Assessing String Transformability with Substring Sort Operations in Python

💡 Problem Formulation: Given two strings, the task is to determine if one string can be transformed into another through a series of substring sort operations. In these operations, you can take any substring within the string and reorder its characters in any way. The goal is to find out if by only using these operations, the source string can be turned into the target string. For example, transforming the string "abc" into "cba" is possible by reversing the whole string, which is a valid sort operation.

Method 1: Greedy Approach

This method involves checking the relative ordering of characters in the strings, moving from left to right. We ensure that for each character of the target string, it is possible to move it leftward to match, without disturbing the relative order of other characters that must come before it, taking advantage of the fact that substring sorting can move characters leftward.

Here’s an example:

def canTransform(source, target):
    if sorted(source) != sorted(target):
        return False
    source = list(source)
    for i in range(len(target)):
        if target[i] in source:
            source.remove(target[i])
            source.insert(i, target[i])
        else:
            return False
    return True

print(canTransform("abc", "cba"))  # Expected to return True

The output of this code snippet is:

True

This Python code verifies if the target string "cba" can be constructed from the source string "abc" by performing substring sort operations. The function canTransform compares sorted versions of the source and target strings to ensure they consist of the same characters. It then tries to reconstruct the target sequence from the source by removing and inserting characters at their targeted indices. If all characters match and can be moved to their respective positions, the function returns True, indicating the transformation is possible.

Method 2: Counting Method

Using the counting method, we map the frequency of each character in both strings and sequentially compare these distributions to determine if the target string is a valid permutation that can be achieved by sorting substrings of the source string.

Here’s an example:

from collections import Counter

def canTransformWithCount(source, target):
    if Counter(source) != Counter(target):
        return False
    
    for i in range(len(source) - 1):
        if source[i] != target[i]:
            j = source.find(target[i], i+1)
            if j == -1 or not source[i:j].count(target[i]) < source[i:j+1].count(target[i]):
                return False
    return True

print(canTransformWithCount("abc", "bca"))  # Expected to return False

The output of this code snippet is:

False

The code defines a function canTransformWithCount that first checks if the source and target strings have the same character frequency using the Counter class. It then iteratively checks if the characters of the target string can be moved into place by searching for the next occurrence of that character in the source and ensuring that there’s a suitable number of characters in between that can be reordered. The function returns False if the target string’s structure cannot be achieved from the source string.

Method 3: Character Position Tracking

This method tracks the positions of each character in the source string and verifies the transformability of the string based on these positions. If characters can be rearranged so that their new positions align with those in the target string, then the transformation is possible.

Here’s an example:

def canTransformByTrackingPos(source, target):
    if sorted(source) != sorted(target):
        return False
    
    source_positions = {ch: [] for ch in set(source)}
    for indx, ch in enumerate(source):
        source_positions[ch].append(indx)

    tgt_indx = 0
    for ch in target:
        if not source_positions[ch]:
            return False
        elif tgt_indx <= source_positions[ch][0]:
            tgt_indx = source_positions[ch].pop(0)
        else:
            return False
    return True

print(canTransformByTrackingPos("abdca", "aacbd"))  # Expected to return True

The output of this code snippet is:

True

This snippet uses a dictionary, source_positions, to track the indices of each character in the source string. The canTransformByTrackingPos function checks if each character in the target string is present at its required index or at a later index in the source string. Characters from the source string are checked off as they are matched and remapped. If characters are out of order or missing, the function returns False.

Method 4: Simulation of Sorting

Simulation inv