feat: add solutions to lc problem: No.0753 (#3939)

No.0753.Cracking the Safe

Author: yanglbme

Diff for: solution/0700-0799/0753.Cracking the Safe/README.md

@@ -189,6 +189,32 @@ func crackSafe(n int, k int) string {
 }
 ```
 
+#### TypeScript
+
+```ts
+function crackSafe(n: number, k: number): string {
+    function dfs(u: number): void {
+        for (let x = 0; x < k; x++) {
+            const e = u * 10 + x;
+            if (!vis.has(e)) {
+                vis.add(e);
+                const v = e % mod;
+                dfs(v);
+                ans.push(x.toString());
+            }
+        }
+    }
+
+    const mod = Math.pow(10, n - 1);
+    const vis = new Set<number>();
+    const ans: string[] = [];
+
+    dfs(0);
+    ans.push('0'.repeat(n - 1));
+    return ans.join('');
+}
+```
+
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 <!-- solution:end -->

Diff for: solution/0700-0799/0753.Cracking the Safe/README_EN.md

@@ -76,7 +76,13 @@ Thus "01100" will unlock the safe. "10011", and "11001&
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Eulerian Circuit
+
+We can construct a directed graph based on the description in the problem: each point is considered as a length $n-1$ $k$-string, and each edge carries a character from $0$ to $k-1$. If there is a directed edge $e$ from point $u$ to point $v$, and the character carried by $e$ is $c$, then the last $k-1$ characters of $u+c$ form the string $v$. At this point, the edge $u+c$ represents a password of length $n$.
+
+In this directed graph, there are $k^{n-1}$ points, each point has $k$ outgoing edges and $k$ incoming edges. Therefore, this directed graph has an Eulerian circuit, and the path traversed by the Eulerian circuit is the answer to the problem.
+
+The time complexity is $O(k^n)$, and the space complexity is $O(k^n)$.
 
 <!-- tabs:start -->
 
@@ -181,6 +187,32 @@ func crackSafe(n int, k int) string {
 }
 ```
 
+#### TypeScript
+
+```ts
+function crackSafe(n: number, k: number): string {
+    function dfs(u: number): void {
+        for (let x = 0; x < k; x++) {
+            const e = u * 10 + x;
+            if (!vis.has(e)) {
+                vis.add(e);
+                const v = e % mod;
+                dfs(v);
+                ans.push(x.toString());
+            }
+        }
+    }
+
+    const mod = Math.pow(10, n - 1);
+    const vis = new Set<number>();
+    const ans: string[] = [];
+
+    dfs(0);
+    ans.push('0'.repeat(n - 1));
+    return ans.join('');
+}
+```
+
 <!-- tabs:end -->
 
 <!-- solution:end -->

Diff for: solution/0700-0799/0753.Cracking the Safe/Solution.ts

@@ -0,0 +1,21 @@
+function crackSafe(n: number, k: number): string {
+    function dfs(u: number): void {
+        for (let x = 0; x < k; x++) {
+            const e = u * 10 + x;
+            if (!vis.has(e)) {
+                vis.add(e);
+                const v = e % mod;
+                dfs(v);
+                ans.push(x.toString());
+            }
+        }
+    }
+
+    const mod = Math.pow(10, n - 1);
+    const vis = new Set<number>();
+    const ans: string[] = [];
+
+    dfs(0);
+    ans.push('0'.repeat(n - 1));
+    return ans.join('');
+}

Diff for: solution/0700-0799/0754.Reach a Number/README.md

@@ -68,15 +68,15 @@ tags:
 
 ### 方法一：数学分析
 
-由于对称性，每次可以选择向左或向右移动，因此，我们可以将 $target$ 统一取绝对值。
+由于对称性，每次可以选择向左或向右移动，因此，我们可以将 $\textit{target}$ 统一取绝对值。
 
 定义 $s$ 表示当前所处的位置，用变量 $k$ 记录移动的次数。初始时 $s$ 和 $k$ 均为 $0$。
 
-我们将 $s$ 一直循环累加，直到满足 $s\ge target$ 并且 $(s-target)\mod 2 = 0$，此时的移动次数 $k$ 就是答案，直接返回。
+我们将 $s$ 一直循环累加，直到满足 $s\ge \textit{target}$ 并且 $(s-\textit{target}) \bmod 2 = 0$，此时的移动次数 $k$ 就是答案，直接返回。
 
-为什么？因为如果 $s\ge target$ 且 $(s-target)\mod 2 = 0$，我们只需要把前面 $\frac{s-target}{2}$ 这个正整数变为负数，就能使得 $s$ 与 $target$ 相等。正整数变负数的过程，实际上是将移动的方向改变，但实际移动次数仍然不变。
+为什么？因为如果 $s\ge \textit{target}$ 且 $(s-\textit{target})\mod 2 = 0$，我们只需要把前面 $\frac{s-\textit{target}}{2}$ 这个正整数变为负数，就能使得 $s$ 与 $\textit{target}$ 相等。正整数变负数的过程，实际上是将移动的方向改变，但实际移动次数仍然不变。
 
-时间复杂度 $O(\sqrt{\left | target \right | })$，空间复杂度 $O(1)$。
+时间复杂度 $O(\sqrt{\left | \textit{target} \right | })$，空间复杂度 $O(1)$。
 
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Diff for: solution/0700-0799/0754.Reach a Number/README_EN.md

@@ -64,7 +64,17 @@ On the 2<sup>nd</sup> move, we step from 1 to 3 (2 steps).
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Mathematical Analysis
+
+Due to symmetry, each time we can choose to move left or right, so we can take the absolute value of $\textit{target}$.
+
+Define $s$ as the current position, and use the variable $k$ to record the number of moves. Initially, both $s$ and $k$ are $0$.
+
+We keep adding to $s$ in a loop until $s \ge \textit{target}$ and $(s - \textit{target}) \bmod 2 = 0$. At this point, the number of moves $k$ is the answer, and we return it directly.
+
+Why? Because if $s \ge \textit{target}$ and $(s - \textit{target}) \bmod 2 = 0$, we only need to change the sign of the positive integer $\frac{s - \textit{target}}{2}$ to negative, so that $s$ equals $\textit{target}$. Changing the sign of a positive integer essentially means changing the direction of the move, but the actual number of moves remains the same.
+
+The time complexity is $O(\sqrt{\left | \textit{target} \right | })$, and the space complexity is $O(1)$.
 
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Diff for: solution/0700-0799/0755.Pour Water/README_EN.md

@@ -80,7 +80,11 @@ Finally, the fourth droplet falls at index k = 3. Since moving left would not ev
 
 <!-- solution:start -->
 
-### Solution 1
+### Solution 1: Simulation
+
+We can simulate the process of each unit of water dropping. Each time a drop falls, we first try to move left. If it can move to a lower height, it moves to the lowest height; if it cannot move to a lower height, we try to move right. If it can move to a lower height, it moves to the lowest height; if it cannot move to a lower height, it rises at the current position.
+
+The time complexity is $O(v \times n)$, and the space complexity is $O(1)$, where $v$ and $n$ are the number of water drops and the length of the height array, respectively.
 
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