2825. Make String a Subsequence Using Cyclic Increments
Difficulty: Medium
Topics: Two Pointers, String
You are given two 0-indexed strings str1 and str2.
In an operation, you select a set of indices in str1, and for each index i in the set, increment str1[i] to the next character cyclically. That is 'a' becomes 'b', 'b' becomes 'c', and so on, and 'z' becomes 'a'.
Return true if it is possible to make str2 a subsequence of str1 by performing the operation at most once, and false otherwise.
Note: A subsequence of a string is a new string that is formed from the original string by deleting some (possibly none) of the characters without disturbing the relative positions of the remaining characters.
Example 1:
- Input: str1 = "abc", str2 = "ad"
- Output: true
-
Explanation: Select index 2 in str1.
- Increment str1[2] to become 'd'.
- Hence, str1 becomes "abd" and str2 is now a subsequence. Therefore, true is returned.
Example 2:
- Input: str1 = "zc", str2 = "ad"
- Output: true
-
Explanation: Select indices 0 and 1 in str1.
- Increment str1[0] to become 'a'.
- Increment str1[1] to become 'd'.
- Hence, str1 becomes "ad" and str2 is now a subsequence. Therefore, true is returned.
Example 3:
- Input: str1 = "ab", str2 = "d"
- Output: false
-
Explanation: In this example, it can be shown that it is impossible to make str2 a subsequence of str1 using the operation at most once.
- Therefore, false is returned.
Constraints:
- 1 5
- 1 5
- str1 and str2 consist of only lowercase English letters.
Hint:
- Consider the indices we will increment separately.
- We can maintain two pointers: pointer i for str1 and pointer j for str2, while ensuring they remain within the bounds of the strings.
- If both str1[i] and str2[j] match, or if incrementing str1[i] matches str2[j], we increase both pointers; otherwise, we increment only pointer i.
- It is possible to make str2 a subsequence of str1 if j is at the end of str2, after we can no longer find a match.
Solution:
We need to check if we can make str2 a subsequence of str1 by performing at most one cyclic increment operation on any characters in str1:
Explanation:
- We will use two pointers, i for str1 and j for str2.
- If the character at str1[i] matches str2[j], we move both pointers forward.
- If str1[i] can be incremented to match str2[j] (cyclically), we try to match them and then move both pointers.
- If neither of the above conditions holds, we only move the pointer i for str1.
- Finally, if we can match all characters of str2, then it is possible to make str2 a subsequence of str1, otherwise not.
Let's implement this solution in PHP: 2825. Make String a Subsequence Using Cyclic Increments
<?php /** * @param String $str1 * @param String $str2 * @return Boolean */ function canMakeSubsequence($str1, $str2) { ... ... ... /** * go to ./solution.php */ } // Example Usage $str1 = "abc"; $str2 = "ad"; echo canMakeSubsequence($str1, $str2) ? 'true' : 'false'; // Output: true $str1 = "zc"; $str2 = "ad"; echo canMakeSubsequence($str1, $str2) ? 'true' : 'false'; // Output: true $str1 = "ab"; $str2 = "d"; echo canMakeSubsequence($str1, $str2) ? 'true' : 'false'; // Output: false ?>
Explanation:
- Two Pointers: i and j are initialized to the start of str1 and str2, respectively.
-
Matching Logic: Inside the loop, we check if the characters at str1[i] and str2[j] are the same or if we can increment str1[i] to match str2[j] cyclically.
- The cyclic increment condition is handled using (ord($str1[$i]) 1 - ord('a')) % 26 which checks if str1[i] can be incremented to match str2[j].
- Subsequence Check: If we have iterated through str2 completely (i.e., j == m), it means str2 is a subsequence of str1. Otherwise, it's not.
Time Complexity:
- The algorithm iterates through str1 once, and each character in str2 is checked only once, so the time complexity is O(n), where n is the length of str1.
Space Complexity:
- The space complexity is O(1) since we only use a few pointers and do not need extra space dependent on the input size.
This solution efficiently checks if it's possible to make str2 a subsequence of str1 with at most one cyclic increment operation.
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