3302. Find the Lexicographically Smallest Valid Sequence
Explanation:
To solve this problem, we can use backtracking to find the lexicographically smallest valid sequence of indices. We will iterate over all possible indices and recursively try out each index to see if it leads to a valid solution. We will keep track of the selected indices and check if the concatenated characters at those indices in word1 form a string that is almost equal to word2.
Algorithm:
- Initialize an empty array to store the result.
- Implement a backtracking function that takes the current index to consider, the current sequence of selected indices, and the number of characters matched so far.
- In the backtracking function:
a. If the number of characters matched is equal to the length of
word2, check if the selected indices form a valid sequence. If valid, update the result with the current sequence. b. Otherwise, iterate over all possible indices and recursively call the function with the next index to consider. - Start the backtracking process with the initial index as 0 and an empty sequence of selected indices.
- Return the result as the lexicographically smallest valid sequence of indices.
Time Complexity:
The time complexity of this algorithm is O(n!) where n is the length of word2. This is because we are trying out all possible combinations of indices.
Space Complexity:
The space complexity is O(n) where n is the length of word2, due to the recursion stack.
:
class Solution {
public int[] smallestValidSequence(String word1, String word2) {
List<Integer> result = new ArrayList<>();
backtracking(0, word1, word2, new ArrayList<>(), result);
return result.stream().mapToInt(Integer::intValue).toArray();
}
private void backtracking(int index, String word1, String word2, List<Integer> selectedIndices, List<Integer> result) {
if (selectedIndices.size() == word2.length()) {
if (isValidSequence(selectedIndices, word1, word2)) {
result.clear();
result.addAll(selectedIndices);
}
return;
}
for (int i = index; i < word1.length(); i++) {
selectedIndices.add(i);
backtracking(i + 1, word1, word2, selectedIndices, result);
selectedIndices.remove(selectedIndices.size() - 1);
}
}
private boolean isValidSequence(List<Integer> selectedIndices, String word1, String word2) {
StringBuilder sb = new StringBuilder();
for (int index : selectedIndices) {
sb.append(word1.charAt(index));
}
return sb.toString().equals(word2);
}
}Code Editor (Testing phase)
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