Minimize Global Replacements to Make Values Contiguous

Question

The question asks the candidate to determine the minimum number of global replacements needed to ensure that each unique value in an array appears in a contiguous block.

Codemia · Accepted Answer

The goal is to transform an array such that all occurrences of each unique value appear in contiguous blocks. For example, given the array `[1, 2, 1, 3, 2]`, we want to transform it into something like `[1, 1, 2, 2, 3]` with the minimum number of replacements.

To solve this problem, we can use a two-step approach. First, we will identify the segments of contiguous values in the array. Second, we will calculate the minimum number of replacements needed to merge these segments into contiguous blocks for each unique value.

1. Traverse the array and count the number of segments for each unique value.  
2. For each unique value, calculate the number of segments that need to be merged.  
3. The minimum replacements will be equal to the total segments minus one for each unique value.

Here is the Python code implementing this logic:
```python
def min_replacements(arr):
    from collections import defaultdict
    segments = defaultdict(int)
    n = len(arr)

# Count segments
    for i in range(n):
        if i == 0 or arr[i] != arr[i - 1]:
            segments[arr[i]] += 1

# Calculate minimum replacements
    min_replacements = 0
    for count in segments.values():
        min_replacements += count - 1

return min_replacements
```
This code efficiently counts the segments and computes the minimum replacements needed.

The time complexity of this solution is O(n), where n is the length of the array, as we traverse the array once to count segments. The space complexity is O(k), where k is the number of unique values in the array, due to the storage of segment counts.

Interviewers will be looking for a clear understanding of the problem and an efficient approach to solving it. They want to see how well you can articulate your thought process, handle edge cases, and write clean code. Additionally, they will assess your ability to analyze the algorithm's complexity.

Minimize Global Replacements to Make Values Contiguous

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