feat: add solutions to lc problem: No.3958 (#5251)

Author: yanglbme

solution/0900-0999/0987.Vertical Order Traversal of a Binary Tree/README.md

@@ -352,11 +352,11 @@ $$
 
 - 时间复杂度：$O(n \log n)$。
 
-  BFS 遍历所有节点需要 $O(n)$ 时间。各列中的节点值排序总复杂度为 $O(n \log n)$，于是有 $O(n \log n)$。
+    BFS 遍历所有节点需要 $O(n)$ 时间。各列中的节点值排序总复杂度为 $O(n \log n)$，于是有 $O(n \log n)$。
 
 - 空间复杂度：$O(n)$。
 
-  队列、双端队列以及结果数组最多存储所有节点，因此空间复杂度为 $O(n)$。
+    队列、双端队列以及结果数组最多存储所有节点，因此空间复杂度为 $O(n)$。
 
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solution/0900-0999/0987.Vertical Order Traversal of a Binary Tree/README_EN.md

@@ -313,6 +313,7 @@ function verticalTraversal(root: TreeNode | null): number[][] {
 We perform a breadth-first search (BFS) on the tree.
 
 Since our final answer must be returned from leftmost column to rightmost column, we maintain:
+
 - `leftmostCol`: smallest column index currently stored.
 - `rightmostCol`: largest column index currently stored.
 
@@ -325,10 +326,9 @@ When a newly visited node belongs to a column outside the current range:
 - If its column index $>$ `rightmostCol`, we append a new column container to the back of deque.
 
 - For any column index `col`, its corresponding position in `columnsValues` can be computed as:
-- 
-$$
-col - `leftmostCol`
-$$
+- $$
+  col - `leftmostCol`
+  $$
 
 This allows us to locate target column in constant time.
 
@@ -344,13 +344,13 @@ Finally, we output all columns from left to right.
 Assume binary tree contains $n$ nodes.
 
 - Time Complexity: $O(n \log n)$
-  
-  BFS visits every node exactly once, which takes $O(n)$ time. Sorting values is $O(n \log n)$ time in worst case.
-  Therefore, overall time complexity is $O(n \log n)$.
+
+    BFS visits every node exactly once, which takes $O(n)$ time. Sorting values is $O(n \log n)$ time in worst case.
+    Therefore, overall time complexity is $O(n \log n)$.
 
 - Space Complexity: $O(n)$
 
-  BFS queue, deque structure, and result container may collectively store all nodes, resulting in $O(n)$ space.
+    BFS queue, deque structure, and result container may collectively store all nodes, resulting in $O(n)$ space.
 
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solution/3900-3999/3958.Minimum Cost to Split into Ones II/README.md

