diff --git a/solution/3000-3099/3073.Maximum Increasing Triplet Value/README.md b/solution/3000-3099/3073.Maximum Increasing Triplet Value/README.md index ed0e1989bed17..d7a29461e28d1 100644 --- a/solution/3000-3099/3073.Maximum Increasing Triplet Value/README.md +++ b/solution/3000-3099/3073.Maximum Increasing Triplet Value/README.md @@ -49,24 +49,624 @@ ## 解法 -### 方法一 +### 方法一:后缀最大值 + 有序集合 + +我们不妨考虑枚举 $nums[j]$,那么我们需要在 $j$ 的左侧找到一个最大的 $nums[i]$,使得 $nums[i] < nums[j]$,并且在 $j$ 的右侧找到一个最大的 $nums[k]$,使得 $nums[k] > nums[j]$。 + +因此,我们可以预处理出数组 $right$,其中 $right[i]$ 表示 $nums[i]$ 右侧的最大值。然后我们可以使用有序集合来维护 $nums[j]$ 左侧的值,这样我们就可以在 $O(\log n)$ 的时间内找到最大的小于 $nums[j]$ 的 $nums[i]$。 + +时间复杂度 $O(n \times \log n)$,空间复杂度 $O(n)$。其中 $n$ 为数组 $nums$ 的长度。 ```python +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 ans ``` ```java - +class 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 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; + } +} ``` ```cpp - +class Solution { +public: + int maximumTripletValue(vector& nums) { + int n = nums.size(); + vector right(n, nums.back()); + for (int i = n - 2; ~i; --i) { + right[i] = max(nums[i], right[i + 1]); + } + set 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; + } +}; ``` ```go +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 +} +``` + +```ts +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(); + 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 = (lhs: T, rhs: T) => number; + +class RBTreeNode { + data: T; + count: number; + left: RBTreeNode | null; + right: RBTreeNode | null; + parent: RBTreeNode | null; + color: number; + constructor(data: T) { + this.data = data; + this.left = this.right = this.parent = null; + this.color = 0; + this.count = 1; + } + + sibling(): RBTreeNode | 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 { + root: RBTreeNode | null; + lt: (l: T, r: T) => boolean; + constructor(compare: Compare = (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): 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): 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, p2: RBTreeNode): void { + const tmp = p1.color; + p1.color = p2.color; + p2.color = tmp; + } + + swapData(p1: RBTreeNode, p2: RBTreeNode): void { + const tmp = p1.data; + p1.data = p2.data; + p2.data = tmp; + } + + fixAfterInsert(pt: RBTreeNode): 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): 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): RBTreeNode | 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): RBTreeNode { + let temp = x; + while (temp.left) temp = temp.left; + return temp; + } + } + + fixDoubleBlack(x: RBTreeNode): 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 | 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 = this.root!): Generator { + 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 = this.root!): Generator { + 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 { + _size: number; + tree: RBTree; + compare: Compare; + constructor( + collection: T[] | Compare = [], + compare: Compare = (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 { + for (const val of this.values()) yield val; + } + + *keys(): Generator { + for (const val of this.values()) yield val; + } + + *values(): Generator { + for (const val of this.tree.inOrder()) yield val; + return undefined; + } + /** + * Return a generator for reverse order traversing the set + */ + *rvalues(): Generator { + for (const val of this.tree.reverseInOrder()) yield val; + return undefined; + } +} ``` diff --git a/solution/3000-3099/3073.Maximum Increasing Triplet Value/README_EN.md b/solution/3000-3099/3073.Maximum Increasing Triplet Value/README_EN.md index e9baf64d3b3d6..9c0ca9ec1e554 100644 --- a/solution/3000-3099/3073.Maximum Increasing Triplet Value/README_EN.md +++ b/solution/3000-3099/3073.Maximum Increasing Triplet Value/README_EN.md @@ -52,24 +52,624 @@ ## Solutions -### Solution 1 +### Solution 1: Suffix Maximum + Ordered Set + +We can consider enumerating $nums[j]$. Then, we need to find the largest $nums[i]$ on the left of $j$ such that $nums[i] < nums[j]$, and find the largest $nums[k]$ on the right of $j$ such that $nums[k] > nums[j]$. + +Therefore, we can preprocess an array $right$, where $right[i]$ represents the maximum value to the right of $nums[i]$. Then, we can use an ordered set to maintain the values on the left of $nums[j]$, so that we can find the largest $nums[i]$ less than $nums[j]$ in $O(\log n)$ time. + +The time complexity is $O(n \times \log n)$, and the space complexity is $O(n)$, where $n$ is the length of the array $nums$. ```python - +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 ans ``` ```java - +class 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 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; + } +} ``` ```cpp - +class Solution { +public: + int maximumTripletValue(vector& nums) { + int n = nums.size(); + vector right(n, nums.back()); + for (int i = n - 2; ~i; --i) { + right[i] = max(nums[i], right[i + 1]); + } + set 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; + } +}; ``` ```go +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 +} +``` +```ts +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(); + 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 = (lhs: T, rhs: T) => number; + +class RBTreeNode { + data: T; + count: number; + left: RBTreeNode | null; + right: RBTreeNode | null; + parent: RBTreeNode | null; + color: number; + constructor(data: T) { + this.data = data; + this.left = this.right = this.parent = null; + this.color = 0; + this.count = 1; + } + + sibling(): RBTreeNode | 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 { + root: RBTreeNode | null; + lt: (l: T, r: T) => boolean; + constructor(compare: Compare = (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): 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): 