In this article, I will share some common phrases and sentences you can use when solving LeetCode problems during a whiteboard interview.

確認需求的句子，可以參考 溝通合作用語。

Ask about the input range and consider edge cases / 詢問 input 範圍和考慮 edge cases

Number

• What is the range of the value?
• Are there rounding requirements?

String

• What is the maximum length of the string?
• What character the string may contain?
• Are there case sensitivity or whitespace constraints?

Array / Matrix

• What is the size of the array/matrix?
• What is the range of values in the array/matrix?
• Does the array contain negative numbers, duplicates, or can it be empty?

Lnked List

• What is the length of the linked list?
• What is the range of node values?

Tree

• How many nodes are in the tree?
• What is the range of node values?
• Is it a perfect, full, or complete binary tree?

• 滿二元樹 (Full binary tree): 除了樹葉以外，每個節點都有兩個小孩。
• 完全二元樹 (Complete binary tree): 各層節點全滿，除了最後一層，最後一層節點全部靠左。
• 完美二元樹 (Perfect binary tree): 各層節點全滿。同時也是 full binary tree 和 complete binary tree 。

Graph

• How many nodes and edges are there?
• What is the range of node/edge values?

To ensure we are on the right track, could you please confirm that this input/output example matches your expectations?

為了確保我們方向正確（步調一致），您能否確認這個輸入/輸出範例是否符合您的期望？

be on the right track 做法、方法適當/正確

I want to make sure I understand the scope fully. What are the definitive constraints or specifications I need to adhere to before I begin coding?

我想確保我完全理解範圍。在我開始寫程式之前，有哪些明確的限制或規格是我需要遵守的？

Based on my understanding, I'm anticipating that cases like ... will be key edge cases. Is that accurate?

基於我的理解，我預期像 ... 這樣的案例會是關鍵的極端案例。請問這樣理解準確嗎？

What’s the input range?

輸入的範圍是多少？

Can the input be empty or null?

輸入會是空的或 null 嗎？

Can the numbers be negative?

數字可能是負的嗎？

Should I handle duplicates?

需要處理重複的值嗎？

What should I return if the input is invalid?

若輸入無效，應該回傳什麼？

The expected output is...

預期輸出是...

Provide test cases / 舉測試案例

If I have an array like [2,7,11,15] and the target is 9, the two indices would be 0 and 1, right?

如果我有一個像 [2, 7, 11, 15] 這樣的陣列，而目標值是 9，那麼這兩個索引應該是 0 和 1，對吧？

Am I to assume that each input would only have one solution?

我可以假設每個輸入只有一個解嗎？

Am I to assume... 我是不是該假設...?

If we run the test with the functoin, the result is 10.

如果我們用這個函式執行測試，結果是 10。

Let's walk through a simple example to confirm our understanding.

讓我們走過一個簡單的範例來確認我們的理解。

Explain the solution approach and ideas / 解題方向、想法說明

To solve this problem, I plan to use a data structure called a hashmap, because it uses a key-value format and allows quick access to the value we want, thereby reducing time complexity.

為了解決這個問題，我打算使用一種稱為哈希表（hashmap）的資料結構，因為它採用鍵值對的格式，能夠快速存取我們想要的值，從而降低時間複雜度。

I plan to use...

My approach would be implementing Dijkstra's algorithm to optimize for time complexity in finding the shortest path.

我的方法是實作 Dijkstra 演算法，以優化尋找最短路徑時的時間複雜度。

My approach would be...

I think the Union-Find algorithm would be suitable here, as it efficiently handles dynamic connectivity problems in a graph.

我認為 Union-Find 演算法在這裡會很合適，因為它能有效處理圖中的動態連通性問題。

would be suitable here...

Although a brute force approach is feasible, it would lead to a Time Limit Exceeded error.

雖然暴力法可行，但它會導致超時錯誤。

For efficient prefix searching, a Trie is the optimal data structure.

為了高效的前綴搜尋，前綴樹是最佳的資料結構。

A greedy algorithm can find the solution by making the locally optimal choice at each step.

貪婪演算法可以透過在每一步做出局部最佳選擇來找到解。

I'm using backtracking to explore all possible combinations and prune invalid paths."

我正在使用回溯法來探索所有可能的組合並修剪無效路徑。

We can prune the search space by sorting the input first.

我們可以透過先對輸入進行排序來修剪搜尋空間。

My initial thought process was to use recursion, but that led to redundant calculations.

我最初的思考過程是使用遞迴，但那導致了重複計算。

My initial thought process was...

Before writing the recursive function, let's first establish a base case: if the array is empty, return zero.

