2454. 下一个更大元素 IV

题目描述

给你一个下标从 0 开始的非负整数数组 nums 。对于 nums 中每一个整数，你必须找到对应元素的 第二大 整数。

如果 nums[j] 满足以下条件，那么我们称它为 nums[i] 的 第二大 整数：

• j > i
• nums[j] > nums[i]
• 恰好存在 一个 k 满足 i < k < j 且 nums[k] > nums[i] 。

如果不存在 nums[j] ，那么第二大整数为 -1 。

• 比方说，数组 [1, 2, 4, 3] 中，1 的第二大整数是 4 ，2 的第二大整数是 3 ，3 和 4 的第二大整数是 -1 。

请你返回一个整数数组 answer ，其中 answer[i]是 nums[i] 的第二大整数。

 

示例 1：

输入：nums = [2,4,0,9,6]
输出：[9,6,6,-1,-1]
解释：
下标为 0 处：2 的右边，4 是大于 2 的第一个整数，9 是第二个大于 2 的整数。
下标为 1 处：4 的右边，9 是大于 4 的第一个整数，6 是第二个大于 4 的整数。
下标为 2 处：0 的右边，9 是大于 0 的第一个整数，6 是第二个大于 0 的整数。
下标为 3 处：右边不存在大于 9 的整数，所以第二大整数为 -1 。
下标为 4 处：右边不存在大于 6 的整数，所以第二大整数为 -1 。
所以我们返回 [9,6,6,-1,-1] 。

示例 2：

输入：nums = [3,3]
输出：[-1,-1]
解释：
由于每个数右边都没有更大的数，所以我们返回 [-1,-1] 。

 

提示：

• 1 <= nums.length <= 105
• 0 <= nums[i] <= 109

解法

方法一：排序 + 有序集合

我们可以将数组中的元素转成二元组 $(x, i)$，其中 $x$ 为元素的值，$i$ 为元素的下标。然后按照元素的值从大到小排序。

接下来，我们遍历排序后的数组，维护一个有序集合，其中存储的是元素的下标。当我们遍历到元素 $(x, i)$ 时，所有大于 $x$ 的元素的下标都已经在有序集合中了。我们只需要在有序集合中，找到 $i$ 的下下一个元素的下标 $j$，那么 $j$ 对应的元素就是 $x$ 的第二大元素。然后，我们将 $i$ 加入到有序集合中。继续遍历下一个元素。

时间复杂度 $O(n \times \log n)$，空间复杂度 $O(n)$。其中 $n$ 为数组的长度。

Python3JavaC++TypeScript

from sortedcontainers import SortedList


class Solution:
    def secondGreaterElement(self, nums: List[int]) -> List[int]:
        arr = [(x, i) for i, x in enumerate(nums)]
        arr.sort(key=lambda x: -x[0])
        sl = SortedList()
        n = len(nums)
        ans = [-1] * n
        for _, i in arr:
            j = sl.bisect_right(i)
            if j + 1 < len(sl):
                ans[i] = nums[sl[j + 1]]
            sl.add(i)
        return ans

class Solution {
    public int[] secondGreaterElement(int[] nums) {
        int n = nums.length;
        int[] ans = new int[n];
        Arrays.fill(ans, -1);
        int[][] arr = new int[n][0];
        for (int i = 0; i < n; ++i) {
            arr[i] = new int[] {nums[i], i};
        }
        Arrays.sort(arr, (a, b) -> a[0] == b[0] ? a[1] - b[1] : b[0] - a[0]);
        TreeSet<Integer> ts = new TreeSet<>();
        for (int[] pair : arr) {
            int i = pair[1];
            Integer j = ts.higher(i);
            if (j != null && ts.higher(j) != null) {
                ans[i] = nums[ts.higher(j)];
            }
            ts.add(i);
        }
        return ans;
    }
}

class Solution {
public:
    vector<int> secondGreaterElement(vector<int>& nums) {
        int n = nums.size();
        vector<int> ans(n, -1);
        vector<pair<int, int>> arr(n);
        for (int i = 0; i < n; ++i) {
            arr[i] = {-nums[i], i};
        }
        sort(arr.begin(), arr.end());
        set<int> ts;
        for (auto& [_, i] : arr) {
            auto it = ts.upper_bound(i);
            if (it != ts.end() && ts.upper_bound(*it) != ts.end()) {
                ans[i] = nums[*ts.upper_bound(*it)];
            }
            ts.insert(i);
        }
        return ans;
    }
};

