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feat: update solutions to lc problems: No.633~635 (doocs#2481)
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‎solution/0600-0699/0633.Sum of Square Numbers/README.md

Lines changed: 30 additions & 22 deletions
Original file line numberDiff line numberDiff line change
@@ -37,7 +37,11 @@
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## 解法
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40-
### 方法一
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### 方法一：数学 + 双指针
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42+
我们可以使用双指针的方法来解决这个问题，定义两个指针 $a$ 和 $b$，分别指向 $0$ 和 $\sqrt{c}$。在每一步中，我们会计算 $s = a^2 + b^2$ 的值，然后比较 $s$ 与 $c$ 的大小。如果 $s = c$，我们就找到了两个整数 $a$ 和 $b$，使得 $a^2 + b^2 = c$。如果 $s < c$，我们将 $a$ 的值增加 $1$，如果 $s > c$，我们将 $b$ 的值减小 $1$。我们不断进行这个过程直到找到答案，或者 $a$ 的值大于 $b$ 的值，返回 `false`。
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时间复杂度 $O(\sqrt{c})$，其中 $c$ 是给定的非负整数。空间复杂度 $O(1)$。
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<!-- tabs:start -->
4347

@@ -80,14 +84,17 @@ class Solution {
8084
class Solution {
8185
public:
8286
bool judgeSquareSum(int c) {
83-
long a = 0, b = (long) sqrt(c);
87+
long long a = 0, b = sqrt(c);
8488
while (a <= b) {
85-
long s = a * a + b * b;
86-
if (s == c) return true;
87-
if (s < c)
89+
long long s = a * a + b * b;
90+
if (s == c) {
91+
return true;
92+
}
93+
if (s < c) {
8894
++a;
89-
else
95+
} else {
9096
--b;
97+
}
9198
}
9299
return false;
93100
}
@@ -114,12 +121,13 @@ func judgeSquareSum(c int) bool {
114121

115122
```ts
116123
function judgeSquareSum(c: number): boolean {
117-
let a = 0,
118-
b = Math.floor(Math.sqrt(c));
124+
let [a, b] = [0, Math.floor(Math.sqrt(c))];
119125
while (a <= b) {
120-
let sum = a ** 2 + b ** 2;
121-
if (sum == c) return true;
122-
if (sum < c) {
126+
const s = a * a + b * b;
127+
if (s === c) {
128+
return true;
129+
}
130+
if (s < c) {
123131
++a;
124132
} else {
125133
--b;
@@ -131,22 +139,22 @@ function judgeSquareSum(c: number): boolean {
131139

132140
```rust
133141
use std::cmp::Ordering;
142+
134143
impl Solution {
135144
pub fn judge_square_sum(c: i32) -> bool {
136-
let c = c as i64;
137-
let mut left = 0;
138-
let mut right = (c as f64).sqrt() as i64;
139-
while left <= right {
140-
let num = left * left + right * right;
141-
match num.cmp(&c) {
145+
let mut a: i64 = 0;
146+
let mut b: i64 = (c as f64).sqrt() as i64;
147+
while a <= b {
148+
let s = a * a + b * b;
149+
match s.cmp(&(c as i64)) {
150+
Ordering::Equal => {
151+
return true;
152+
}
142153
Ordering::Less => {
143-
left += 1;
154+
a += 1;
144155
}
145156
Ordering::Greater => {
146-
right -= 1;
147-
}
148-
Ordering::Equal => {
149-
return true;
157+
b -= 1;
150158
}
151159
}
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}

‎solution/0600-0699/0633.Sum of Square Numbers/README_EN.md

Lines changed: 30 additions & 22 deletions
Original file line numberDiff line numberDiff line change
@@ -33,7 +33,11 @@
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## Solutions
3535

36-
### Solution 1
36+
### Solution 1: Mathematics + Two Pointers
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We can use the two-pointer method to solve this problem. Define two pointers $a$ and $b$, pointing to $0$ and $\sqrt{c}$ respectively. In each step, we calculate the value of $s = a^2 + b^2$, and then compare the size of $s$ and $c$. If $s = c$, we have found two integers $a$ and $b$ such that $a^2 + b^2 = c$. If $s < c$, we increase the value of $a$ by $1$. If $s > c$, we decrease the value of $b$ by $1$. We continue this process until we find the answer, or the value of $a$ is greater than the value of $b$, and return `false`.
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The time complexity is $O(\sqrt{c})$, where $c$ is the given non-negative integer. The space complexity is $O(1)$.
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<!-- tabs:start -->
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@@ -76,14 +80,17 @@ class Solution {
7680
class Solution {
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public:
7882
bool judgeSquareSum(int c) {
79-
long a = 0, b = (long) sqrt(c);
83+
long long a = 0, b = sqrt(c);
8084
while (a <= b) {
81-
long s = a * a + b * b;
82-
if (s == c) return true;
83-
if (s < c)
85+
long long s = a * a + b * b;
86+
if (s == c) {
87+
return true;
88+
}
89+
if (s < c) {
8490
++a;
85-
else
91+
} else {
8692
--b;
93+
}
8794
}
8895
return false;
8996
}
@@ -110,12 +117,13 @@ func judgeSquareSum(c int) bool {
110117

