Question: Design a Data Structure SpecialStack that supports all the stack operations like push(), pop(), isEmpty(), isFull() and an additional operation getMin() which should return minimum element from the SpecialStack. All these operations of SpecialStack must be O(1). To implement SpecialStack, you should only use standard Stack data structure and no other data structure like arrays, list, . etc.
Example:
Consider the following SpecialStack 16 --> TOP 15 29 19 18 When getMin() is called it should return 15, which is the minimum element in the current stack. If we do pop two times on stack, the stack becomes 29 --> TOP 19 18 When getMin() is called, it should return 18 which is the minimum in the current stack.
Solution:
Use two stacks: one to store actual stack elements and the other as an auxiliary stack to store minimum values. The idea is to do push() and pop() operations in such a way that the top of the auxiliary stack is always the minimum. Let us see how push() and pop() operations work.
Push(int x) // inserts an element x to Special Stack
- 1) push x to the first stack (the stack with actual elements)
- 2) compare x with the top element of the second stack (the auxiliary stack). Let the top element be y.
- If x is smaller than y then push x to the auxiliary stack.
- If x is greater than y then push y to the auxiliary stack.
int Pop() // removes an element from Special Stack and return the removed element
- pop the top element from the auxiliary stack.
- pop the top element from the actual stack and return it. Step 1 is necessary to make sure that the auxiliary stack is also updated for future operations.
int getMin() // returns the minimum element from Special Stack
- Return the top element of the auxiliary stack.
We can see that all the above operations are O(1).
Let us see an example. Let us assume that both stacks are initially empty and 18, 19, 29, 15, and 16 are inserted to the SpecialStack.
When we insert 18, both stacks change to following. Actual Stack 18 <--- top Auxiliary Stack 18 <---- top When 19 is inserted, both stacks change to following. Actual Stack 19 <--- top 18 Auxiliary Stack 18 <---- top 18 When 29 is inserted, both stacks change to following. Actual Stack 29 <--- top 19 18 Auxiliary Stack 18 <---- top 18 18 When 15 is inserted, both stacks change to following. Actual Stack 15 <--- top 29 19 18 Auxiliary Stack 15 <---- top 18 18 18 When 16 is inserted, both stacks change to following. Actual Stack 16 <--- top 15 29 19 18 Auxiliary Stack 15 <---- top 15 18 18 18
The following is the implementation for SpecialStack class. In the below implementation, SpecialStack inherits from Stack and has one Stack object min which works as an auxiliary stack.
C++
#include <iostream> #include <stdlib.h> using namespace std; /* A simple stack class with basic stack functionalities */class Stack { private: static const int max = 100; int arr[max]; int top; public: Stack() { top = -1; } bool isEmpty(); bool isFull(); int pop(); void push(int x); }; /* Stack's member method to check if the stack is empty */bool Stack::isEmpty() { if (top == -1) return true; return false; } /* Stack's member method to check if the stack is full */bool Stack::isFull() { if (top == max - 1) return true; return false; } /* Stack's member method to remove an element from it */int Stack::pop() { if (isEmpty()) { cout << "Stack Underflow"; abort(); } int x = arr[top]; top--; return x; } /* Stack's member method to insert an element to it */void Stack::push(int x) { if (isFull()) { cout << "Stack Overflow"; abort(); } top++; arr[top] = x; } /* A class that supports all the stack operations and one additional operation getMin() that returns the minimum element from stack at any time. This class inherits from the stack class and uses an auxiliary stack that holds minimum elements */class SpecialStack : public Stack { Stack min; public: int pop(); void push(int x); int getMin(); }; /* SpecialStack's member method to insert an element to it. This method makes sure that the min stack is also updated with appropriate minimum values */void SpecialStack::push(int x) { if (isEmpty() == true) { Stack::push(x); min.push(x); } else { Stack::push(x); int y = min.pop(); min.push(y); if (x < y) min.push(x); else min.push(y); } } /* SpecialStack's member method to remove an element from it. This method removes top element from min stack also. */int SpecialStack::pop() { int x = Stack::pop(); min.pop(); return x; } /* SpecialStack's member method to get minimum element from it. */int SpecialStack::getMin() { int x = min.pop(); min.push(x); return x; } /* Driver program to test SpecialStack methods */int main() { SpecialStack s; s.push(10); s.push(20); s.push(30); cout << s.getMin() << endl; s.push(5); cout << s.getMin(); return 0; } |
Java