function secondGreaterElement(nums: number[]): number[] {
    const n = nums.length;
    const arr: number[][] = [];
    for (let i = 0; i < n; ++i) {
        arr.push([nums[i], i]);
    }
    arr.sort((a, b) => (a[0] == b[0] ? a[1] - b[1] : b[0] - a[0]));
    const ans = Array(n).fill(-1);
    const ts = new TreeSet<number>();
    for (const [_, i] of arr) {
        let j = ts.higher(i);
        if (j !== undefined) {
            j = ts.higher(j);
            if (j !== undefined) {
                ans[i] = nums[j];
            }
        }
        ts.add(i);
    }
    return ans;
}

type Compare<T> = (lhs: T, rhs: T) => number;

class RBTreeNode<T = number> {
    data: T;
    count: number;
    left: RBTreeNode<T> | null;
    right: RBTreeNode<T> | null;
    parent: RBTreeNode<T> | null;
    color: number;
    constructor(data: T) {
        this.data = data;
        this.left = this.right = this.parent = null;
        this.color = 0;
        this.count = 1;
    }

    sibling(): RBTreeNode<T> | null {
        if (!this.parent) return null; // sibling null if no parent
        return this.isOnLeft() ? this.parent.right : this.parent.left;
    }

    isOnLeft(): boolean {
        return this === this.parent!.left;
    }

    hasRedChild(): boolean {
        return (
            Boolean(this.left && this.left.color === 0) ||
            Boolean(this.right && this.right.color === 0)
        );
    }
}

class RBTree<T> {
    root: RBTreeNode<T> | null;
    lt: (l: T, r: T) => boolean;
    constructor(compare: Compare<T> = (l: T, r: T) => (l < r ? -1 : l > r ? 1 : 0)) {
        this.root = null;
        this.lt = (l: T, r: T) => compare(l, r) < 0;
    }

    rotateLeft(pt: RBTreeNode<T>): void {
        const right = pt.right!;
        pt.right = right.left;

        if (pt.right) pt.right.parent = pt;
        right.parent = pt.parent;

        if (!pt.parent) this.root = right;
        else if (pt === pt.parent.left) pt.parent.left = right;
        else pt.parent.right = right;

        right.left = pt;
        pt.parent = right;
    }

    rotateRight(pt: RBTreeNode<T>): void {
        const left = pt.left!;
        pt.left = left.right;

        if (pt.left) pt.left.parent = pt;
        left.parent = pt.parent;

        if (!pt.parent) this.root = left;
        else if (pt === pt.parent.left) pt.parent.left = left;
        else pt.parent.right = left;

        left.right = pt;
        pt.parent = left;
    }

    swapColor(p1: RBTreeNode<T>, p2: RBTreeNode<T>): void {
        const tmp = p1.color;
        p1.color = p2.color;
        p2.color = tmp;
    }

    swapData(p1: RBTreeNode<T>, p2: RBTreeNode<T>): void {
        const tmp = p1.data;
        p1.data = p2.data;
        p2.data = tmp;
    }

    fixAfterInsert(pt: RBTreeNode<T>): void {
        let parent = null;
        let grandParent = null;

        while (pt !== this.root && pt.color !== 1 && pt.parent?.color === 0) {
            parent = pt.parent;
            grandParent = pt.parent.parent;

            /*  Case : A
                Parent of pt is left child of Grand-parent of pt */
            if (parent === grandParent?.left) {
                const uncle = grandParent.right;

                /* Case : 1
                   The uncle of pt is also red
                   Only Recoloring required */
                if (uncle && uncle.color === 0) {
                    grandParent.color = 0;
                    parent.color = 1;
                    uncle.color = 1;
                    pt = grandParent;
                } else {
                    /* Case : 2
                       pt is right child of its parent
                       Left-rotation required */
                    if (pt === parent.right) {
                        this.rotateLeft(parent);
                        pt = parent;
                        parent = pt.parent;
                    }

