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面试题 03.02. 栈的最小值

题目描述

请设计一个栈，除了常规栈支持的pop与push函数以外，还支持min函数，该函数返回栈元素中的最小值。执行push、pop和min操作的时间复杂度必须为O(1)。


示例：

MinStack minStack = new MinStack();
minStack.push(-2);
minStack.push(0);
minStack.push(-3);
minStack.getMin();   --> 返回 -3.
minStack.pop();
minStack.top();      --> 返回 0.
minStack.getMin();   --> 返回 -2.

解法

方法一：双栈

我们用两个栈来实现，其中stk1 用来存储数据，stk2 用来存储当前栈中的最小值。初始时，stk2 中存储一个极大值。

  • 当我们向栈中压入一个元素 x 时，我们将 x 压入 stk1，并将 min(x, stk2[-1]) 压入 stk2。
  • 当我们从栈中弹出一个元素时，我们将 stk1 和 stk2 的栈顶元素都弹出。
  • 当我们要获取当前栈中的栈顶元素时，我们只需要返回 stk1 的栈顶元素即可。
  • 当我们要获取当前栈中的最小值时，我们只需要返回 stk2 的栈顶元素即可。

时间复杂度：对于每个操作，时间复杂度均为 \(O(1)\)，空间复杂度 \(O(n)\)。

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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()

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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();
 */

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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();
 */

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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();
 */

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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()
 */

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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()
    }
}

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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();
 */

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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();
 */

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