Question
Design a max stack that supports push, pop, top, peekMax and popMax.
- push(x) – Push element x onto stack.
- pop() – Remove the element on top of the stack and return it.
- top() – Get the element on the top.
- peekMax() – Retrieve the maximum element in the stack.
- popMax() – Retrieve the maximum element in the stack, and remove it. If you - find more than one maximum elements, only remove the top-most one.
Example 1:
MaxStack stack = new MaxStack();
stack.push(5);
stack.push(1);
stack.push(5);
stack.top(); -> 5
stack.popMax(); -> 5
stack.top(); -> 1
stack.peekMax(); -> 5
stack.pop(); -> 1
stack.top(); -> 5
Solution I
Use two stacks
Code
class MaxStack {
Stack<Integer> stack;
Stack<Integer> maxStack;
/** initialize your data structure here. */
public MaxStack() {
stack = new Stack<>();
maxStack = new Stack<>();
}
public void push(int x) {
int max = maxStack.isEmpty() ? x : maxStack.peek();
maxStack.push(max > x ? max : x);
stack.push(x);
}
public int pop() {
maxStack.pop();
return stack.pop();
}
public int top() {
return stack.peek();
}
public int peekMax() {
return maxStack.peek();
}
public int popMax() {
int max = maxStack.peek();
Stack<Integer> buffer = new Stack<>();
while(stack.peek() != max) {
buffer.push(pop());
}
pop();
while(!buffer.isEmpty()) push(buffer.pop());
return max;
}
}
Performance
O(n) for popMax and O(1) for other operations.
Solution I
Use heap (TreeMap) + double linked list
Code
class MaxStack {
TreeMap<Integer, List<Node>> map;
DoubleLinkedList dll;
public MaxStack() {
map = new TreeMap();
dll = new DoubleLinkedList();
}
public void push(int x) {
Node node = dll.add(x);
if(!map.containsKey(x))
map.put(x, new ArrayList<Node>());
map.get(x).add(node);
}
public int pop() {
int val = dll.pop();
List<Node> L = map.get(val);
L.remove(L.size() - 1);
if (L.isEmpty()) map.remove(val);
return val;
}
public int top() {
return dll.peek();
}
public int peekMax() {
return map.lastKey();
}
public int popMax() {
int max = peekMax();
List<Node> L = map.get(max);
Node node = L.remove(L.size() - 1);
dll.unlink(node);
if (L.isEmpty()) map.remove(max);
return max;
}
}
class DoubleLinkedList {
Node head, tail;
public DoubleLinkedList() {
head = new Node(0);
tail = new Node(0);
head.next = tail;
tail.prev = head;
}
public Node add(int val) {
Node x = new Node(val);
x.next = tail;
x.prev = tail.prev;
tail.prev = tail.prev.next = x;
return x;
}
public int pop() {
return unlink(tail.prev).val;
}
public int peek() {
return tail.prev.val;
}
public Node unlink(Node node) {
node.prev.next = node.next;
node.next.prev = node.prev;
return node;
}
}
class Node {
int val;
Node prev, next;
public Node(int v) {val = v;}
}
Performance
O(logn) for all operations and O(1) for peek.