                    /* Case : 3
                       pt is left child of its parent
                       Right-rotation required */
                    this.rotateRight(grandParent);
                    this.swapColor(parent!, grandParent);
                    pt = parent!;
                }
            } else {
                /* Case : B
               Parent of pt is right child of Grand-parent of pt */
                const uncle = grandParent!.left;

                /*  Case : 1
                    The uncle of pt is also red
                    Only Recoloring required */
                if (uncle != null && uncle.color === 0) {
                    grandParent!.color = 0;
                    parent.color = 1;
                    uncle.color = 1;
                    pt = grandParent!;
                } else {
                    /* Case : 2
                       pt is left child of its parent
                       Right-rotation required */
                    if (pt === parent.left) {
                        this.rotateRight(parent);
                        pt = parent;
                        parent = pt.parent;
                    }

                    /* Case : 3
                       pt is right child of its parent
                       Left-rotation required */
                    this.rotateLeft(grandParent!);
                    this.swapColor(parent!, grandParent!);
                    pt = parent!;
                }
            }
        }
        this.root!.color = 1;
    }

    delete(val: T): boolean {
        const node = this.find(val);
        if (!node) return false;
        node.count--;
        if (!node.count) this.deleteNode(node);
        return true;
    }

    deleteAll(val: T): boolean {
        const node = this.find(val);
        if (!node) return false;
        this.deleteNode(node);
        return true;
    }

    deleteNode(v: RBTreeNode<T>): void {
        const u = BSTreplace(v);

        // True when u and v are both black
        const uvBlack = (u === null || u.color === 1) && v.color === 1;
        const parent = v.parent!;

        if (!u) {
            // u is null therefore v is leaf
            if (v === this.root) this.root = null;
            // v is root, making root null
            else {
                if (uvBlack) {
                    // u and v both black
                    // v is leaf, fix double black at v
                    this.fixDoubleBlack(v);
                } else {
                    // u or v is red
                    if (v.sibling()) {
                        // sibling is not null, make it red"
                        v.sibling()!.color = 0;
                    }
                }
                // delete v from the tree
                if (v.isOnLeft()) parent.left = null;
                else parent.right = null;
            }
            return;
        }

        if (!v.left || !v.right) {
            // v has 1 child
            if (v === this.root) {
                // v is root, assign the value of u to v, and delete u
                v.data = u.data;
                v.left = v.right = null;
            } else {
                // Detach v from tree and move u up
                if (v.isOnLeft()) parent.left = u;
                else parent.right = u;
                u.parent = parent;
                if (uvBlack) this.fixDoubleBlack(u);
                // u and v both black, fix double black at u
                else u.color = 1; // u or v red, color u black
            }
            return;
        }

        // v has 2 children, swap data with successor and recurse
        this.swapData(u, v);
        this.deleteNode(u);

        // find node that replaces a deleted node in BST
        function BSTreplace(x: RBTreeNode<T>): RBTreeNode<T> | null {
            // when node have 2 children
            if (x.left && x.right) return successor(x.right);
            // when leaf
            if (!x.left && !x.right) return null;
            // when single child
            return x.left ?? x.right;
        }
        // find node that do not have a left child
        // in the subtree of the given node
        function successor(x: RBTreeNode<T>): RBTreeNode<T> {
            let temp = x;
            while (temp.left) temp = temp.left;
            return temp;
        }
    }

    fixDoubleBlack(x: RBTreeNode<T>): void {
        if (x === this.root) return; // Reached root

        const sibling = x.sibling();
        const parent = x.parent!;
        if (!sibling) {
            // No sibiling, double black pushed up
            this.fixDoubleBlack(parent);
        } else {
            if (sibling.color === 0) {
                // Sibling red
                parent.color = 0;
                sibling.color = 1;
                if (sibling.isOnLeft()) this.rotateRight(parent);
                // left case
                else this.rotateLeft(parent); // right case
                this.fixDoubleBlack(x);
            } else {
                // Sibling black
                if (sibling.hasRedChild()) {
                    // at least 1 red children
                    if (sibling.left && sibling.left.color === 0) {
                        if (sibling.isOnLeft()) {
                            // left left
                            sibling.left.color = sibling.color;
                            sibling.color = parent.color;
                            this.rotateRight(parent);
                        } else {
                            // right left
                            sibling.left.color = parent.color;
                            this.rotateRight(sibling);
                            this.rotateLeft(parent);
                        }
                    } else {
                        if (sibling.isOnLeft()) {
                            // left right
                            sibling.right!.color = parent.color;
                            this.rotateLeft(sibling);
                            this.rotateRight(parent);
                        } else {
                            // right right
                            sibling.right!.color = sibling.color;
                            sibling.color = parent.color;
                            this.rotateLeft(parent);
                        }
                    }
                    parent.color = 1;
                } else {
                    // 2 black children
                    sibling.color = 0;
                    if (parent.color === 1) this.fixDoubleBlack(parent);
                    else parent.color = 1;
                }
            }
        }
    }

