui-san-xie-yi-ti-shuang-jie-ji-sh-7yyo/) | 简单 | 🤩🤩🤩🤩 |
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| [1588. 所有奇数长度子数组的和](https://leetcode-cn.com/problems/sum-of-all-odd-length-subarrays/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/sum-of-all-odd-length-subarrays/solution/gong-shui-san-xie-yi-ti-shuang-jie-qian-18jq3/) | 简单 | 🤩🤩🤩🤩 |
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| [1610. 可见点的最大数目](https://leetcode-cn.com/problems/maximum-number-of-visible-points/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/maximum-number-of-visible-points/solution/gong-shui-san-xie-qiu-ji-jiao-ji-he-ti-b-0bid/) | 困难 | 🤩🤩🤩🤩 |
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| [1716. 计算力扣银行的钱](https://leetcode-cn.com/problems/calculate-money-in-leetcode-bank/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/calculate-money-in-leetcode-bank/solution/gong-shui-san-xie-jian-dan-mo-ni-ti-by-a-ifit/) | 简单 | 🤩🤩🤩🤩 |
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| [1720. 解码异或后的数组](https://leetcode-cn.com/problems/decode-xored-array/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/decode-xored-array/solution/gong-shui-san-xie-li-yong-yi-huo-xing-zh-p1bi/) | 简单 | 🤩🤩🤩 |
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| [1734. 解码异或后的排列](https://leetcode-cn.com/problems/decode-xored-permutation/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/decode-xored-permutation/solution/gong-shui-san-xie-note-bie-pian-li-yong-zeh6o/) | 中等 | 🤩🤩🤩🤩 |
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| [1738. 找出第 K 大的异或坐标值](https://leetcode-cn.com/problems/find-kth-largest-xor-coordinate-value/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/find-kth-largest-xor-coordinate-value/solution/gong-shui-san-xie-xiang-jie-li-yong-er-w-ai0d/) | 中等 | 🤩🤩🤩 |

‎Index/模拟.md‎

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| [1614. 括号的最大嵌套深度](https://leetcode-cn.com/problems/maximum-nesting-depth-of-the-parentheses/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/maximum-nesting-depth-of-the-parentheses/solution/gong-shui-san-xie-jian-dan-mo-ni-ti-by-a-pf5d/) | 简单 | 🤩🤩🤩🤩🤩 |
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| [1629. 按键持续时间最长的键](https://leetcode-cn.com/problems/slowest-key/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/slowest-key/solution/gong-shui-san-xie-jian-dan-mo-ni-ti-by-a-zjwb/) | 简单 | 🤩🤩🤩🤩🤩 |
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| [1646. 获取生成数组中的最大值](https://leetcode-cn.com/problems/get-maximum-in-generated-array/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/get-maximum-in-generated-array/solution/gong-shui-san-xie-jian-dan-mo-ni-ti-by-a-sj53/) | 简单 | 🤩🤩🤩🤩 |
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| [1716. 计算力扣银行的钱](https://leetcode-cn.com/problems/calculate-money-in-leetcode-bank/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/calculate-money-in-leetcode-bank/solution/gong-shui-san-xie-jian-dan-mo-ni-ti-by-a-ifit/) | 简单 | 🤩🤩🤩🤩 |
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| [1720. 解码异或后的数组](https://leetcode-cn.com/problems/decode-xored-array/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/decode-xored-array/solution/gong-shui-san-xie-li-yong-yi-huo-xing-zh-p1bi/) | 简单 | 🤩🤩🤩 |
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| [1736. 替换隐藏数字得到的最晚时间](https://leetcode-cn.com/problems/latest-time-by-replacing-hidden-digits/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/latest-time-by-replacing-hidden-digits/solution/gong-shui-san-xie-ti-huan-yin-cang-shu-z-2l1h/) | 简单 | 🤩🤩🤩🤩 |
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| [1743. 从相邻元素对还原数组](https://leetcode-cn.com/problems/restore-the-array-from-adjacent-pairs/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/restore-the-array-from-adjacent-pairs/solution/gong-shui-san-xie-yi-ti-shuang-jie-dan-x-elpx/) | 中等 | 🤩🤩🤩🤩 |
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### 题目描述
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这是 LeetCode 上的 **[1716. 计算力扣银行的钱](https://leetcode-cn.com/problems/calculate-money-in-leetcode-bank/solution/gong-shui-san-xie-jian-dan-mo-ni-ti-by-a-ifit/)** ,难度为 **简单**。
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Tag : 「数学」、「模拟」
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Hercy 想要为购买第一辆车存钱。他 **每天** 都往力扣银行里存钱。
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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。
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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。
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示例 1:
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```
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输入:n = 4
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输出:10
