Approach

When answering the question "How can you write a function to calculate the minimum cost of merging stones?", it's essential to follow a structured framework. Here’s how you can approach this:

1. Understand the Problem Statement: Clearly define the problem and the requirements for merging stones.

2. Identify Constraints: Note any constraints or limitations that may impact your approach.

3. Choose the Right Algorithm: Select an optimal algorithm for solving the problem, such as dynamic programming.

4. Design the Function: Outline the function's structure, inputs, and outputs.

5. Code the Solution: Implement the function with clear logic and comments.

6. Test the Function: Verify the function with different test cases to ensure accuracy.

Key Points

• Clarity of the Problem: Ensure that you fully comprehend the task before diving into coding.

• Efficiency: Aim for a solution that runs efficiently, especially for larger datasets.

• Dynamic Programming: This is often the best approach for problems that involve making decisions based on previous results.

• Code Readability: Write clean, understandable code with proper naming conventions and comments.

• Testing: Always perform thorough testing to catch edge cases.

Standard Response

To calculate the minimum cost of merging stones, we can utilize a dynamic programming approach. Below is a comprehensive function that demonstrates how to perform this calculation in Python.

def mergeStones(stones, K):
 if not stones or (len(stones) - 1) % (K - 1) != 0:
 return -1

 n = len(stones)
 dp = [[[0] * (n + 1) for _ in range(n)] for _ in range(n)]
 prefix_sum = [0] * (n + 1)

 for i in range(n):
 prefix_sum[i + 1] = prefix_sum[i] + stones[i]

 for length in range(2, n + 1): # length of the range
 for i in range(n - length + 1): # start index
 j = i + length - 1 # end index
 dp[i][j][1] = float('inf')
 for k in range(i, j):
 dp[i][j][1] = min(dp[i][j][1], dp[i][k][1] + dp[k + 1][j][1])

 if (length - 1) % (K - 1) == 0:
 dp[i][j][1] += prefix_sum[j + 1] - prefix_sum[i]

 for m in range(2, K + 1):
 dp[i][j][m] = dp[i][j][1]

 for k in range(i, j):
 for m in range(2, K + 1):
 dp[i][j][m] = min(dp[i][j][m], dp[i][k][m - 1] + dp[k + 1][j][1])

 return dp[0][n - 1][K]

Explanation of the Code:

• Input: The function takes a list of integers stones representing the weight of each stone and an integer K representing the number of stones to merge at once.

• Dynamic Programming Table: A 3D list dp is created to store the minimum costs for merging stones.

• Prefix Sum Array: To optimize the sum calculation of stone weights, a prefix sum array is employed.

• Logic Flow: The function employs nested loops to build the solution iteratively, calculating the minimum cost for every possible segment of stones.

Tips & Variations

Common Mistakes to Avoid:

• Ignoring Edge Cases: Always check for scenarios where the input list is empty or does not meet the merging criteria.

• Inefficient Algorithms: Avoid using brute force methods that do not scale well with larger input sizes.

• Complex Logic: Ensure that the logic used is straightforward and well-commented to avoid confusion.

Alternative Ways to Answer:

• Recursive Approach: Explain how a recursive solution might work, although it's less efficient without memoization.

• Greedy Algorithm: Discuss the feasibility of a greedy approach, though it's usually not optimal for this problem.

Role-Specific Variations:

• Technical Roles: Focus on implementation details, performance optimization, and edge case handling.

• Managerial Roles: Emphasize your understanding of algorithmic efficiency and team collaboration on coding problems.

• Creative Roles: Illustrate how problem-solving in coding can relate to creative thinking and innovation in projects.

Follow-Up Questions:

• **What would you change in your solution if the merging cost was