2825. Make String a Subsequence Using Cyclic Increments

Problem Description

The problem presented requires determining whether str2 can become a subsequence of str1 by performing a specific operation on str1. The operation involves selecting a set of indices in str1 and incrementing the character at each index to the next character in a cyclic manner. This means that the alphabet is considered to be circular and incrementing 'z' would result in 'a'.

A subsequence is defined as a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements. The goal is to verify if by applying the operation at most once, str2 can be made a subsequence of str1.

Note that the problem specifies that the operation can be performed at most once, meaning you cannot perform this operation multiple times on str1. The string str2 must either already be a subsequence of str1 or be one operation away from being a subsequence.

Intuition

The solution approach is based on the idea that for str2 to be a subsequence of str1, each character in str2 must appear in str1 in the same order, with the possibility of characters in str2 being one cyclic increment away from the characters in str1.

To implement this, iterate through each character in str1 and simulate the operation. For each character in str1, determine what the next cyclic character would be ('z' to 'a', and any other character to its successor). If the current character in str1, or its cyclic successor, matches the current character in str2, then that means this character is in the correct position, or one operation away from it, to form a subsequence.

Using a pointer i, keep track of the position in str2 that you are trying to match with str1. Initialize this pointer to 0, and move it forward through str2 each time you find a match or a potential match after a cyclic increment in str1.

If you reach the end of str2 by advancing this pointer throughout the iteration, it means that all characters in str2 are present in str1 in order or one operation away, and str2 is (or can become) a subsequence of str1. If the pointer i is equal to the length of str2 by the end of the iteration through str1, return true; otherwise, false.

This approach allows checking whether str2 can be obtained by performing at most one operation on str1, complying with the problem's constraints.

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Solution Approach

The implementation of the solution in Python is straightforward and does not require the use of any complex data structures or patterns. It mainly utilizes basic control structures and string operations to achieve the goal.

Here is a step-by-step walk-through of the provided solution code:

A method canMakeSubsequence is defined in the Solution class. It takes two parameters: str1 and str2 (the input strings).
An index variable i is initialized to 0. This variable is used to keep track of the current position in str2 that we are trying to match against str1.
A for loop is used to iterate over each character c in str1.
Inside the loop, a new variable d is calculated. It contains the next character cyclically after c. If c is 'z', d would be 'a', otherwise d is the character that comes after c in the ASCII table, obtained by chr(ord(c) + 1).
The loop checks if i is still within the bounds of str2 (i < len(str2)), and if the current character of str2 (str2[i]) matches either the current character c from str1, or the next cyclic character d. The in operator checks membership within a tuple made of c and d.
If a match or potential match after a cyclic increment is found, i is incremented by 1, signifying that we have found the current character of str2 in the str1 or one operation away from it.
After the loop finishes, the algorithm checks whether i has advanced to the end of str2 by comparing i with the length of str2. If they are equal, it means str2 can be a subsequence of str1 after performing the operation at most once. Thus, it returns true.
If the end of str2 has not been reached, it indicates that str2 cannot be made a subsequence of str1 with at most one operation, so the method returns false.

This solution is efficient because it requires only a single pass through str1 and stops as soon as all characters in str2 are accounted for. Since there are no additional data structures used, the space complexity is O(1), and the time complexity is O(n), where n is the length of str1.

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Example Walkthrough

Let's illustrate the solution approach with an example using str1 = "abcde" and str2 = "axz". We want to determine whether we can transform str2 into a subsequence of str1 by performing the character increment operation at most once.

We begin with i = 0, which represents the position in str2 that we're looking to match in str1.
As we iterate through str1, we compare the characters in str2 with the characters in str1 and their cyclic successor.
We start with the first character of str1, which is a. We see that str2[i] is also a. Since they match, we can increment i to 1.
We proceed to the second character in str1, which is b. We check its cyclic successor, which is c. Neither match str2[i], which is now x, so we don't increment i.
We move to the third character in str1, c. Its successor is d, and str2[i] is x. There's no match, so we leave i unchanged.
Next is d in str1, with its successor being e. str2[i] is still x. No match, so i remains at 1.
The final character in str1 is e, and its successor is f (cyclic incrementing from z to a, but regular increment otherwise). Yet again, there's no match with str2[i], which remains x.
We exit the loop and compare i with the length of str2. We see that i is still 1, but the length of str2 is 3. Since i does not equal the length of str2, we cannot make str2 a subsequence of str1 with at most one operation, and we return false.

In this example, the character x in str2 cannot be matched in str1 since there is no character that can be incremented cyclically to x in str1. Therefore, str2 cannot become a subsequence of str1 with just one operation according to our given rules.