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, p2: RBTreeNode): void { + const tmp = p1.color; + p1.color = p2.color; + p2.color = tmp; + } + + swapData(p1: RBTreeNode, p2: RBTreeNode): void { + const tmp = p1.data; + p1.data = p2.data; + p2.data = tmp; + } + + fixAfterInsert(pt: RBTreeNode): 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): 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): RBTreeNode | 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): RBTreeNode { + let temp = x; + while (temp.left) temp = temp.left; + return temp; + } + } + + fixDoubleBlack(x: RBTreeNode): 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 | 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 = this.root!): Generator { + 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 = this.root!): Generator { + 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 { + _size: number; + tree: RBTree; + compare: Compare; + constructor( + collection: T[] | Compare = [], + compare: Compare = (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 { + for (const val of this.values()) yield val; + } + + *keys(): Generator { + for (const val of this.values()) yield val; + } + + *values(): Generator { + for (const val of this.tree.inOrder()) yield val; + return undefined; + } + + /** + * Return a generator for reverse order traversing the set + */ + *rvalues(): Generator { + for (const val of this.tree.reverseInOrder()) yield val; + return undefined; + } +} ``` diff --git a/solution/3000-3099/3073.Maximum Increasing Triplet Value/Solution.cpp b/solution/3000-3099/3073.Maximum Increasing Triplet Value/Solution.cpp new file mode 100644 index 0000000000000..0f2da931dbf80 --- /dev/null +++ b/solution/3000-3099/3073.Maximum Increasing Triplet Value/Solution.cpp @@ -0,0 +1,24 @@ +class Solution { +public: + int maximumTripletValue(vector& nums) { + int n = nums.size(); + vector right(n, nums.back()); + for (int i = n - 2; ~i; --i) { + right[i] = max(nums[i], right[i + 1]); + } + set 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; + } +}; \ No newline at end of file diff --git a/solution/3000-3099/3073.Maximum Increasing Triplet Value/Solution.go b/solution/3000-3099/3073.Maximum Increasing Triplet Value/Solution.go new file mode 100644 index 0000000000000..47b627993bab4 --- /dev/null +++ b/solution/3000-3099/3073.Maximum Increasing Triplet Value/Solution.go @@ -0,0 +1,20 @@ +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 +} \ No newline at end of file diff --git a/solution/3000-3099/3073.Maximum Increasing Triplet Value/Solution.java b/solution/3000-3099/3073.Maximum Increasing Triplet Value/Solution.java new file mode 100644 index 0000000000000..fc85c250c4b95 --- /dev/null +++ b/solution/3000-3099/3073.Maximum Increasing Triplet Value/Solution.java @@ -0,0 +1,23 @@ +class 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 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; + } +} \ No newline at end of file diff --git a/solution/3000-3099/3073.Maximum Increasing Triplet Value/Solution.py b/solution/3000-3099/3073.Maximum Increasing Triplet Value/Solution.py new file mode 100644 index 0000000000000..3433d42888733 --- /dev/null +++ b/solution/3000-3099/3073.Maximum Increasing Triplet Value/Solution.py @@ -0,0 +1,18 @@ +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 ans diff --git a/solution/3000-3099/3073.Maximum Increasing Triplet Value/Solution.ts b/solution/3000-3099/3073.Maximum Increasing Triplet Value/Solution.ts new file mode 100644 index 0000000000000..2e20fa217164c --- /dev/null +++ b/solution/3000-3099/3073.Maximum Increasing Triplet Value/Solution.ts @@ -0,0 +1,510 @@ +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(); + 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 = (lhs: T, rhs: T) => number; + +class RBTreeNode { + data: T; + count: number; + left: RBTreeNode | null; + right: RBTreeNode | null; + parent: RBTreeNode | null; + color: number; + constructor(data: T) { + this.data = data; + this.left = this.right = this.parent = null; + this.color = 0; + this.count = 1; + } + + sibling(): RBTreeNode | 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 { + root: RBTreeNode | null; + lt: (l: T, r: T) => boolean; + constructor(compare: Compare = (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): 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): 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, p2: RBTreeNode): void { + const tmp = p1.color; + p1.color = p2.color; + p2.color = tmp; + } + + swapData(p1: RBTreeNode, p2: RBTreeNode): void { + const tmp = p1.data; + p1.data = p2.data; + p2.data = tmp; + } + + fixAfterInsert(pt: RBTreeNode): 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): 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): RBTreeNode | 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): RBTreeNode { + let temp = x; + while (temp.left) temp = temp.left; + return temp; + } + } + + fixDoubleBlack(x: RBTreeNode): 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 | 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 = this.root!): Generator { + 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 = this.root!): Generator { + 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 { + _size: number; + tree: RBTree; + compare: Compare; + constructor( + collection: T[] | Compare = [], + compare: Compare = (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 { + for (const val of this.values()) yield val; + } + + *keys(): Generator { + for (const val of this.values()) yield val; + } + + *values(): Generator { + for (const val of this.tree.inOrder()) yield val; + return undefined; + } + + /** + * Return a generator for reverse order traversing the set + */ + *rvalues(): Generator { + for (const val of this.tree.reverseInOrder()) yield val; + return undefined; + } +}