// Java implementation of SpecialStack // Note : here we use Stack class for // Stack implementation import java.util.Stack; /* A class that supports all the stack operations and one additional operation getMin() that returns the minimum element from stack at any time. This class inherits from the stack class and uses an auxiliary stack that holds minimum elements */ class SpecialStack extends Stack<Integer> { Stack<Integer> min = new Stack<>(); /* SpecialStack's member method to insert an element to it. This method makes sure that the min stack is also updated with appropriate minimum values */ void push(int x) { if (isEmpty() == true) { super.push(x); min.push(x); } else { super.push(x); int y = min.pop(); min.push(y); if (x < y) min.push(x); else min.push(y); } } /* SpecialStack's member method to insert an element to it. This method makes sure that the min stack is also updated with appropriate minimum values */ public Integer pop() { int x = super.pop(); min.pop(); return x; } /* SpecialStack's member method to get minimum element from it. */ int getMin() { int x = min.pop(); min.push(x); return x; } /* Driver program to test SpecialStack methods */ public static void main(String[] args) { SpecialStack s = new SpecialStack(); s.push(10); s.push(20); s.push(30); System.out.println(s.getMin()); s.push(5); System.out.println(s.getMin()); } } // This code is contributed by Sumit Ghosh |
Python3
# Python3 program for the # above approach # A simple stack class with # basic stack functionalities class stack: def __init__(self): self.array = [] self.top = -1 self.max = 100 # Stack's member method to check # if the stack is empty def isEmpty(self): if self.top == -1: return True else: return False # Stack's member method to check # if the stack is full def isFull(self): if self.top == self.max - 1: return True else: return False # Stack's member method to # insert an element to it def push(self, data): if self.isFull(): print('Stack OverFlow') return else: self.top += 1 self.array.append(data) # Stack's member method to # remove an element from it def pop(self): if self.isEmpty(): print('Stack UnderFlow') return else: self.top -= 1 return self.array.pop() # A class that supports all the stack # operations and one additional # operation getMin() that returns the # minimum element from stack at # any time. This class inherits from # the stack class and uses an # auxiliary stack that holds # minimum elements class SpecialStack(stack): def __init__(self): super().__init__() self.Min = stack() # SpecialStack's member method to # insert an element to it. This method # makes sure that the min stack is also # updated with appropriate minimum # values def push(self, x): if self.isEmpty(): super().push(x) self.Min.push(x) else: super().push(x) y = self.Min.pop() self.Min.push(y) if x <= y: self.Min.push(x) else: self.Min.push(y) # SpecialStack's member method to # remove an element from it. This # method removes top element from # min stack also. def pop(self): x = super().pop() self.Min.pop() return x # SpecialStack's member method # to get minimum element from it. def getmin(self): x = self.Min.pop() self.Min.push(x) return x # Driver code if __name__ == '__main__': s = SpecialStack() s.push(10) s.push(20) s.push(30) print(s.getmin()) s.push(5) print(s.getmin()) # This code is contributed by rachitkatiyar99 |
C#
using System; using System.Collections.Generic; // A class that supports all the stack operations // and one additional operation `GetMin` // that returns the minimum element from the stack at any time. // This class inherits from the `Stack` class and uses an // auxiliary stack to hold minimum elements. class SpecialStack : Stack<int> { // Auxiliary stack to store minimum elements. Stack<int> min = new Stack<int>(); // Method to insert an element to the stack. // Makes sure that the min stack is also updated // with appropriate minimum values. public void Push(int x) { if (Count == 0) { // If the stack is empty, simply add the // element and push it to the `min` stack. base.Push(x); min.Push(x); } else { // Add the element to the stack. base.Push(x); int y = min.Pop(); min.Push(y); // If the current element is less than the current minimum, // add it to the `min` stack. if (x < y) min.Push(x); else min.Push(y); } } // Method to remove an element from the stack. // Makes sure that the min stack is also updated with // appropriate minimum values. public new int Pop() { // Pop the element from the stack. int x = base.Pop(); // Pop the minimum value from the `min` stack. min.Pop(); return x; } // Method to get the minimum element from the stack. public int GetMin() { int x = min.Pop(); min.Push(x); return x; } static void Main(string[] args) { SpecialStack s = new SpecialStack(); s.Push(10); s.Push(20); s.Push(30); Console.WriteLine(s.GetMin()); s.Push(5); Console.WriteLine(s.GetMin()); Console.ReadLine(); } } |
Javascript
class stack { constructor() { this.array = []; this.top = -1; this.max = 100; } isEmpty() { if (this.top == -1) { return true; } else { return false; } } isFull() { if (this.top == this.max - 1) { return true; } else { return false; } } push(data) { if (this.isFull()) { console.log("Stack OverFlow"); return; } else { this.top += 1; this.array.push(data); } } pop() { if (this.isEmpty()) { console.log("Stack UnderFlow"); return; } else { this.top -= 1; return this.array.pop(); } } } class SpecialStack extends stack { constructor() { super(); this.Min = new stack(); } push(x) { if (this.isEmpty()) { super.push(x); this.Min.push(x); } else { super.push(x); let y = this.Min.pop(); this.Min.push(y); if (x <= y) { this.Min.push(x); } else { this.Min.push(y); } } } pop() { let x = super.pop(); this.Min.pop(); return x; } getmin() { let x = this.Min.pop(); this.Min.push(x); return x; } } let s = new SpecialStack(); s.push(10); s.push(20); s.push(30); console.log(s.getmin()); s.push(5); console.log(s.getmin()); |
