710056. Stack Permutations
Stack Permutations
Summary
Given a stack of integers, generate all possible permutations of its elements. This problem involves manipulating an array using a stack data structure, making it a combination of arrays and stacks.
Detailed Explanation
To solve this problem, we can use the concept of recursive backtracking to generate all possible permutations. We'll start by popping all elements from the stack and storing them in an array. Then, we'll use recursion to generate all permutations of the remaining stack (which will be an empty stack eventually).
Here's a step-by-step breakdown of the solution:
- Initialize an empty stack
stackand a result listpermutations. - Pop all elements from the stack and store them in the
permutationslist. - If the stack is empty, add the current permutation to the
permutationslist and return. - Otherwise, recursively generate all permutations of the remaining stack (i.e., the stack with the last element removed).
- For each permutation generated in step 4, insert the last popped element at every possible position to create a new permutation.
- Add these new permutations to the
permutationslist and return.
Time complexity: O(n!), where n is the number of elements in the original stack. This is because we're generating all possible permutations of the elements. Space complexity: O(n), for storing the permutations.
Here's an ASCII art diagram illustrating the process:
+---------------+
| Stack: [1, 2, 3] |
+---------------+
|
| Pop all elements
v
+---------------+
| Permutations: [] |
+---------------+
|
| Recursively generate permutations of remaining stack
v
+---------------+
| Permutations: [[1], [2], [3]] |
+---------------+
|
| Insert last popped element at every possible position
v
+---------------+
| Permutations: [[1, 2], [1, 3], [2, 3], [1], [2], [3]] |
+---------------+
Optimized Solutions
Java
import java.util.*;
public class StackPermutations {
public List<List<Integer>> getStackPermutations(int[] stack) {
List<List<Integer>> permutations = new ArrayList<>();
backtrack(stack, new ArrayList<>(), permutations);
return permutations;
}
private void backtrack(int[] stack, List<Integer> current, List<List<Integer>> permutations) {
if (stack.length == 0) {
permutations.add(new ArrayList<>(current));
return;
}
for (int i = 0; i <= current.size(); i++) {
current.add(stack[stack.length - 1]);
backtrack(Arrays.copyOfRange(stack, 0, stack.length - 1), current, permutations);
current.remove(current.size() - 1);
}
}
public static void main(String[] args) {
StackPermutations sp = new StackPermutations();
int[] stack = {1, 2, 3};
List<List<Integer>> permutations = sp.getStackPermutations(stack);
System.out.println(permutations);
}
}