@@ -0,0 +1,182 @@
+---
+comments: true
+difficulty: 中等
+edit_url: https://github.com/doocs/leetcode/edit/main/solution/3900-3999/3958.Minimum%20Cost%20to%20Split%20into%20Ones%20II/README.md
+---
+
+<!-- problem:start -->
+
+# [3958. Minimum Cost to Split into Ones II 🔒](https://leetcode.cn/problems/minimum-cost-to-split-into-ones-ii)
+
+[English Version](/solution/3900-3999/3958.Minimum%20Cost%20to%20Split%20into%20Ones%20II/README_EN.md)
+
+## 题目描述
+
+<!-- description:start -->
+
+<p>You are given an integer <code>n</code>.</p>
+
+<p>In one operation, you may split an integer <code>x</code> into two positive integers <code>a</code> and <code>b</code> such that <code>a + b = x</code>.</p>
+
+<p>The cost of this operation is <code>a * b</code>.</p>
+
+<p>Return the <strong>minimum</strong> total cost required to split the integer <code>n</code> into <code>n</code> ones.</p>
+
+<p>&nbsp;</p>
+<p><strong class="example">Example 1:</strong></p>
+
+<div class="example-block">
+<p><strong>Input:</strong> <span class="example-io">n = 3</span></p>
+
+<p><strong>Output:</strong> <span class="example-io">3</span></p>
+
+<p><strong>Explanation:</strong></p>
+
+<p>One optimal set of operations is:</p>
+
+<table border="1" bordercolor="#ccc" cellpadding="5" cellspacing="0" style="border-collapse:collapse;">
+	<tbody>
+		<tr>
+			<th><code>x</code></th>
+			<th><code>a</code></th>
+			<th><code>b</code></th>
+			<th><code>a + b</code></th>
+			<th><code>a * b</code></th>
+			<th>Cost</th>
+		</tr>
+		<tr>
+			<td>3</td>
+			<td>1</td>
+			<td>2</td>
+			<td>3</td>
+			<td>2</td>
+			<td>2</td>
+		</tr>
+		<tr>
+			<td>2</td>
+			<td>1</td>
+			<td>1</td>
+			<td>2</td>
+			<td>1</td>
+			<td>1</td>
+		</tr>
+	</tbody>
+</table>
+
+<p>Thus, the minimum total cost is <code>2 + 1 = 3</code>.</p>
+</div>
+
+<p><strong class="example">Example 2:</strong></p>
+
+<div class="example-block">
+<p><strong>Input:</strong> <span class="example-io">n = 4</span></p>
+
+<p><strong>Output:</strong> <span class="example-io">6</span></p>
+
+<p><strong>Explanation:​​​​​​​</strong></p>
+
+<p>One optimal set of operations is:</p>
+
+<table border="1" bordercolor="#ccc" cellpadding="5" cellspacing="0" style="border-collapse:collapse;">
+	<tbody>
+		<tr>
+			<th><code>x</code></th>
+			<th><code>a</code></th>
+			<th><code>b</code></th>
+			<th><code>a + b</code></th>
+			<th><code>a * b</code></th>
+			<th>Cost</th>
+		</tr>
+		<tr>
+			<td>4</td>
+			<td>2</td>
+			<td>2</td>
+			<td>4</td>
+			<td>4</td>
+			<td>4</td>
+		</tr>
+		<tr>
+			<td>2</td>
+			<td>1</td>
+			<td>1</td>
+			<td>2</td>
+			<td>1</td>
+			<td>1</td>
+		</tr>
+	</tbody>
+</table>
+
+<p>Thus, the minimum total cost is <code>4 + 1 + 1 = 6</code>.</p>
+</div>
+
+<p>&nbsp;</p>
+<p><strong>Constraints:</strong></p>
+
+<ul>
+	<li><code>1 &lt;= n &lt;= 5 * 10<sup>7</sup></code></li>
+</ul>
+
+<!-- description:end -->
+
+## 解法
+
+<!-- solution:start -->
+
+### 方法一：数学
+
+要使得成本最小，我们应该首先将 $n$ 拆分成 $1$ 和 $n - 1$，所需成本为 $n - 1$；然后将 $n - 1$ 拆分成 $1$ 和 $n - 2$，所需成本为 $n - 2$。依此类推，得到总成本为 $1 + 2 + \dots + (n - 1) = \frac{n \times (n - 1)}{2}$。
+
+时间复杂度 $O(1)$，空间复杂度 $O(1)$。
+
+<!-- tabs:start -->
+
+#### Python3
+
+```python
+class Solution:
+    def minCost(self, n: int) -> int:
+        return n * (n - 1) // 2
+```
+
+#### Java
+
+```java
+class Solution {
+    public long minCost(int n) {
+        return 1L * n * (n - 1) / 2;
+    }
+}
+```
+
+#### C++
+
+```cpp
+class Solution {
+public:
+    long long minCost(int n) {
+        return 1LL * n * (n - 1) / 2;
+    }
+};
+```
+
+#### Go
+
+```go
+func minCost(n int) int64 {
+	return int64(n * (n - 1) / 2)
+}
+```
+
+#### TypeScript
+
+```ts
+function minCost(n: number): number {
+    return (n * (n - 1)) / 2;
+}
+```
+
+<!-- tabs:end -->
+
+<!-- solution:end -->
+
+<!-- problem:end -->