feat: update lc problems

solution/0000-0099/0052.N-Queens II/README.md

@@ -66,7 +66,7 @@
 ```python
 class Solution:
     def totalNQueens(self, n: int) -> int:
-        def dfs(i):
+        def dfs(i: int):
             if i == n:
                 nonlocal ans
                 ans += 1
@@ -184,6 +184,34 @@ func totalNQueens(n int) (ans int) {
 }
 ```
 
+### **TypeScript**
+
+```ts
+function totalNQueens(n: number): number {
+    const cols: boolean[] = Array(10).fill(false);
+    const dg: boolean[] = Array(20).fill(false);
+    const udg: boolean[] = Array(20).fill(false);
+    let ans = 0;
+    const dfs = (i: number) => {
+        if (i === n) {
+            ++ans;
+            return;
+        }
+        for (let j = 0; j < n; ++j) {
+            let [a, b] = [i + j, i - j + n];
+            if (cols[j] || dg[a] || udg[b]) {
+                continue;
+            }
+            cols[j] = dg[a] = udg[b] = true;
+            dfs(i + 1);
+            cols[j] = dg[a] = udg[b] = false;
+        }
+    };
+    dfs(0);
+    return ans;
+}
+```
+
 ### **...**
 
 ```

solution/0000-0099/0052.N-Queens II/README_EN.md

@@ -54,7 +54,7 @@ The time complexity is $O(n!)$, and the space complexity is $O(n)$. Here, $n$ is
 ```python
 class Solution:
     def totalNQueens(self, n: int) -> int:
-        def dfs(i):
+        def dfs(i: int):
             if i == n:
                 nonlocal ans
                 ans += 1
@@ -170,6 +170,34 @@ func totalNQueens(n int) (ans int) {
 }
 ```
 
+### **TypeScript**
+
+```ts
+function totalNQueens(n: number): number {
+    const cols: boolean[] = Array(10).fill(false);
+    const dg: boolean[] = Array(20).fill(false);
+    const udg: boolean[] = Array(20).fill(false);
+    let ans = 0;
+    const dfs = (i: number) => {
+        if (i === n) {
+            ++ans;
+            return;
+        }
+        for (let j = 0; j < n; ++j) {
+            let [a, b] = [i + j, i - j + n];
+            if (cols[j] || dg[a] || udg[b]) {
+                continue;
+            }
+            cols[j] = dg[a] = udg[b] = true;
+            dfs(i + 1);
+            cols[j] = dg[a] = udg[b] = false;
+        }
+    };
+    dfs(0);
+    return ans;
+}
+```
+
 ### **...**
 
 ```

solution/0000-0099/0052.N-Queens II/Solution.py

@@ -1,21 +1,21 @@
-class Solution:
-    def totalNQueens(self, n: int) -> int:
-        def dfs(i):
-            if i == n:
-                nonlocal ans
-                ans += 1
-                return
-            for j in range(n):
-                a, b = i + j, i - j + n
-                if cols[j] or dg[a] or udg[b]:
-                    continue
-                cols[j] = dg[a] = udg[b] = True
-                dfs(i + 1)
-                cols[j] = dg[a] = udg[b] = False
-
-        cols = [False] * 10
-        dg = [False] * 20
-        udg = [False] * 20
-        ans = 0
-        dfs(0)
-        return ans
+class Solution:
+    def totalNQueens(self, n: int) -> int:
+        def dfs(i: int):
+            if i == n:
+                nonlocal ans
+                ans += 1
+                return
+            for j in range(n):
+                a, b = i + j, i - j + n
+                if cols[j] or dg[a] or udg[b]:
+                    continue
+                cols[j] = dg[a] = udg[b] = True
+                dfs(i + 1)
+                cols[j] = dg[a] = udg[b] = False
+
+        cols = [False] * 10
+        dg = [False] * 20
+        udg = [False] * 20
+        ans = 0
+        dfs(0)
+        return ans

solution/0000-0099/0052.N-Queens II/Solution.ts

@@ -0,0 +1,23 @@
+function totalNQueens(n: number): number {
+    const cols: boolean[] = Array(10).fill(false);
+    const dg: boolean[] = Array(20).fill(false);
+    const udg: boolean[] = Array(20).fill(false);
+    let ans = 0;
+    const dfs = (i: number) => {
+        if (i === n) {
+            ++ans;
+            return;
+        }
+        for (let j = 0; j < n; ++j) {
+            let [a, b] = [i + j, i - j + n];
+            if (cols[j] || dg[a] || udg[b]) {
+                continue;
+            }
+            cols[j] = dg[a] = udg[b] = true;
+            dfs(i + 1);
+            cols[j] = dg[a] = udg[b] = false;
+        }
+    };
+    dfs(0);
+    return ans;
+}

solution/0000-0099/0063.Unique Paths II/README.md

@@ -55,7 +55,7 @@
 
 首先初始化 $dp$ 第一列和第一行的所有值，然后遍历其它行和列，有两种情况：
 
--   若 $obstacleGrid[i][j] = 1$，说明路径数为 $0$，那么 $dp[i][j] = 0 ￥；
+-   若 $obstacleGrid[i][j] = 1$，说明路径数为 $0$，那么 $dp[i][j] = 0$；
 -   若 ￥ obstacleGrid[i][j] = 0$，则 $dp[i][j] = dp[i - 1][j] + dp[i][j - 1]$。
 
