| comments | difficulty | edit_url | tags | ||
|---|---|---|---|---|---|
true |
中等 |
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给定一个数组 nums，返回满足 i < j < k 且 nums[i] < nums[j] < nums[k] 的三元组 (i, j, k) 的 最大值。
三元组 (i, j, k) 的 值 为 nums[i] - nums[j] + nums[k]。
示例 1:
输入：nums = [5,6,9] 输出：8 解释：对于一个递增的三元组，我们只有一个选择，那就是选择所有三个元素。三元组的值为 5 - 6 + 9 = 8。
示例 2:
输入：nums = [1,5,3,6] 输出：4 解释：只有两个递增三元组： (0, 1, 3)：这个三元组的值为 nums[0] - nums[1] + nums[3] = 1 - 5 + 6 = 2。 (0, 2, 3)：这个三元组的值为 nums[0] - nums[2] + nums[3] = 1 - 3 + 6 = 4。 因此答案是 4。
提示:
3 <= nums.length <= 1051 <= nums[i] <= 109- 输入数据保证至少一个三元组满足给定条件。
我们不妨考虑枚举
因此，我们可以预处理出数组
时间复杂度
from sortedcontainers import SortedList
class Solution:
def maximumTripletValue(self, nums: List[int]) -> int:
n = len(nums)
right = [nums[-1]] * n
for i in range(n - 2, -1, -1):
right[i] = max(nums[i], right[i + 1])
sl = SortedList([nums[0]])
ans = 0
for j in range(1, n - 1):
if right[j + 1] > nums[j]:
i = sl.bisect_left(nums[j]) - 1
if i >= 0:
ans = max(ans, sl[i] - nums[j] + right[j + 1])
sl.add(nums[j])
return ansclass Solution {
public int maximumTripletValue(int[] nums) {
int n = nums.length;
int[] right = new int[n];
right[n - 1] = nums[n - 1];
for (int i = n - 2; i >= 0; --i) {
right[i] = Math.max(nums[i], right[i + 1]);
}
TreeSet<Integer> ts = new TreeSet<>();
ts.add(nums[0]);
int ans = 0;
for (int j = 1; j < n - 1; ++j) {
if (right[j + 1] > nums[j]) {
Integer it = ts.lower(nums[j]);
if (it != null) {
ans = Math.max(ans, it - nums[j] + right[j + 1]);
}
}
ts.add(nums[j]);
}
return ans;
}
}class Solution {
public:
int maximumTripletValue(vector<int>& nums) {
int n = nums.size();
vector<int> right(n, nums.back());
for (int i = n - 2; ~i; --i) {
right[i] = max(nums[i], right[i + 1]);
}
set<int> ts;
ts.insert(nums[0]);
int ans = 0;
for (int j = 1; j < n - 1; ++j) {
if (right[j + 1] > nums[j]) {
auto it = ts.lower_bound(nums[j]);
if (it != ts.begin()) {
--it;
ans = max(ans, *it - nums[j] + right[j + 1]);
}
}
ts.insert(nums[j]);
}
return ans;
}
};func maximumTripletValue(nums []int) (ans int) {
n := len(nums)
right := make([]int, n)
right[n-1] = nums[n-1]
for i := n - 2; i >= 0; i-- {
right[i] = max(nums[i], right[i+1])
}
ts := treemap.NewWithIntComparator()
ts.Put(nums[0], nil)
for j := 1; j < n-1; j++ {
if right[j+1] > nums[j] {
val, _ := ts.Floor(nums[j] - 1)
if val != nil {
ans = max(ans, val.(int)-nums[j]+right[j+1])
}
}
ts.Put(nums[j], nil)
}
return
}function maximumTripletValue(nums: number[]): number {
const n = nums.length;
const right: number[] = Array(n).fill(nums[n - 1]);
for (let i = n - 2; ~i; --i) {
right[i] = Math.max(nums[i], right[i + 1]);
}
const ts = new TreeSet<number>();
ts.add(nums[0]);
let ans = 0;
for (let j = 1; j < n - 1; ++j) {
if (right[j + 1] > nums[j]) {
const val = ts.lower(nums[j]);
if (val !== undefined) {
ans = Math.max(ans, val - nums[j] + right[j + 1]);
}
}
ts.add(nums[j]);
}
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;
}
}