Output
10 5
Complexity Analysis:
- Time Complexity:
- For insert operation: O(1) (As insertion ‘push’ in a stack takes constant time)
- For delete operation: O(1) (As deletion ‘pop’ in a stack takes constant time)
- For ‘Get Min’ operation: O(1) (As we have used an auxiliary stack which has it’s top as the minimum element)
- Auxiliary Space: O(n).
Use of auxiliary stack for storing values.
Space Optimized Version
The above approach can be optimized. We can limit the number of elements in the auxiliary stack. We can push only when the incoming element of the main stack is smaller than or equal to the top of the auxiliary stack. Similarly during pop, if the pop-off element equal to the top of the auxiliary stack, remove the top element of the auxiliary stack. Following is the modified implementation of push() and pop().
C++
/* SpecialStack's member method to insert an element to it. This method makes sure that the min stack is also updated with appropriate minimum values */void SpecialStack::push(int x) { if (isEmpty() == true) { Stack::push(x); min.push(x); } else { Stack::push(x); int y = min.pop(); min.push(y); /* push only when the incoming element of main stack is smaller than or equal to top of auxiliary stack */ if (x <= y) min.push(x); } } /* SpecialStack's member method to remove an element from it. This method removes top element from min stack also. */int SpecialStack::pop() { int x = Stack::pop(); int y = min.pop(); /* Push the popped element y back only if it is not equal to x */ if (y != x) min.push(y); return x; } |
Java
/* SpecialStack's member method to insert an element to it. This method makes sure that the min stack is also updated with appropriate minimum values */ void push(int x) { if (isEmpty() == true) { super.push(x); min.push(x); } else { super.push(x); int y = min.pop(); min.push(y); /* push only when the incoming element of main stack is smaller than or equal to top of auxiliary stack */ if (x <= y) min.push(x); } } /* SpecialStack's member method to remove an element from it. This method removes top element from min stack also. */public Integer pop() { int x = super.pop(); int y = min.pop(); /* Push the popped element y back only if it is not equal to x */ if (y != x) min.push(y); return x; } // This code is contributed by Sumit Ghosh |
Python3
''' SpecialStack's member method to insert an element to it. This method makes sure that the min stack is also updated with appropriate minimum values ''' def push(x): if (isEmpty() == True): super.append(x); min.append(x); else: super.append(x); y = min.pop(); min.append(y); ''' push only when the incoming element of main stack is smaller than or equal to top of auxiliary stack ''' if (x <= y): min.append(x); ''' SpecialStack's member method to remove an element from it. This method removes top element from min stack also. '''def pop(): x = super.pop(); y = min.pop(); ''' Push the popped element y back only if it is not equal to x ''' if (y != x): min.append(y); return x; # This code contributed by umadevi9616 |
C#
/* SpecialStack's member method to insert an element to it. This method makes sure that the min stack is also updated with appropriate minimum values */ void push(int x) { if (min.Count==0) { super.Push(x); min.Push(x); } else { super.Push(x); int y = min.Pop(); min.Push(y); /* push only when the incoming element of main stack is smaller than or equal to top of auxiliary stack */ if (x <= y) min.Push(x); } } /* SpecialStack's member method to remove an element from it. This method removes top element from min stack also. */public int pop() { int x = super.Pop(); int y = min.Pop(); /* Push the popped element y back only if it is not equal to x */ if (y != x) min.Push(y); return x; } // This code is contributed by umadevi9616 |
Javascript
<script> /* SpecialStack's member method to insert an element to it. This method makes sure that the min stack is also updated with appropriate minimum values */ function push(x) { if (isEmpty() == true) { super.push(x); min.push(x); } else { super.push(x); var y = min.pop(); min.push(y); /* push only when the incoming element of main stack is smaller than or equal to top of auxiliary stack */ if (x <= y) min.push(x); } } /* SpecialStack's member method to remove an element from it. This method removes top element from min stack also. */ function pop() { var x = super.pop(); var y = min.pop(); /* Push the popped element y back only if it is not equal to x */ if (y != x) min.push(y); return x; } // This code is contributed by umadevi9616 </script> |
Complexity Analysis:
- Time Complexity:
- For Insert operation: O(1) (As insertion ‘push’ in a stack takes constant time)
- For Delete operation: O(1) (As deletion ‘pop’ in a stack takes constant time)
- For ‘Get Min’ operation: O(1) (As we have used an auxiliary which has it’s top as the minimum element)
- Auxiliary Space: O(n).