 最后返回 $dp[m - 1][n - 1]$ 即可。

solution/0000-0099/0065.Valid Number/README.md

@@ -91,7 +91,7 @@
 
 遍历完字符串后，返回 `true`。
 
-时间复杂度 $O(n)$，空间复杂度 $O(1)$。其中 $n$ 为字符串长度。
+时间复杂度 $O(n)$，其中 $n$ 为字符串长度。空间复杂度 $O(1)$。
 
 <!-- tabs:start -->
 

solution/0000-0099/0069.Sqrt(x)/README.md

@@ -41,7 +41,15 @@
 
 <!-- 这里可写通用的实现逻辑 -->
 
-二分查找。
+**方法一：二分查找**
+
+我们定义二分查找的左边界 $l = 0$，右边界 $r = x$，然后在 $[l, r]$ 范围内查找平方根。
+
+在每一步查找中，我们找出中间值 $mid = (l + r + 1) / 2$，如果 $mid > x / mid$，说明平方根在 $[l, mid - 1]$ 范围内，我们令 $r = mid - 1$；否则说明平方根在 $[mid, r]$ 范围内，我们令 $l = mid$。
+
+查找结束后，返回 $l$ 即可。
+
+时间复杂度 $O(\log x)$，空间复杂度 $O(1)$。
 
 <!-- tabs:start -->
 
@@ -52,15 +60,14 @@
 ```python
 class Solution:
     def mySqrt(self, x: int) -> int:
-        left, right = 0, x
-        while left < right:
-            mid = (left + right + 1) >> 1
-            # mid*mid <= x
-            if mid <= x // mid:
-                left = mid
+        l, r = 0, x
+        while l < r:
+            mid = (l + r + 1) >> 1
+            if mid > x // mid:
+                r = mid - 1
             else:
-                right = mid - 1
-        return left
+                l = mid
+        return l
 ```
 
 ### **Java**
@@ -70,17 +77,16 @@ class Solution:
 ```java
 class Solution {
     public int mySqrt(int x) {
-        int left = 0, right = x;
-        while (left < right) {
-            int mid = (left + right + 1) >>> 1;
-            if (mid <= x / mid) {
-                // mid*mid <= x
-                left = mid;
+        int l = 0, r = x;
+        while (l < r) {
+            int mid = (l + r + 1) >>> 1;
+            if (mid > x / mid) {
+                r = mid - 1;
             } else {
-                right = mid - 1;
+                l = mid;
             }
         }
-        return left;
+        return l;
     }
 }
 ```
@@ -91,15 +97,16 @@ class Solution {
 class Solution {
 public:
     int mySqrt(int x) {
-        long long left = 0, right = x;
-        while (left < right) {
-            long long mid = left + ((right - left + 1) >> 1);
-            if (mid <= x / mid)
-                left = mid;
-            else
-                right = mid - 1;
+        int l = 0, r = x;
+        while (l < r) {
+            int mid = (l + r + 1ll) >> 1;
+            if (mid > x / mid) {
+                r = mid - 1;
+            } else {
+                l = mid;
+            }
         }
-        return (int) left;
+        return l;
     }
 };
 ```
@@ -108,16 +115,7 @@ public:
 
 ```go
 func mySqrt(x int) int {
-	left, right := 0, x
-	for left < right {
-		mid := left + (right-left+1)>>1
-		if mid <= x/mid {
-			left = mid
-		} else {
-			right = mid - 1
-		}
-	}
-	return left
+	return sort.Search(x+1, func(i int) bool { return i*i > x }) - 1
 }
 ```
 
@@ -129,17 +127,16 @@ func mySqrt(x int) int {
  * @return {number}
  */
 var mySqrt = function (x) {
-    let left = 0;
-    let right = x;
-    while (left < right) {
-        const mid = (left + right + 1) >>> 1;
-        if (mid <= x / mid) {
-            left = mid;
+    let [l, r] = [0, x];
+    while (l < r) {
+        const mid = (l + r + 1) >> 1;
+        if (mid > x / mid) {
+            r = mid - 1;
         } else {
-            right = mid - 1;
+            l = mid;
         }
     }
-    return left;
+    return l;
 };
 ```
 
@@ -148,20 +145,16 @@ var mySqrt = function (x) {
 ```cs
 public class Solution {
     public int MySqrt(int x) {
-        int left = 0, right = x;
-        while (left < right)
-        {
-            int mid = left + right + 1 >> 1;
-            if (mid <= x / mid)
-            {
-                left = mid;
-            }
-            else
-            {
-                right = mid - 1;
+        int l = 0, r = x;
+        while (l < r) {
+            int mid = (l + r + 1) >>> 1;
+            if (mid > x / mid) {
+                r = mid - 1;
+            } else {
+                l = mid;
             }
         }
-        return left;
+        return l;
     }
 }
 ```
@@ -171,19 +164,19 @@ public class Solution {
 ```rust
 impl Solution {
     pub fn my_sqrt(x: i32) -> i32 {
-        if x < 2 {
-            return x;
-        }
-        let mut l = 1;
-        let mut r = x / 2;
+        let mut l = 0;
+        let mut r = x;
+
         while l < r {
-            let mid = (l + r + 1) >> 1;
-            if x / mid < mid {
+            let mid = (l + r + 1) / 2;
+
+            if mid > x / mid {
                 r = mid - 1;
             } else {
                 l = mid;
             }
         }
+
         l
     }
 }