Description#
Design a max stack data structure that supports the stack operations and supports finding the stack's maximum element.
Implement the MaxStack class:
MaxStack() Initializes the stack object.void push(int x) Pushes element x onto the stack.int pop() Removes the element on top of the stack and returns it.int top() Gets the element on the top of the stack without removing it.int peekMax() Retrieves the maximum element in the stack without removing it.int popMax() Retrieves the maximum element in the stack and removes it. If there is more than one maximum element, only remove the top-most one.
You must come up with a solution that supports O(1) for each top call and O(logn) for each other call.
Example 1:
Input
["MaxStack", "push", "push", "push", "top", "popMax", "top", "peekMax", "pop", "top"]
[[], [5], [1], [5], [], [], [], [], [], []]
Output
[null, null, null, null, 5, 5, 1, 5, 1, 5]
Explanation
MaxStack stk = new MaxStack();
stk.push(5); // [5] the top of the stack and the maximum number is 5.
stk.push(1); // [5, 1] the top of the stack is 1, but the maximum is 5.
stk.push(5); // [5, 1, 5] the top of the stack is 5, which is also the maximum, because it is the top most one.
stk.top(); // return 5, [5, 1, 5] the stack did not change.
stk.popMax(); // return 5, [5, 1] the stack is changed now, and the top is different from the max.
stk.top(); // return 1, [5, 1] the stack did not change.
stk.peekMax(); // return 5, [5, 1] the stack did not change.
stk.pop(); // return 1, [5] the top of the stack and the max element is now 5.
stk.top(); // return 5, [5] the stack did not change.
Constraints:
-107 <= x <= 107- At most
105 calls will be made to push, pop, top, peekMax, and popMax. - There will be at least one element in the stack when
pop, top, peekMax, or popMax is called.
Solutions#
Solution 1#
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| from sortedcontainers import SortedList
class Node:
def __init__(self, val=0):
self.val = val
self.prev: Union[Node, None] = None
self.next: Union[Node, None] = None
class DoubleLinkedList:
def __init__(self):
self.head = Node()
self.tail = Node()
self.head.next = self.tail
self.tail.prev = self.head
def append(self, val) -> Node:
node = Node(val)
node.next = self.tail
node.prev = self.tail.prev
self.tail.prev = node
node.prev.next = node
return node
@staticmethod
def remove(node) -> Node:
node.prev.next = node.next
node.next.prev = node.prev
return node
def pop(self) -> Node:
return self.remove(self.tail.prev)
def peek(self):
return self.tail.prev.val
class MaxStack:
def __init__(self):
self.stk = DoubleLinkedList()
self.sl = SortedList(key=lambda x: x.val)
def push(self, x: int) -> None:
node = self.stk.append(x)
self.sl.add(node)
def pop(self) -> int:
node = self.stk.pop()
self.sl.remove(node)
return node.val
def top(self) -> int:
return self.stk.peek()
def peekMax(self) -> int:
return self.sl[-1].val
def popMax(self) -> int:
node = self.sl.pop()
DoubleLinkedList.remove(node)
return node.val
# Your MaxStack object will be instantiated and called as such:
# obj = MaxStack()
# obj.push(x)
# param_2 = obj.pop()
# param_3 = obj.top()
# param_4 = obj.peekMax()
# param_5 = obj.popMax()
|
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| class Node {
public int val;
public Node prev, next;
public Node() {
}
public Node(int val) {
this.val = val;
}
}
class DoubleLinkedList {
private final Node head = new Node();
private final Node tail = new Node();
public DoubleLinkedList() {
head.next = tail;
tail.prev = head;
}
public Node append(int val) {
Node node = new Node(val);
node.next = tail;
node.prev = tail.prev;
tail.prev = node;
node.prev.next = node;
return node;
}
public static Node remove(Node node) {
node.prev.next = node.next;
node.next.prev = node.prev;
return node;
}
public Node pop() {
return remove(tail.prev);
}
public int peek() {
return tail.prev.val;
}
}
class MaxStack {
private DoubleLinkedList stk = new DoubleLinkedList();
private TreeMap<Integer, List<Node>> tm = new TreeMap<>();
public MaxStack() {
}
public void push(int x) {
Node node = stk.append(x);
tm.computeIfAbsent(x, k -> new ArrayList<>()).add(node);
}
public int pop() {
Node node = stk.pop();
List<Node> nodes = tm.get(node.val);
int x = nodes.remove(nodes.size() - 1).val;
if (nodes.isEmpty()) {
tm.remove(node.val);
}
return x;
}
public int top() {
return stk.peek();
}
public int peekMax() {
return tm.lastKey();
}
public int popMax() {
int x = peekMax();
List<Node> nodes = tm.get(x);
Node node = nodes.remove(nodes.size() - 1);
if (nodes.isEmpty()) {
tm.remove(x);
}
DoubleLinkedList.remove(node);
return x;
}
}
/**
* Your MaxStack object will be instantiated and called as such:
* MaxStack obj = new MaxStack();
* obj.push(x);
* int param_2 = obj.pop();
* int param_3 = obj.top();
* int param_4 = obj.peekMax();
* int param_5 = obj.popMax();
*/
|
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| class MaxStack {
public:
MaxStack() {
}
void push(int x) {
stk.push_back(x);
tm.insert({x, --stk.end()});
}
int pop() {
auto it = --stk.end();
int ans = *it;
auto mit = --tm.upper_bound(ans);
tm.erase(mit);
stk.erase(it);
return ans;
}
int top() {
return stk.back();
}
int peekMax() {
return tm.rbegin()->first;
}
int popMax() {
auto mit = --tm.end();
auto it = mit->second;
int ans = *it;
tm.erase(mit);
stk.erase(it);
return ans;
}
private:
multimap<int, list<int>::iterator> tm;
list<int> stk;
};
/**
* Your MaxStack object will be instantiated and called as such:
* MaxStack* obj = new MaxStack();
* obj->push(x);
* int param_2 = obj->pop();
* int param_3 = obj->top();
* int param_4 = obj->peekMax();
* int param_5 = obj->popMax();
*/
|
