Sort a stack
geeksforgeeks Sort a stack using recursion
问题描述
Given a stack, sort it using recursion. Use of any loop constructs like while, for..etc is not allowed. We can only use the following ADT functions on Stack S:
is_empty(S) : Tests whether stack is empty or not.
push(S) : Adds new element to the stack.
pop(S) : Removes top element from the stack.
top(S) : Returns value of the top element. Note that this
function does not remove element from the stack.
Example:
Input: -3 <--- Top
14
18
-5
30
Output: 30 <--- Top
18
14
-3
-5
Algorithm
This problem is mainly a variant of Reverse stack using recursion.
The idea of the solution is to hold all values in Function Call Stack until the stack becomes empty. When the stack becomes empty, insert all held items one by one in sorted order. Here sorted order is important.
We can use below algorithm to sort stack elements:
sortStack(stack S)
if stack is not empty:
temp = pop(S);
sortStack(S);
sortedInsert(S, temp);
Below algorithm is to insert element is sorted order:
sortedInsert(Stack S, element)
if stack is empty OR element > top element
push(S, elem)
else
temp = pop(S)
sortedInsert(S, element)
push(S, temp)
Implementation
Below is the implementation of above algorithm.
// C program to sort a stack using recursion
#include <stdio.h>
#include <stdlib.h>
// Stack is represented using linked list
struct stack
{
int data;
struct stack *next;
};
// Utility function to initialize stack
void initStack(struct stack **s)
{
*s = NULL;
}
// Utility function to chcek if stack is empty
int isEmpty(struct stack *s)
{
if (s == NULL)
return 1;
return 0;
}
// Utility function to push an item to stack
void push(struct stack **s, int x)
{
struct stack *p = (struct stack *)malloc(sizeof(*p));
if (p == NULL)
{
fprintf(stderr, "Memory allocation failed.\n");
return;
}
p->data = x;
p->next = *s;
*s = p;
}
// Utility function to remove an item from stack
int pop(struct stack **s)
{
int x;
struct stack *temp;
x = (*s)->data;
temp = *s;
(*s) = (*s)->next;
free(temp);
return x;
}
// Function to find top item
int top(struct stack *s)
{
return (s->data);
}
// Recursive function to insert an item x in sorted way
void sortedInsert(struct stack **s, int x)
{
// Base case: Either stack is empty or newly inserted
// item is greater than top (more than all existing)
if (isEmpty(*s) || x > top(*s))
{
push(s, x);
return;
}
// If top is greater, remove the top item and recur
int temp = pop(s);
sortedInsert(s, x);
// Put back the top item removed earlier
push(s, temp);
}
// Function to sort stack
void sortStack(struct stack **s)
{
// If stack is not empty
if (!isEmpty(*s))
{
// Remove the top item
int x = pop(s);
// Sort remaining stack
sortStack(s);
// Push the top item back in sorted stack
sortedInsert(s, x);
}
}
// Utility function to print contents of stack
void printStack(struct stack *s)
{
while (s)
{
printf("%d ", s->data);
s = s->next;
}
printf("\n");
}
// Driver Program
int main(void)
{
struct stack *top;
initStack(&top);
push(&top, 30);
push(&top, -5);
push(&top, 18);
push(&top, 14);
push(&top, -3);
printf("Stack elements before sorting:\n");
printStack(top);
sortStack(&top);
printf("\n\n");
printf("Stack elements after sorting:\n");
printStack(top);
return 0;
}
geeksforgeeks Sort a stack using a temporary stack
问题描述
Given a stack of integers, sort it in ascending（升序） order using another temporary stack.
Examples:
Input : [34, 3, 31, 98, 92, 23]
Output : [3, 23, 31, 34, 92, 98]
Input : [3, 5, 1, 4, 2, 8]
Output : [1, 2, 3, 4, 5, 8]
Algorithm
- Create a temporary stack say tmpStack.
- While input stack is NOT empty do this:
- Pop an element from input stack call it temp
- while temporary stack is NOT empty and top of temporary stack is greater than temp, pop from temporary stack and push it to the input stack
- push temp in temporary stack
- The sorted numbers are in tmpStack
Here is a dry run of above pseudo code.
input: [34, 3, 31, 98, 92, 23]
Element taken out: 23
input: [34, 3, 31, 98, 92]
tmpStack: [23]
Element taken out: 92
input: [34, 3, 31, 98]
tmpStack: [23, 92]
Element taken out: 98
input: [34, 3, 31]
tmpStack: [23, 92, 98]
Element taken out: 31
input: [34, 3, 98, 92]
tmpStack: [23, 31]
Element taken out: 92
input: [34, 3, 98]
tmpStack: [23, 31, 92]
Element taken out: 98
input: [34, 3]
tmpStack: [23, 31, 92, 98]
Element taken out: 3
input: [34, 98, 92, 31, 23]
tmpStack: [3]
Element taken out: 23
input: [34, 98, 92, 31]
tmpStack: [3, 23]
Element taken out: 31
input: [34, 98, 92]
tmpStack: [3, 23, 31]
Element taken out: 92
input: [34, 98]
tmpStack: [3, 23, 31, 92]
Element taken out: 98
input: [34]
tmpStack: [3, 23, 31, 92, 98]
Element taken out: 34
input: [98, 92]
tmpStack: [3, 23, 31, 34]
Element taken out: 92
input: [98]
tmpStack: [3, 23, 31, 34, 92]
Element taken out: 98
input: []
tmpStack: [3, 23, 31, 34, 92, 98]
final sorted list: [3, 23, 31, 34, 92, 98]
Implementation
// C++ program to sort a stack using an
// auxiliary stack.
#include <bits/stdc++.h>
using namespace std;
// This function return the sorted stack
stack<int> sortStack(stack<int> &input)
{
stack<int> tmpStack;
while (!input.empty())
{
// pop out the first element
int tmp = input.top();
input.pop();
// while temporary stack is not empty and top
// of stack is greater than temp
while (!tmpStack.empty() && tmpStack.top() > tmp)
{
// pop from temporary stack and push
// it to the input stack
input.push(tmpStack.top());
tmpStack.pop();
}
// push temp in tempory of stack
tmpStack.push(tmp);
}
return tmpStack;
}
// main function
int main()
{
stack<int> input;
input.push(34);
input.push(3);
input.push(31);
input.push(98);
input.push(92);
input.push(23);
// This is the temporary stack
stack<int> tmpStack = sortStack(input);
cout << "Sorted numbers are:\n";
while (!tmpStack.empty())
{
cout << tmpStack.top()<< " ";
tmpStack.pop();
}
}
SUMMARY : 上述算法非常类似于All nearest smaller values
TODO
https://www.geeksforgeeks.org/sort-a-stack-using-recursion/
https://www.geeksforgeeks.org/sort-stack-using-temporary-stack/
https://gkoberger.github.io/stacksort/
https://stackoverflow.com/questions/4826311/how-to-sort-a-stack-using-only-stack-operations