Merge pull request #292 from SharingSource/ac_oier

✨feat: Add 507

Author: SharingSource

Index/数学.md

@@ -29,6 +29,7 @@
 | [470. 用 Rand7() 实现 Rand10()](https://leetcode-cn.com/problems/implement-rand10-using-rand7/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/implement-rand10-using-rand7/solution/gong-shui-san-xie-k-jin-zhi-zhu-wei-shen-zmd4/) | 中等 | 🤩🤩🤩🤩 |
 | [477. 汉明距离总和](https://leetcode-cn.com/problems/total-hamming-distance/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/total-hamming-distance/solution/gong-shui-san-xie-ying-yong-cheng-fa-yua-g21t/) | 简单 | 🤩🤩🤩 |
 | [483. 最小好进制](https://leetcode-cn.com/problems/smallest-good-base/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/smallest-good-base/solution/gong-shui-san-xie-xiang-jie-ru-he-fen-xi-r94g/) | 困难 | 🤩🤩🤩🤩 |
+| [507. 完美数](https://leetcode-cn.com/problems/perfect-number/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/perfect-number/solution/gong-shui-san-xie-jian-dan-mo-ni-tong-ji-e6jk/) | 简单 | 🤩🤩🤩 |
 | [523. 连续的子数组和](https://leetcode-cn.com/problems/continuous-subarray-sum/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/continuous-subarray-sum/solution/gong-shui-san-xie-tuo-zhan-wei-qiu-fang-1juse/) | 中等 | 🤩🤩🤩🤩 |
 | [552. 学生出勤记录 II](https://leetcode-cn.com/problems/student-attendance-record-ii/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/student-attendance-record-ii/solution/gong-shui-san-xie-yi-ti-san-jie-ji-yi-hu-fdfx/) | 困难 | 🤩🤩🤩🤩 |
 | [633. 平方数之和](https://leetcode-cn.com/problems/sum-of-square-numbers/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/sum-of-square-numbers/solution/gong-shui-san-xie-yi-ti-san-jie-mei-ju-s-7qi5/) | 简单 | 🤩🤩 |

Index/模拟.md

@@ -51,6 +51,7 @@
 | [495. 提莫攻击](https://leetcode-cn.com/problems/teemo-attacking/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/teemo-attacking/solution/gong-shui-san-xie-jian-dan-mo-ni-ti-by-a-gteh/) | 简单 | 🤩🤩🤩🤩🤩 |
 | [500. 键盘行](https://leetcode-cn.com/problems/keyboard-row/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/keyboard-row/solution/gong-shui-san-xie-jian-dan-zi-fu-chuan-m-zx6b/) | 简单 | 🤩🤩🤩🤩 |
 | [506. 相对名次](https://leetcode-cn.com/problems/relative-ranks/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/relative-ranks/solution/gong-shui-san-xie-jian-dan-pai-xu-mo-ni-cmuzj/) | 简单 | 🤩🤩🤩🤩 |
+| [507. 完美数](https://leetcode-cn.com/problems/perfect-number/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/perfect-number/solution/gong-shui-san-xie-jian-dan-mo-ni-tong-ji-e6jk/) | 简单 | 🤩🤩🤩 |
 | [520. 检测大写字母](https://leetcode-cn.com/problems/detect-capital/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/detect-capital/solution/gong-shui-san-xie-jian-dan-zi-fu-chuan-m-rpor/) | 简单 | 🤩🤩🤩🤩 |
 | [528. 按权重随机选择](https://leetcode-cn.com/problems/random-pick-with-weight/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/random-pick-with-weight/solution/gong-shui-san-xie-yi-ti-shuang-jie-qian-8bx50/) | 中等 | 🤩🤩🤩🤩 |
 | [541. 反转字符串 II](https://leetcode-cn.com/problems/reverse-string-ii/) | [LeetCode 题解链接](https://leetcode-cn.com/problems/reverse-string-ii/solution/gong-shui-san-xie-jian-dan-zi-fu-chuan-m-p88f/) | 简单 | 🤩🤩🤩🤩🤩 |

LeetCode/501-510/507. 完美数（简单）.md

@@ -0,0 +1,88 @@
+### 题目描述
+
+这是 LeetCode 上的 **[507. 完美数](https://leetcode-cn.com/problems/perfect-number/solution/gong-shui-san-xie-jian-dan-mo-ni-tong-ji-e6jk/)** ，难度为 **简单**。
+
+Tag : 「模拟」、「数论」、「数学」
+
+
+
+对于一个 正整数，如果它和除了它自身以外的所有 **正因子** 之和相等，我们称它为 「完美数」。
+
+给定一个 整数 `n`， 如果是完美数，返回 `true`，否则返回 `false`。
+
+示例 1：
+```
+输入：num = 28
+
+输出：true
+
+解释：28 = 1 + 2 + 4 + 7 + 14
+1, 2, 4, 7, 和 14 是 28 的所有正因子。
+```
+示例 2：
+```
+输入：num = 6
+
+输出：true
+```
+示例 3：
+```
+输入：num = 496
+
+输出：true
+```
+示例 4：
+```
+输入：num = 8128
+
+输出：true
+```
+示例 5：
+```
+输入：num = 2
+
+输出：false
+```
+
+提示：
+* $1 <= num <= 10^8$
+
+---
+
+### 数学
+
+我们知道正因数总是成对的出现，因此我们可以仅枚举每对正因数的较小数，即从 $[1, \sqrt{num}]$ 范围内进行枚举（其中 $nums > 1$）。
+
+同时为避免使用 `sqrt` 库函数和溢出，使用 $i <= \frac{num}{i}$ 作为上界判断。
+
+代码：
+```Java
+class Solution {
+    public boolean checkPerfectNumber(int num) {
+        if (num == 1) return false;
+        int ans = 1;
+        for (int i = 2; i <= num / i; i++) {
+            if (num % i == 0) {
+                ans += i;
+                if (i * i != num) ans += num / i;
+            }
+        }
+        return ans == num;
+    }
+}
+```
+* 时间复杂度：$O(\sqrt{num})$
+* 空间复杂度：$O(1)$
+
+---
+
+### 最后
+
+这是我们「刷穿 LeetCode」系列文章的第 `No.507` 篇，系列开始于 2021/01/01，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。
+
+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。
+
+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 。
+
+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。
+