#1585

Hard

auto_awesomeGreedy choice plus invariant validation

LeetCode Problem Workspace

Check If String Is Transformable With Substring Sort Operations

This problem requires checking if string 's' can be transformed into string 't' using substring sort operations.

Problem Statement

Given two strings s and t, your task is to determine if you can transform string s into string t. You can use an operation that sorts any substring of s at any time, and this operation can be applied multiple times.

To solve this problem, return true if it's possible to transform s into t using the substring sort operation. Otherwise, return false. You can assume that both strings have the same length and consist of digits only.

Examples

Example 1

Input: s = "84532", t = "34852"

Output: true

You can transform s into t using the following sort operations: "84532" (from index 2 to 3) -> "84352" "84352" (from index 0 to 2) -> "34852"

Example 2

Input: s = "34521", t = "23415"

Output: true

You can transform s into t using the following sort operations: "34521" -> "23451" "23451" -> "23415"

Example 3

Input: s = "12345", t = "12435"

Output: false

Example details omitted.

Constraints

s.length == t.length
1 <= s.length <= 105
s and t consist of only digits.

Solution Approach

Greedy Choice and Substring Sorting

The solution involves greedy choices where we aim to sequentially match characters from string s to string t. By focusing on the first unmatching character in s, we determine if it's possible to move it to the correct position using substring sorting.

Invariant Validation

To confirm the transformation is possible, we validate an invariant: every digit in s must be able to reach its corresponding position in t by sorting specific substrings. This involves ensuring that, as we process s and t, the order and relative positions of digits are respected.

Efficient Sorting with Character Tracking

Efficiently tracking which characters are already placed correctly and which need sorting is key. A greedy approach ensures that at every step, we consider the next smallest possible digit that needs to be moved into place.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time and space complexity depend on the final approach chosen for substring sorting. A greedy strategy that uses efficient character tracking might optimize the solution to operate in linear or near-linear time with respect to the input string length.

What Interviewers Usually Probe

Evaluate how well the candidate handles greedy choices and substring sorting interactions.
Look for how the candidate ensures all character movements are valid and whether they recognize the invariant requirement.
Assess if the candidate considers the problem's edge cases and whether their solution handles large input sizes efficiently.

Common Pitfalls or Variants

Common pitfalls

Not correctly handling the order of digits when applying substring sorts.
Missing edge cases where a digit may not be movable to its correct position.
Overcomplicating the solution without leveraging efficient greedy techniques or invariant checks.

Follow-up variants

Consider variants where the input string contains characters other than digits, such as lowercase letters.
What if the allowed operations include other kinds of substring transformations beyond sorting?
Explore a variant where you are given a partial target string t, and must determine the smallest substring sorts needed to complete it.

FAQ

What is the key approach to solving the 'Check If String Is Transformable With Substring Sort Operations' problem?

The key approach involves using a greedy strategy with substring sorting, ensuring each digit in string 's' can be placed correctly in string 't' by considering the order and relative positions of characters.

Can the problem be solved with a brute force approach?

While a brute force approach might work for smaller inputs, it's inefficient for large cases. A greedy strategy with character tracking ensures a more optimal solution.

What is the main failure mode of this problem?

The main failure mode occurs when the greedy choice fails to respect the invariant condition, causing digits to be incorrectly ordered after substring sorting.

How does greedy choice apply to this problem?

Greedy choice is used to select the smallest possible digit that needs to be placed in its correct position, ensuring efficient transformation while maintaining the required order.

What are some potential optimizations for solving this problem?

Optimizing the tracking of placed characters and minimizing unnecessary substring sorts are key ways to optimize this problem, especially when handling large strings.

terminal

Solution

Solution 1: Bubble Sort

The problem is essentially equivalent to determining whether any substring of length 2 in string $s$ can be swapped using bubble sort to obtain $t$.

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class Solution:
    def isTransformable(self, s: str, t: str) -> bool:
        pos = defaultdict(deque)
        for i, c in enumerate(s):
            pos[int(c)].append(i)
        for c in t:
            x = int(c)
            if not pos[x] or any(pos[i] and pos[i][0] < pos[x][0] for i in range(x)):
                return False
            pos[x].popleft()
        return True

Continue Practicing

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