111118
```ts
112119
function judgeSquareSum(c: number): boolean {
113-
let a = 0,
114-
b = Math.floor(Math.sqrt(c));
120+
let [a, b] = [0, Math.floor(Math.sqrt(c))];
115121
while (a <= b) {
116-
let sum = a ** 2 + b ** 2;
117-
if (sum == c) return true;
118-
if (sum < c) {
122+
const s = a * a + b * b;
123+
if (s === c) {
124+
return true;
125+
}
126+
if (s < c) {
119127
++a;
120128
} else {
121129
--b;
@@ -127,22 +135,22 @@ function judgeSquareSum(c: number): boolean {
127135

128136
```rust
129137
use std::cmp::Ordering;
138+
130139
impl Solution {
131140
pub fn judge_square_sum(c: i32) -> bool {
132-
let c = c as i64;
133-
let mut left = 0;
134-
let mut right = (c as f64).sqrt() as i64;
135-
while left <= right {
136-
let num = left * left + right * right;
137-
match num.cmp(&c) {
141+
let mut a: i64 = 0;
142+
let mut b: i64 = (c as f64).sqrt() as i64;
143+
while a <= b {
144+
let s = a * a + b * b;
145+
match s.cmp(&(c as i64)) {
146+
Ordering::Equal => {
147+
return true;
148+
}
138149
Ordering::Less => {
139-
left += 1;
150+
a += 1;
140151
}
141152
Ordering::Greater => {
142-
right -= 1;
143-
}
144-
Ordering::Equal => {
145-
return true;
153+
b -= 1;
146154
}
147155
}
148156
}

‎solution/0600-0699/0633.Sum of Square Numbers/Solution.cpp

Lines changed: 8 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -1,14 +1,17 @@
11
class Solution {
22
public:
33
bool judgeSquareSum(int c) {
4-
long a = 0, b = (long) sqrt(c);
4+
long long a = 0, b = sqrt(c);
55
while (a <= b) {
6-
long s = a * a + b * b;
7-
if (s == c) return true;
8-
if (s < c)
6+
long long s = a * a + b * b;
7+
if (s == c) {
8+
return true;
9+
}
10+
if (s < c) {
911
++a;
10-
else
12+
} else {
1113
--b;
14+
}
1215
}
1316
return false;
1417
}

‎solution/0600-0699/0633.Sum of Square Numbers/Solution.rs

Lines changed: 11 additions & 11 deletions
Original file line numberDiff line numberDiff line change
@@ -1,20 +1,20 @@
11
use std::cmp::Ordering;
2+
23
impl Solution {
34
pub fn judge_square_sum(c: i32) -> bool {
4-
let c = c as i64;
5-
let mut left = 0;
6-
let mut right = (c as f64).sqrt() as i64;
7-
while left <= right {
8-
let num = left * left + right * right;
9-
match num.cmp(&c) {
5+
let mut a: i64 = 0;
6+
let mut b: i64 = (c as f64).sqrt() as i64;
7+
while a <= b {
8+
let s = a * a + b * b;
9+
match s.cmp(&(c as i64)) {
10+
Ordering::Equal => {
11+
return true;
12+
}
1013
Ordering::Less => {
11-
left += 1;
14+
a += 1;
1215
}
1316
Ordering::Greater => {
14-
right -= 1;
15-
}
16-
Ordering::Equal => {
17-
return true;
17+
b -= 1;
1818
}
1919
}
2020
}

