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# min-stack

Min Stack

## Problem Description

Design a stack that supports push, pop, top, and retrieving the minimum element in constant time.
push(x) -- Push element x onto stack.
pop() -- Removes the element on top of the stack.
top() -- Get the top element.
getMin() -- Retrieve the minimum element in the stack.
Example:
MinStack minStack = new MinStack();
minStack.push(-2);
minStack.push(0);
minStack.push(-3);
minStack.getMin(); --> Returns -3.
minStack.pop();
minStack.top(); --> Returns 0.
minStack.getMin(); --> Returns -2.

## Solution 1 (two stack)

Intuitive solution is to use 2 stacks, one stack to maintain value, and one stack to maintain min value.
For example: Min Stack with 2 Stacks

### Complexity Analysis

Time Complexity: `O(N)`
Space Complexity: `O(N)`

### Code

class MinStack {
Stack<Integer> stack;
Stack<Integer> minStack;
/** initialize your data structure here. */
public MinStack() {
stack = new Stack<>();
minStack = new Stack<>();
}
public void push(int x) {
stack.push(x);
int curr = minStack.isEmpty() ? x : minStack.peek();
minStack.push(curr > x ? x : curr);
}
public void pop() {
stack.pop();
minStack.pop();
}
public int top() {
return stack.peek();
}
public int getMin() {
return minStack.peek();
}
}

## Solution 2 (one stack)

From solution 1, we observe that we maintain 2 stacks every operation and 1 stack to keep one state, and with that thought, we can use one stack to maintain 2 states, how to maintain 2 states in one action, using helper class.
helper class Node with value and min value, and stack to maintain Node status.
for example: Min Stack with 1 Stack

### Complexity Analysis

Time Complexity: `O(N)`
Space Complexity: `O(N)`

### Code

class MinStack {
Stack<Node> stack;
/** initialize your data structure here. */
public MinStack() {
stack = new Stack<>();
}
public void push(int x) {
if (stack.isEmpty()) {
stack.push(new Node(x, x));
} else {
Node top = stack.peek();
stack.push(top.min < x ? new Node(x, top.min) : new Node(x, x));
}
}
public void pop() {
stack.pop();
}
public int top() {
return stack.peek().val;
}
public int getMin() {
return stack.peek().min;
}
class Node {
int val;
int min;
public Node(int val, int min) {
this.val = val;
this.min = min;
}
}
}