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解释:第 4 天后,总额为 1 +たす 2 +たす 3 +たす 4 =わ 10 。
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```
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示例 2:
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```
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输入:n = 10
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输出:37
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解释:第 10 天后,总额为 (1 + 2 + 3 + 4 + 5 + 6 + 7) + (2 + 3 + 4) = 37 。注意到第二个星期一,Hercy 存入 2 块钱。
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```
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示例 3:
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```
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输入:n = 20
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输出:96
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解释:第 20 天后,总额为 (1 + 2 + 3 + 4 + 5 + 6 + 7) + (2 + 3 + 4 + 5 + 6 + 7 + 8) + (3 + 4 + 5 + 6 + 7 + 8) = 96 。
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```
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提示:
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* 1ドル <= n <= 1000$
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---
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### 模拟
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根据题意进行模拟即可,分两步进行计算。
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先计算完整周:共 $a = \left \lfloor \frac{n}{7} \right \rfloor$ 周,第一周起始日金额为 1ドル,ドル每周的起始日的金额递增 1ドル,ドル周内金额可使用「等差数列求和」公式直接求解。
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然后再计算最后一周(若有)的金额:共 $b = n \pmod 7$ 天,使用紧接的起始日金额继续进行累加即可。
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代码:
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```Java
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class Solution {
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public int totalMoney(int n) {
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int a = n / 7, b = n % 7;
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int ans = 0, k = 1;
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while (a-- > 0) {
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ans += (k + (k + 6)) * 7 / 2;
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k++;
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}
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while (b-- > 0) ans += k++;
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return ans;
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}
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}
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```
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* 时间复杂度:$O(a + b)$
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* 空间复杂度:$O(1)$
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---
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### (优化)模拟
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更近一步,每个完整周的起始日金额相比上周起始日金额多 1ドル,ドル同时周内每日金额递增 1ドル,ドル因此相邻完整周的金额之和也满足「等差」性质,可直接使用「等差数列求和」公式 $O(1)$ 求解完整周部分的金额之和;周后一周(若有)的金额也是同理。
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代码:
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```Java
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class Solution {
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public int totalMoney(int n) {
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int a = n / 7, b = n % 7;
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int a1 = (1 + 7) * 7 / 2, an = (a + (a + 6)) * 7 / 2;
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int s1 = (a1 + an) * a / 2;
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a++;
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int s2 = (a + (a + b - 1)) * b / 2;
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return s1 + s2;
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}
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}
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```
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* 时间复杂度:$O(1)$
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* 空间复杂度:$O(1)$
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---
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### 最后
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这是我们「刷穿 LeetCode」系列文章的第 `No.1716` 篇,系列开始于 2021年01月01日,截止于起始日 LeetCode 上共有 1916 道题目,部分是有锁题,我们将先把所有不带锁的题目刷完。
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在这个系列文章里面,除了讲解解题思路以外,还会尽可能给出最为简洁的代码。如果涉及通解还会相应的代码模板。
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为了方便各位同学能够电脑上进行调试和提交代码,我建立了相关的仓库:https://github.com/SharingSource/LogicStack-LeetCode 。
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在仓库地址里,你可以看到系列文章的题解链接、系列文章的相应代码、LeetCode 原题链接和其他优选题解。
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