Solution Implementation

1class Solution:
2    def canMakeSubsequence(self, text: str, subsequence: str) -> bool:
3        index = 0  # Initialize a pointer for the position in subsequence
4      
5        # Loop through each character in text
6        for character in text:
7            # Determine the next character after 'character' in alphabet, wrap around if it is 'z'
8            next_char = 'a' if character == 'z' else chr(ord(character) + 1)
9          
10            # Check if the current pointer is within bounds of subsequence
11            if index < len(subsequence):
12                # If the current character in text is the same as the current character in subsequence
13                # Or if it is the next character in the alphabet, move the pointer in subsequence
14                if subsequence[index] in (character, next_char):
15                    index += 1
16                  
17        # After the loop, if the pointer has reached the length of subsequence
18        # It means the subsequence can be formed, hence return True
19        return index == len(subsequence)
20

1class Solution {
2
3    /**
4     * Checks if str2 is a subsequence of str1 with the character replacement rule.
5     * Each character in str1 can remain the same or be replaced by the next
6     * character in alphabetical order to match a character in str2.
7     *
8     * @param str1 The string to be transformed.
9     * @param str2 The target subsequence.
10     * @return true if str2 is a subsequence of str1 after allowed transformations.
11     */
12    public boolean canMakeSubsequence(String str1, String str2) {
13        int currentIndex = 0; // Pointer into str2 to track our current progress.
14        int lengthOfStr2 = str2.length(); // Total length of str2.
15
16        // Iterate through each character of str1.
17        for (char currentChar : str1.toCharArray()) {
18            // Calculate the next character in the alphabetical order ('z' wraps to 'a').
19            char nextChar = currentChar == 'z' ? 'a' : (char) (currentChar + 1);
20
21            // Check if the current character in str1 matches the current or next valid character in str2.
22            if (currentIndex < lengthOfStr2 && 
23                (str2.charAt(currentIndex) == currentChar || str2.charAt(currentIndex) == nextChar)) {
24                currentIndex++; // Move to the next character in str2.
25            }
26        }
27
28        // str2 is a subsequence of str1 only if we have traversed its entire length.
29        return currentIndex == lengthOfStr2;
30    }
31}
32

1class Solution {
2public:
3    bool canMakeSubsequence(string s1, string s2) {
4        // Initialize the index for traversing s2
5        int index = 0;
6        // Get the length of s2 for boundary checks
7        int s2Length = s2.size();
8
9        // Iterate over each character in s1
10        for (char currentChar : s1) {
11            // Determine the next character in the alphabet, wrapping around if 'z' is reached
12            char nextChar = currentChar == 'z' ? 'a' : static_cast<char>(currentChar + 1);
13
14            // Check if the current character of s2 matches currentChar or nextChar
15            // and ensure we have not exceeded the bounds of s2
16            if (index < s2Length && (s2[index] == currentChar || s2[index] == nextChar)) {
17                // Move to next character in s2
18                ++index;
19            }
20        }
21
22        // Return true if we have traversed the whole s2, making it a subsequence
23        return index == s2Length;
24    }
25};
26

1function canMakeSubsequence(sourceString: string, targetString: string): boolean {
2    // Initialize a pointer to track the characters in targetString
3    let pointer = 0;
4  
5    // Get the length of targetString for comparison
6    const targetLength = targetString.length;
7  
8    // Loop through the characters of sourceString to check if a subsequence can be made
9    for (const sourceChar of sourceString) {
10      
11        // Determine the character that follows sourceChar in the alphabet,
12        // wrapping around from 'z' to 'a'
13        const nextChar = sourceChar === 'z' ? 'a' : String.fromCharCode(sourceChar.charCodeAt(0) + 1);
14      
15        // If the current character in the targetString matches sourceChar
16        // or the next character in the alphabetical sequence,
17        // increment the pointer to continue with the next character
18        if (pointer < targetLength && (targetString[pointer] === sourceChar || targetString[pointer] === nextChar)) {
19            pointer++;
20        }
21    }
22  
23    // A subsequence can be made if the pointer has reached the end of targetString
24    return pointer === targetLength;
25}
26

Time and Space Complexity

The given Python code determines whether str2 can be formed as a subsequence of str1 by either taking a character as it is or replacing it with the next character in the alphabet (with 'z' converted to 'a').

Time Complexity

The time complexity of the code is determined by the single loop that iterates over the characters of str1. For each character c in str1:

A constant-time operation is done to find the next character d (except for 'z', which turns to 'a').
A constant-time operation in is used to check if str2[i] is one of the two characters (c, d).

Since these operations are constant time, and the loop runs for each character in str1, the time complexity is O(n), where n is the length of str1.

Space Complexity

The space complexity of the code:

It uses a fixed number of simple variables (i, c, d), which require O(1) space.
No additional data structures are allocated proportionally to the size of the input.

Thus, the overall space complexity of the code is O(1) – constant space complexity.

Learn more about how to find time and space complexity quickly using problem constraints.

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