The complexity in the worst case is the same as above but in other cases, it will take slightly less space than the above approach as repetition is neglected.
Further optimized O(1) time complexity and O(1) space complexity solution :
The above approach can be optimized further and the solution can be made to work in O(1) time complexity and O(1) space complexity. The idea is to store min element found till current insertion) along with all the elements as a reminder of a DUMMY_VALUE, and the actual element as a multiple of the DUMMY_VALUE.
For example, while pushing an element ‘e’ into the stack, store it as (e * DUMMY_VALUE + minFoundSoFar), this way we know what was the minimum value present in the stack at the time ‘e’ was being inserted.
To pop the actual value just return e/DUMMY_VALUE and set the new minimum as (minFoundSoFar % DUMMY_VALUE).
Note: Following method will fail if we try to insert DUMMY_VALUE in the stack, so we have to make our selection of DUMMY_VALUE carefully.
Let’s say the following elements are being inserted in the stack – 3 2 6 1 8 5
d is dummy value.
s is wrapper stack
top is top element of the stack
min is the minimum value at that instant when the elements were inserted/removed
The following steps shows the current state of the above variables at any instant –
- s.push(3);
min=3 //updated min as stack here is empty
s = {3*d + 3}
top = (3*d + 3)/d = 3
- s.push(2);
min = 2 //updated min as min > current element
s = {3*d + 3-> 2*d + 2}
top = (2*d + 2)/d = 2
- s.push(6);
min = 2
s = {3*d + 3-> 2*d + 2-> 6*d + 2}
top = (6*d + 2)/d = 6
- s.push(1);
min = 1 //updated min as min > current element
s = {3*d + 3-> 2*d + 2-> 6*d + 2 -> 1*d + 1}
top = (1*d + 1)/d = 1
- s.push(8);
min = 1
s = {3*d + 3-> 2*d + 2-> 6*d + 2 -> 1*d + 1 -> 8*d + 1}
top = (8*d + 1)/d = 8
- s.push(5);
min = 1
s = {3*d + 3-> 2*d + 2-> 6*d + 2 -> 1*d + 1 -> 8*d + 1 -> 5*d + 1}
top = (5*d + 1)/d = 5
- s.pop();
s = {3*d + 3 -> 2*d + 2 -> 6*d + 2 -> 1*d + 1 -> 8*d + 1 -> 5*d + 1}
top = (5*d + 1)/d = 5
min = (8*d + 1)%d = 1 // min is always remainder of the second top element in stack.
