Delete Columns to Make Sorted in Python

Given an array of N lowercase letter strings of equal length, we need to find the minimum number of column deletions required to make all remaining columns sorted in non-decreasing order.

When we delete columns at specific indices, the remaining characters form new columns. Each remaining column must be sorted for the solution to be valid.

Problem Understanding

Consider the array ["abcdef", "uvwxyz"] with deletion indices {0, 2, 3}:

• After deletions: ["bef", "vyz"]
• Remaining columns: ["b","v"], ["e","y"], ["f","z"]
• All columns are sorted in non-decreasing order

Algorithm

The approach involves these steps:

• Transform strings into a matrix where each column represents character positions
• Check each column to see if it's already sorted
• Count columns that need deletion (unsorted columns)
• Return the total count

Implementation

class Solution:
    def minDeletionSize(self, A):
        return sum([1 for col in zip(*A) if list(col) != sorted(col)])

# Test the solution
ob = Solution()
result = ob.minDeletionSize(["cba", "daf", "ghi"])
print("Minimum deletions needed:", result)

Minimum deletions needed: 1

Step-by-Step Example

def solve_step_by_step(A):
    print("Input array:", A)
    
    # Create columns using zip
    columns = list(zip(*A))
    print("Columns:", columns)
    
    deletions_needed = 0
    for i, col in enumerate(columns):
        is_sorted = list(col) == sorted(col)
        print(f"Column {i}: {col} - Sorted: {is_sorted}")
        if not is_sorted:
            deletions_needed += 1
    
    print(f"Total deletions needed: {deletions_needed}")
    return deletions_needed

# Test with example
solve_step_by_step(["cba", "daf", "ghi"])

Input array: ['cba', 'daf', 'ghi']
Columns: (('c', 'd', 'g'), ('b', 'a', 'h'), ('a', 'f', 'i'))
Column 0: ('c', 'd', 'g') - Sorted: True
Column 1: ('b', 'a', 'h') - Sorted: False
Column 2: ('a', 'f', 'i') - Sorted: True
Total deletions needed: 1

How It Works

The solution uses zip(*A) to transpose the array, converting rows to columns. For each column, it compares the original order with the sorted order. If they don't match, the column needs deletion.

Conclusion

This problem is solved by checking each column's sort status and counting unsorted columns. The zip(*A) transpose operation elegantly converts string positions into comparable columns.