    insert(data: T): boolean {
        // search for a position to insert
        let parent = this.root;
        while (parent) {
            if (this.lt(data, parent.data)) {
                if (!parent.left) break;
                else parent = parent.left;
            } else if (this.lt(parent.data, data)) {
                if (!parent.right) break;
                else parent = parent.right;
            } else break;
        }

        // insert node into parent
        const node = new RBTreeNode(data);
        if (!parent) this.root = node;
        else if (this.lt(node.data, parent.data)) parent.left = node;
        else if (this.lt(parent.data, node.data)) parent.right = node;
        else {
            parent.count++;
            return false;
        }
        node.parent = parent;
        this.fixAfterInsert(node);
        return true;
    }

    find(data: T): RBTreeNode<T> | null {
        let p = this.root;
        while (p) {
            if (this.lt(data, p.data)) {
                p = p.left;
            } else if (this.lt(p.data, data)) {
                p = p.right;
            } else break;
        }
        return p ?? null;
    }

    *inOrder(root: RBTreeNode<T> = this.root!): Generator<T, undefined, void> {
        if (!root) return;
        for (const v of this.inOrder(root.left!)) yield v;
        yield root.data;
        for (const v of this.inOrder(root.right!)) yield v;
    }

    *reverseInOrder(root: RBTreeNode<T> = this.root!): Generator<T, undefined, void> {
        if (!root) return;
        for (const v of this.reverseInOrder(root.right!)) yield v;
        yield root.data;
        for (const v of this.reverseInOrder(root.left!)) yield v;
    }
}

class TreeSet<T = number> {
    _size: number;
    tree: RBTree<T>;
    compare: Compare<T>;
    constructor(
        collection: T[] | Compare<T> = [],
        compare: Compare<T> = (l: T, r: T) => (l < r ? -1 : l > r ? 1 : 0),
    ) {
        if (typeof collection === 'function') {
            compare = collection;
            collection = [];
        }
        this._size = 0;
        this.compare = compare;
        this.tree = new RBTree(compare);
        for (const val of collection) this.add(val);
    }

    size(): number {
        return this._size;
    }

    has(val: T): boolean {
        return !!this.tree.find(val);
    }

    add(val: T): boolean {
        const successful = this.tree.insert(val);
        this._size += successful ? 1 : 0;
        return successful;
    }

    delete(val: T): boolean {
        const deleted = this.tree.deleteAll(val);
        this._size -= deleted ? 1 : 0;
        return deleted;
    }

    ceil(val: T): T | undefined {
        let p = this.tree.root;
        let higher = null;
        while (p) {
            if (this.compare(p.data, val) >= 0) {
                higher = p;
                p = p.left;
            } else {
                p = p.right;
            }
        }
        return higher?.data;
    }

    floor(val: T): T | undefined {
        let p = this.tree.root;
        let lower = null;
        while (p) {
            if (this.compare(val, p.data) >= 0) {
                lower = p;
                p = p.right;
            } else {
                p = p.left;
            }
        }
        return lower?.data;
    }

    higher(val: T): T | undefined {
        let p = this.tree.root;
        let higher = null;
        while (p) {
            if (this.compare(val, p.data) < 0) {
                higher = p;
                p = p.left;
            } else {
                p = p.right;
            }
        }
        return higher?.data;
    }

    lower(val: T): T | undefined {
        let p = this.tree.root;
        let lower = null;
        while (p) {
            if (this.compare(p.data, val) < 0) {
                lower = p;
                p = p.right;
            } else {
                p = p.left;
            }
        }
        return lower?.data;
    }

    first(): T | undefined {
        return this.tree.inOrder().next().value;
    }

    last(): T | undefined {
        return this.tree.reverseInOrder().next().value;
    }

    shift(): T | undefined {
        const first = this.first();
        if (first === undefined) return undefined;
        this.delete(first);
        return first;
    }

    pop(): T | undefined {
        const last = this.last();
        if (last === undefined) return undefined;
        this.delete(last);
        return last;
    }