- s.pop();
s = {3*d + 3 -> 2*d + 2-> 6*d + 2 -> 1*d + 1 -> 8*d + 1}
top = (8*d + 1)/d = 8
min = (1*d + 1)%d = 1
- s.pop()
s = {3*d + 3 -> 2*d + 2-> 6*d + 2 -> 1*d + 1}
top = (1*d + 1)/d = 1
min = (6*d + 2)%d = 2
- s.pop()
s = {3*d + 3-> 2*d + 2-> 6*d + 2}
top = (6*d + 2)/d = 6
min = (2*d + 2)%d = 2
- s.pop()
s = {3*d + 3-> 2*d + 2}
top = (2*d + 2)/d = 2
min = (3*d + 3)%d = 3
- s.pop()
s = {3*d + 3}
top = (3*d + 3)/d = 3
min = -1 // since stack is now empty
C++
#include <iostream> #include <stack> #include <vector> using namespace std; /* A special stack having peek() pop() and * push() along with additional getMin() that * returns minimum value in a stack without * using extra space and all operations in O(1) * time.. ???? */class SpecialStack { // Sentinel value for min int min = -1; // DEMO_VALUE static const int demoVal = 9999; stack<int> st; public: void getMin() { cout << "min is: " << min << endl; } void push(int val) { // If stack is empty OR current element // is less than min, update min. if (st.empty() || val < min) { min = val; } // Encode the current value with // demoVal, combine with min and // insert into stack st.push(val * demoVal + min); cout << "pushed: " << val << endl; } int pop() { // if stack is empty return -1; if ( st.empty() ) { cout << "stack underflow" << endl ; return -1; } int val = st.top(); st.pop(); // If stack is empty, there would // be no min value present, so // make min as -1 if (!st.empty()) min = st.top() % demoVal; else min = -1; cout << "popped: " << val / demoVal << endl; // Decode actual value from // encoded value return val / demoVal; } int peek() { // Decode actual value // from encoded value return st.top() / demoVal; } }; // Driver Code int main() { SpecialStack s; vector<int> arr = { 3, 2, 6, 1, 8, 5, 5, 5, 5 }; for(int i = 0; i < arr.size(); i++) { s.push(arr[i]); s.getMin(); } cout << endl; for(int i = 0; i < arr.size(); i++) { s.pop(); s.getMin(); } return 0; } // This code is contributed by scisaif |
Java
import java.util.Stack; /* A special stack having peek() pop() and push() along with * additional getMin() that returns minimum value in a stack * without using extra space and all operations in O(1) * time.. 🙂 * */public class SpecialStack { int min = -1; // sentinel value for min static int demoVal = 9999; // DEMO_VALUE Stack<Integer> st = new Stack<Integer>(); void getMin() { System.out.println("min is: " + min); } void push(int val) { // if stack is empty OR current element is less than // min, update min.. if (st.isEmpty() || val < min) { min = val; } st.push(val * demoVal + min); // encode the current value with // demoVal, combine with min and // insert into stack System.out.println("pushed: " + val); } int pop() { // if stack is empty return -1; if (st.isEmpty() ) { System.out.println("stack underflow"); return -1; } int val = st.pop(); if (!st.isEmpty()) // if stack is empty, there would // be no min value present, so // make min as -1 min = st.peek() % demoVal; else min = -1; System.out.println("popped: " + val / demoVal); return val / demoVal; // decode actual value from // encoded value } int peek() { return st.peek() / demoVal; // decode actual value // from encoded value } // Driver Code public static void main(String[] args) { SpecialStack s = new SpecialStack(); int[] arr = { 3, 2, 6, 1, 8, 5, 5, 5, 5 }; for (int i = 0; i < arr.length; i++) { s.push(arr[i]); s.getMin(); } System.out.println(); for (int i = 0; i < arr.length; i++) { s.pop(); s.getMin(); } } } |
Python3
# A special stack having peek() pop() and # push() along with additional getMin() that # returns minimum value in a stack without # using extra space and all operations in O(1) # time.. ???? class SpecialStack: def __init__(self): # Sentinel value for min self.minm = -1 # DEMO_VALUE SpecialStack.demoVal = 9999 self.st = [] def getMin(self): print("min is: ", self.minm) def push(self, val): # If stack is empty OR current element # is less than min, update min. if len(self.st) == 0 or val < self.minm: self.minm = val # Encode the current value with # demoVal, combine with min and # insert into stack self.st.append(val*self.demoVal + self.minm) print("pushed: ", val) def pop(self): # if stack is empty return -1 if len(self.st) == 0: print("stack underflow") return -1 val = self.st.pop() # If stack is empty, there would # be no min value present, so # make min as -1 if len(self.st) != 0: self.minm = self.st[-1] % self.demoVal else: self.minm = -1 print("popped: ", val // self.demoVal) # Decode actual value from # encoded value return val // self.demoVal def peek(self): # Decode actual value # from encoded value return self.st[-1] // self.demoVal # Driver Code if __name__ == "__main__": s = SpecialStack() arr = [3, 2, 6, 1, 8, 5, 5, 5, 5] for i in range(len(arr)): s.push(arr[i]) s.getMin() print("\n") for i in range(len(arr)): s.pop() s.getMin() # This code is contributed by pankajkumar70792. |
C#