‎solution/0600-0699/0633.Sum of Square Numbers/Solution.ts

Lines changed: 6 additions & 5 deletions
Original file line numberDiff line numberDiff line change
@@ -1,10 +1,11 @@
11
function judgeSquareSum(c: number): boolean {
2-
let a = 0,
3-
b = Math.floor(Math.sqrt(c));
2+
let [a, b] = [0, Math.floor(Math.sqrt(c))];
43
while (a <= b) {
5-
let sum = a ** 2 + b ** 2;
6-
if (sum == c) return true;
7-
if (sum < c) {
4+
const s = a * a + b * b;
5+
if (s === c) {
6+
return true;
7+
}
8+
if (s < c) {
89
++a;
910
} else {
1011
--b;

‎solution/0600-0699/0634.Find the Derangement of An Array/README.md

Lines changed: 4 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -56,9 +56,7 @@ $$
5656

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最终答案即为 $f[n]$。注意答案的取模操作。
5858

59-
我们发现，状态转移方程中只与 $f[i - 1]$ 和 $f[i - 2]$ 有关，因此我们可以使用两个变量 $a$ 和 $b$ 来分别表示 $f[i - 1]$ 和 $f[i - 2]$，从而将空间复杂度降低到 $O(1)$。
60-
61-
时间复杂度 $O(n)$，空间复杂度 $O(1)$。其中 $n$ 为数组的长度。
59+
时间复杂度 $O(n)$，其中 $n$ 为数组的长度。空间复杂度 $O(1)$。
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6361
<!-- tabs:start -->
6462

@@ -116,7 +114,9 @@ func findDerangement(n int) int {
116114

117115
<!-- tabs:end -->
118116

119-
### 方法二
117+
### 方法二：动态规划（空间优化）
118+
119+
我们发现，状态转移方程中只与 $f[i - 1]$ 和 $f[i - 2]$ 有关，因此我们可以使用两个变量 $a$ 和 $b$ 来分别表示 $f[i - 1]$ 和 $f[i - 2]$，从而将空间复杂度降低到 $O(1)$。
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<!-- tabs:start -->
122122

‎solution/0600-0699/0634.Find the Derangement of An Array/README_EN.md

Lines changed: 21 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -35,7 +35,24 @@
3535

3636
## Solutions
3737

38-
### Solution 1
38+
### Solution 1: Dynamic Programming
39+
40+
We define $f[i]$ as the number of derangement of an array of length $i$. Initially, $f[0] = 1$, $f[1] = 0$. The answer is $f[n]$.
41+
42+
For an array of length $i$, we consider where to place the number $1$. Suppose it is placed in the $j$-th position, where there are $i-1$ choices. Then, the number $j$ has two choices:
43+
44+
- Placed in the first position, then the remaining $i - 2$ positions have $f[i - 2]$ derangements, so there are a total of $(i - 1) \times f[i - 2]$ derangements;
45+
- Not placed in the first position, which is equivalent to the derangement of an array of length $i - 1$, so there are a total of $(i - 1) \times f[i - 1]$ derangements.
46+
47+
In summary, we have the following state transition equation:
48+
49+
$$
50+
f[i] = (i - 1) \times (f[i - 1] + f[i - 2])
51+
$$
52+
53+
The final answer is $f[n]$. Note the modulo operation in the answer.
54+
55+
The time complexity is $O(n)$, where $n$ is the length of the array. The space complexity is $O(1)$.
3956

4057
<!-- tabs:start -->
4158

@@ -93,7 +110,9 @@ func findDerangement(n int) int {
93110

94111
<!-- tabs:end -->
95112

96-
### Solution 2
113+
### Solution 2: Dynamic Programming (Space Optimization)
114+
115+
We notice that the state transition equation only relates to $f[i - 1]$ and $f[i - 2]$. Therefore, we can use two variables $a$ and $b$ to represent $f[i - 1]$ and $f[i - 2]$ respectively, thereby reducing the space complexity to $O(1)$.
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98117
<!-- tabs:start -->
99118

‎solution/0600-0699/0635.Design Log Storage System/README_EN.md

Lines changed: 5 additions & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -56,7 +56,11 @@ logSystem.retrieve(&quot;2016:01:01:01:01:01&quot;, &quot;2017:01:01:23:00:00&qu
5656

5757
## Solutions
5858

59-
### Solution 1
59+
### Solution 1: String Comparison
60+
61+
Store the `id` and `timestamp` of the logs as tuples in an array. Then in the `retrieve()` method, truncate the corresponding parts of `start` and `end` based on `granularity`, and traverse the array, adding the `id` that meets the conditions to the result array.
62+
63+
In terms of time complexity, the time complexity of the `put()` method is $O(1)$, and the time complexity of the `retrieve()` method is $O(n)$, where $n$ is the length of the array.
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6165
<!-- tabs:start -->
6266

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