    *[Symbol.iterator](): Generator<T, void, void> {
        for (const val of this.values()) yield val;
    }

    *keys(): Generator<T, void, void> {
        for (const val of this.values()) yield val;
    }

    *values(): Generator<T, undefined, void> {
        for (const val of this.tree.inOrder()) yield val;
        return undefined;
    }

    /**
     * Return a generator for reverse order traversing the set
     */
    *rvalues(): Generator<T, undefined, void> {
        for (const val of this.tree.reverseInOrder()) yield val;
        return undefined;
    }
}

class TreeMultiSet<T = number> {
    _size: number;
    tree: RBTree<T>;
    compare: Compare<T>;
    constructor(
        collection: T[] | Compare<T> = [],
        compare: Compare<T> = (l: T, r: T) => (l < r ? -1 : l > r ? 1 : 0),
    ) {
        if (typeof collection === 'function') {
            compare = collection;
            collection = [];
        }
        this._size = 0;
        this.compare = compare;
        this.tree = new RBTree(compare);
        for (const val of collection) this.add(val);
    }

    size(): number {
        return this._size;
    }

    has(val: T): boolean {
        return !!this.tree.find(val);
    }

    add(val: T): boolean {
        const successful = this.tree.insert(val);
        this._size++;
        return successful;
    }

    delete(val: T): boolean {
        const successful = this.tree.delete(val);
        if (!successful) return false;
        this._size--;
        return true;
    }

    count(val: T): number {
        const node = this.tree.find(val);
        return node ? node.count : 0;
    }

    ceil(val: T): T | undefined {
        let p = this.tree.root;
        let higher = null;
        while (p) {
            if (this.compare(p.data, val) >= 0) {
                higher = p;
                p = p.left;
            } else {
                p = p.right;
            }
        }
        return higher?.data;
    }

    floor(val: T): T | undefined {
        let p = this.tree.root;
        let lower = null;
        while (p) {
            if (this.compare(val, p.data) >= 0) {
                lower = p;
                p = p.right;
            } else {
                p = p.left;
            }
        }
        return lower?.data;
    }

    higher(val: T): T | undefined {
        let p = this.tree.root;
        let higher = null;
        while (p) {
            if (this.compare(val, p.data) < 0) {
                higher = p;
                p = p.left;
            } else {
                p = p.right;
            }
        }
        return higher?.data;
    }

    lower(val: T): T | undefined {
        let p = this.tree.root;
        let lower = null;
        while (p) {
            if (this.compare(p.data, val) < 0) {
                lower = p;
                p = p.right;
            } else {
                p = p.left;
            }
        }
        return lower?.data;
    }

    first(): T | undefined {
        return this.tree.inOrder().next().value;
    }

    last(): T | undefined {
        return this.tree.reverseInOrder().next().value;
    }

    shift(): T | undefined {
        const first = this.first();
        if (first === undefined) return undefined;
        this.delete(first);
        return first;
    }

    pop(): T | undefined {
        const last = this.last();
        if (last === undefined) return undefined;
        this.delete(last);
        return last;
    }

    *[Symbol.iterator](): Generator<T, void, void> {
        yield* this.values();
    }

    *keys(): Generator<T, void, void> {
        for (const val of this.values()) yield val;
    }

    *values(): Generator<T, undefined, void> {
        for (const val of this.tree.inOrder()) {
            let count = this.count(val);
            while (count--) yield val;
        }
        return undefined;
    }

    /**
     * Return a generator for reverse order traversing the multi-set
     */
    *rvalues(): Generator<T, undefined, void> {
        for (const val of this.tree.reverseInOrder()) {
            let count = this.count(val);
            while (count--) yield val;
        }
        return undefined;
    }
}

评论