using System; using System.Collections.Generic; /* A special stack having peek() pop() and push() along with * additional getMin() that returns minimum value in a stack * without using extra space and all operations in O(1) * time.. 🙂 * */public class SpecialStack { int min = -1; // sentinel value for min static int demoVal = 9999; // DEMO_VALUE Stack<int> st = new Stack<int>(); void getMin() { Console.WriteLine("min is: " + min); } void push(int val) { // if stack is empty OR current element is less than // min, update min.. if (st.Count==0 || val < min) { min = val; } st.Push(val * demoVal + min); // encode the current value with // demoVal, combine with min and // insert into stack Console.WriteLine("pushed: " + val); } int pop() { // if stack is empty return -1; if (st.Count==0 ) { Console.WriteLine("stack underflow"); return -1; } int val = st.Pop(); if (st.Count!=0) // if stack is empty, there would // be no min value present, so // make min as -1 min = st.Peek() % demoVal; else min = -1; Console.WriteLine("popped: " + val / demoVal); return val / demoVal; // decode actual value from // encoded value } int peek() { return st.Peek() / demoVal; // decode actual value // from encoded value } // Driver Code public static void Main(String[] args) { SpecialStack s = new SpecialStack(); int[] arr = { 3, 2, 6, 1, 8, 5, 5, 5, 5 }; for (int i = 0; i < arr.Length; i++) { s.push(arr[i]); s.getMin(); } Console.WriteLine(); for (int i = 0; i < arr.Length; i++) { s.pop(); s.getMin(); } } } // This code is contributed by gauravrajput1 |
Javascript
/* A special stack having peek() pop() and * push() along with additional getMin() that * returns minimum value in a stack without * using extra space and all operations in O(1) * time.. ???? */ class SpecialStack { constructor(){ // Sentinel value for min this.min = -1; // Demo value this.demoVal = 9999; this.st = []; } getMin() { console.log("min is: ", this.min); } push(val) { // If stack is empty OR current element // is less than min, update min. if ((this.st.length == 0) || (val < this.min)) { this.min = val; } // Encode the current value with // demoVal, combine with min and // insert into stack this.st.push(val * this.demoVal + this.min); console.log("pushed: ", val); } pop() { // if stack is empty return -1; if (this.st.length == 0) { console.log("stack underflow"); return -1; } let val = this.st[this.st.length - 1]; this.st.pop(); // If stack is empty, there would // be no min value present, so // make min as -1 if (this.st.length){ this.min = this.st[this.st.length - 1]% this.demoVal; } else{ this.min = -1; } console.log("popped: ", Math.floor(val / this.demoVal)); // Decode actual value from // encoded value return Math.floor(val / this.demoVal); } peek() { // Decode actual value // from encoded value return Math.floor(this.st[this.st.length - 1] / demoVal); } }; // Driver Code let s = new SpecialStack(); let arr = [3, 2, 6, 1, 8, 5, 5, 5, 5 ]; for(let i = 0; i < arr.length; i++) { s.push(arr[i]); s.getMin(); } console.log(); for(let i = 0; i < arr.length; i++) { s.pop(); s.getMin(); } // This code is contributed by Nidhi goel. |
Output
pushed: 3 min is: 3 pushed: 2 min is: 2 pushed: 6 min is: 2 pushed: 1 min is: 1 pushed: 8 min is: 1 pushed: 5 min is: 1 pushed: 5 min is: 1 pushed: 5 min is: 1 pushed: 5 min is: 1 popped: 5 min is: 1 popped: 5 min is: 1 popped: 5 min is: 1 popped: 5 min is: 1 popped: 8 min is: 1 popped: 1 min is: 2 popped: 6 min is: 2 popped: 2 min is: 3 popped: 3 min is: -1
Complexity Analysis:
For push() operation: O(1) (As insertion ‘push’ in a stack takes constant time)
For pop() operation: O(1) (As pop operation in a stack takes constant time)
For ‘Get Min’ operation: O(1) (As we have maintained min variable throughout the code)
Auxiliary Space: O(1). No extra space is used.
Design a stack that supports getMin() in O(1) time and O(1) extra space
Thanks to @Venki, @swarup, and @Jing Huang for their inputs.
Please write comments if you find the above code incorrect, or find other ways to solve the same problem.
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