在撰寫遞迴函數之前，我們先確定一個基本情況（或基本條件）：如果陣列為空，則回傳零。

Let's first establish a base case. 我們首先確定一個基本案例。

I’ll keep track of the frequency using a hash map.

我需要記錄出現次數。

keep track of 追蹤、記錄、掌握某人或某事的動態或情況。

The key idea is to...

核心想法是...

Let’s break the problem down.

我們先把問題拆解。

Based on my understanding...

根據我的理解。

Write the code / 撰寫程式碼

I first define a function called fourSum. This function takes two parameters: the first is an array, and the second is a number representing the target value for the four-number sum.

我先定義一個函式，叫做 fourSum。這個函式接收兩個參數：第一個是陣列，第二個是一個數字，代表四個數相加的目標值。

define a function called(named) 定一個叫 ? 的函式

take ? parameter(s) 接收 ? 個參數

I’ll start by writing a helper function.

我會先寫一個輔助函式。

Let's initialize the DP table with a size of N+1.

我們用 N+1 的大小來初始化 DP 表。

We need to loop through the array from i equals zero to N minus one.

我們需要從 i 等於零循環遍歷陣列到 N 減一。

I’ll check if my logic works for all cases.

我會確認邏輯是否適用所有情況。

This condition serves as our base case for the recursion.

這個條件充當我們遞迴的基本情況。

Let’s dry run the code.

我們手動跑一次程式看看。

I might have a bug here.

這裡我可能有 bug。

Let’s debug this part.

我們來除錯這一段。

The code looks good to me.

程式看起來沒問題。

I’ll optimize it later if needed.

若有需要，我之後會優化它。

I need a moment to re-evaluate the approach.

我需要一點時間來重新評估這個方法。

This is where we could potentially have an off-by-one error.

這可能是我們可能會出現差一錯誤的地方。

差一錯誤（英語：Off-by-one error，縮寫OBOE）是在計數時由於邊界條件判斷失誤導致結果多了一或少了一的錯誤，通常指電腦編程中迴圈多了一次或者少了一次的程式錯誤，屬於邏輯錯誤的一種。比如，程式設計師在迴圈中進行比較的時候，本該使用「小於等於」，但卻使用了「小於」，或者是程式設計師沒有考慮到一個序列是從0而不是1開始（許多程式語言的陣列下標都是這樣）。

差一錯誤 WIKI

We must handle integer overflow if the numbers are too large.

如果數字太大，我們必須處理整數溢位。

Discuss time and space complexity / 討論時間、空間複雜度

• constant space => 常數空間
• requires additional linear space => 需要額外的線性空間
• space complexity is proportional to the input size => 空間複雜度與輸入大小成正比

We need to optimize the algorithm to achieve Big O of n time instead of n squared.

我們需要優化這個演算法，讓時間複雜度從 O(n²) 降到 O(n)。

Accessing an element in an array is a Big O of one operation.

存取陣列中的元素是 O(1) 的操作。

The space complexity is Big O of n because we are using a hash map to store up to n elements.

空間複雜度是 O(n)，因為我們使用了一個雜湊映射來儲存最多 n 個元素。

There's a time-space trade-off: we use extra space (Big O of n) to achieve a faster runtime (Big O of n).

這裡存在一個時間與空間的權衡取捨：我們使用額外的空間 (O(n)) 來實現更快的運行時間 (O(n))。

time-space trade-off 時間與空間的權衡取捨

This approach trades space for time.

這個方法是以空間換取時間。

This is the optimal time complexity we can achieve for this problem.

這是我們針對這個問題可以達到的最佳時間複雜度。

Other expressions that can be used during the problem-solving process / 其他可以用在解題過程的用語

Since

因為。

範例：

Since this problem is similar to a previous one I solved on LeetCode.

Next

接下來。

範例：

Next, I will use a hash map to optimize the solution for this LeetCode problem and reduce the time complexity.

接下來，我會使用雜湊表來優化這題 LeetCode 的解法，並降低時間複雜度。

And finally

最後。

範例：

And finally, I analyzed the time complexity of my solution and confirmed that it runs in O(n log n) time.

最後，我分析我的解法的時間複雜度，並確認它的執行時間為 O(n log n)。

to verify that...

驗證...是否...。

範例：

To verify that my code handles edge cases, I added custom test inputs with empty arrays and large numbers.

為了確認我的程式能處理邊界情況，我加入了空陣列與大數字的自訂測資。

in some cases

在某些情況下...。

範例：

In some cases, a problem might look like dynamic programming, but a greedy approach works better.

在某些情況下，問題看起來像是動態規劃，但其實用貪心法更有效。