Skip to content

03.02. Min Stack

Description

How would you design a stack which, in addition to push and pop, has a function min which returns the minimum element? Push, pop and min should all operate in 0(1) time.

Example: 


MinStack minStack = new MinStack();

minStack.push(-2);

minStack.push(0);

minStack.push(-3);

minStack.getMin();   --> return -3.

minStack.pop();

minStack.top();      --> return 0.

minStack.getMin();   --> return -2.

Solutions

Solution 1: Double Stack

We use two stacks to implement this, where stk1 is used to store data, and stk2 is used to store the current minimum value in the stack. Initially, stk2 stores a very large value.

  • When we push an element x into the stack, we push x into stk1, and push min(x, stk2[-1]) into stk2.
  • When we pop an element from the stack, we pop the top elements of both stk1 and stk2.
  • When we want to get the top element in the current stack, we just need to return the top element of stk1.
  • When we want to get the minimum value in the current stack, we just need to return the top element of stk2.

For each operation, the time complexity is $O(1)$, and the space complexity is $O(n)$.

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
class MinStack:
    def __init__(self):
        """
        initialize your data structure here.
        """
        self.s = []
        self.mins = [inf]

    def push(self, val: int) -> None:
        self.s.append(val)
        self.mins.append(min(self.mins[-1], val))

    def pop(self) -> None:
        self.s.pop()
        self.mins.pop()

    def top(self) -> int:
        return self.s[-1]

    def getMin(self) -> int:
        return self.mins[-1]


# Your MinStack object will be instantiated and called as such:
# obj = MinStack()
# obj.push(val)
# obj.pop()
# param_3 = obj.top()
# param_4 = obj.getMin()

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
class MinStack {
    private Deque<Integer> stk1 = new ArrayDeque<>();
    private Deque<Integer> stk2 = new ArrayDeque<>();

    /** initialize your data structure here. */
    public MinStack() {
        stk2.push(Integer.MAX_VALUE);
    }

    public void push(int x) {
        stk1.push(x);
        stk2.push(Math.min(x, stk2.peek()));
    }

    public void pop() {
        stk1.pop();
        stk2.pop();
    }

    public int top() {
        return stk1.peek();
    }

    public int getMin() {
        return stk2.peek();
    }
}

/**
 * Your MinStack object will be instantiated and called as such:
 * MinStack obj = new MinStack();
 * obj.push(x);
 * obj.pop();
 * int param_3 = obj.top();
 * int param_4 = obj.getMin();
 */

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
class MinStack {
public:
    /** initialize your data structure here. */
    MinStack() {
        stk2.push(INT_MAX);
    }

    void push(int x) {
        stk1.push(x);
        stk2.push(min(x, stk2.top()));
    }

    void pop() {
        stk1.pop();
        stk2.pop();
    }

    int top() {
        return stk1.top();
    }

    int getMin() {
        return stk2.top();
    }

private:
    stack<int> stk1;
    stack<int> stk2;
};

/**
 * Your MinStack object will be instantiated and called as such:
 * MinStack* obj = new MinStack();
 * obj->push(x);
 * obj->pop();
 * int param_3 = obj->top();
 * int param_4 = obj->getMin();
 */

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
type MinStack struct {
    stk1 []int
    stk2 []int
}

/** initialize your data structure here. */
func Constructor() MinStack {
    return MinStack{[]int{}, []int{math.MaxInt32}}
}

func (this *MinStack) Push(x int) {
    this.stk1 = append(this.stk1, x)
    this.stk2 = append(this.stk2, min(x, this.stk2[len(this.stk2)-1]))
}

func (this *MinStack) Pop() {
    this.stk1 = this.stk1[:len(this.stk1)-1]
    this.stk2 = this.stk2[:len(this.stk2)-1]
}

func (this *MinStack) Top() int {
    return this.stk1[len(this.stk1)-1]
}

func (this *MinStack) GetMin() int {
    return this.stk2[len(this.stk2)-1]
}

/**
 * Your MinStack object will be instantiated and called as such:
 * obj := Constructor();
 * obj.Push(x);
 * obj.Pop();
 * param_3 := obj.Top();
 * param_4 := obj.GetMin();
 */

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
class MinStack {
    stack: number[];
    mins: number[];
    constructor() {
        this.stack = [];
        this.mins = [];
    }

    push(x: number): void {
        this.stack.push(x);
        this.mins.push(Math.min(this.getMin(), x));
    }

    pop(): void {
        this.stack.pop();
        this.mins.pop();
    }

    top(): number {
        return this.stack[this.stack.length - 1];
    }

    getMin(): number {
        return this.mins.length == 0 ? Infinity : this.mins[this.mins.length - 1];
    }
}

/**
 * Your MinStack object will be instantiated and called as such:
 * var obj = new MinStack()
 * obj.push(x)
 * obj.pop()
 * var param_3 = obj.top()
 * var param_4 = obj.getMin()
 */

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
use std::collections::VecDeque;
struct MinStack {
    stack: VecDeque<i32>,
    min_stack: VecDeque<i32>,
}

/**
 * `&self` means the method takes an immutable reference.
 * If you need a mutable reference, change it to `&mut self` instead.
 */
impl MinStack {
    /** initialize your data structure here. */
    fn new() -> Self {
        Self { stack: VecDeque::new(), min_stack: VecDeque::new() }
    }

    fn push(&mut self, x: i32) {
        self.stack.push_back(x);
        if self.min_stack.is_empty() || *self.min_stack.back().unwrap() >= x {
            self.min_stack.push_back(x);
        }
    }

    fn pop(&mut self) {
        let val = self.stack.pop_back().unwrap();
        if *self.min_stack.back().unwrap() == val {
            self.min_stack.pop_back();
        }
    }

    fn top(&self) -> i32 {
        *self.stack.back().unwrap()
    }

    fn get_min(&self) -> i32 {
        *self.min_stack.back().unwrap()
    }
}/**
 * Your MinStack object will be instantiated and called as such:
 * let obj = MinStack::new();
 * obj.push(x);
 * obj.pop();
 * let ret_3: i32 = obj.top();
 * let ret_4: i32 = obj.get_min();
 */

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
public class MinStack {
    private Stack<int> stk1 = new Stack<int>();
    private Stack<int> stk2 = new Stack<int>();

    /** initialize your data structure here. */
    public MinStack() {
        stk2.Push(int.MaxValue);
    }

    public void Push(int x) {
        stk1.Push(x);
        stk2.Push(Math.Min(x, GetMin()));
    }

    public void Pop() {
        stk1.Pop();
        stk2.Pop();
    }

    public int Top() {
        return stk1.Peek();
    }

    public int GetMin() {
        return stk2.Peek();
    }
}

/**
 * Your MinStack object will be instantiated and called as such:
 * MinStack obj = new MinStack();
 * obj.Push(x);
 * obj.Pop();
 * int param_3 = obj.Top();
 * int param_4 = obj.GetMin();
 */

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
class MinStack {
    private var stk1: [Int]
    private var stk2: [Int]

    init() {
        stk1 = []
        stk2 = [Int.max]
    }

    func push(_ x: Int) {
        stk1.append(x)

        stk2.append(min(x, stk2.last!))
    }

    func pop() {
        stk1.removeLast()
        stk2.removeLast()
    }

    func top() -> Int {
        return stk1.last!
    }

    func getMin() -> Int {
        return stk2.last!
    }
}

/**
 * Your MinStack object will be instantiated and called as such:
 * let obj = MinStack();
 * obj.push(x);
 * obj.pop();
 * let param_3 = obj.top();
 * let param_4 = obj.getMin();
 */

Comments