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1438. Longest Continuous Subarray With Absolute Diff Less Than or Equal to Limit
Description
Given an array of integers nums and an integer limit, return the size of the longest non-empty subarray such that the absolute difference between any two elements of this subarray is less than or equal to limit.
Example 1:
Input: nums = [8,2,4,7], limit = 4 Output: 2 Explanation: All subarrays are: [8] with maximum absolute diff |8-8| = 0 <= 4. [8,2] with maximum absolute diff |8-2| = 6 > 4. [8,2,4] with maximum absolute diff |8-2| = 6 > 4. [8,2,4,7] with maximum absolute diff |8-2| = 6 > 4. [2] with maximum absolute diff |2-2| = 0 <= 4. [2,4] with maximum absolute diff |2-4| = 2 <= 4. [2,4,7] with maximum absolute diff |2-7| = 5 > 4. [4] with maximum absolute diff |4-4| = 0 <= 4. [4,7] with maximum absolute diff |4-7| = 3 <= 4. [7] with maximum absolute diff |7-7| = 0 <= 4. Therefore, the size of the longest subarray is 2.
Example 2:
Input: nums = [10,1,2,4,7,2], limit = 5 Output: 4 Explanation: The subarray [2,4,7,2] is the longest since the maximum absolute diff is |2-7| = 5 <= 5.
Example 3:
Input: nums = [4,2,2,2,4,4,2,2], limit = 0 Output: 3
Constraints:
1 <= nums.length <= 1051 <= nums[i] <= 1090 <= limit <= 109
Solutions
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class Solution { public int longestSubarray(int[] nums, int limit) { TreeMap<Integer, Integer> tm = new TreeMap<>(); int ans = 0, j = 0; for (int i = 0; i < nums.length; ++i) { tm.put(nums[i], tm.getOrDefault(nums[i], 0) + 1); while (tm.lastKey() - tm.firstKey() > limit) { tm.put(nums[j], tm.get(nums[j]) - 1); if (tm.get(nums[j]) == 0) { tm.remove(nums[j]); } ++j; } ans = Math.max(ans, i - j + 1); } return ans; } } -
class Solution { public: int longestSubarray(vector<int>& nums, int limit) { multiset<int> s; int ans = 0, j = 0; for (int i = 0; i < nums.size(); ++i) { s.insert(nums[i]); while (*s.rbegin() - *s.begin() > limit) { s.erase(s.find(nums[j++])); } ans = max(ans, i - j + 1); } return ans; } }; -
from sortedcontainers import SortedList class Solution: def longestSubarray(self, nums: List[int], limit: int) -> int: sl = SortedList() ans = j = 0 for i, v in enumerate(nums): sl.add(v) while sl[-1] - sl[0] > limit: sl.remove(nums[j]) j += 1 ans = max(ans, i - j + 1) return ans -
func longestSubarray(nums []int, limit int) (ans int) { tm := treemap.NewWithIntComparator() j := 0 for i, v := range nums { if x, ok := tm.Get(v); ok { tm.Put(v, x.(int)+1) } else { tm.Put(v, 1) } for { a, _ := tm.Min() b, _ := tm.Max() if b.(int)-a.(int) > limit { if x, _ := tm.Get(nums[j]); x.(int) == 1 { tm.Remove(nums[j]) } else { tm.Put(nums[j], x.(int)-1) } j++ } else { break } } ans = max(ans, i-j+1) } return } -
function longestSubarray(nums: number[], limit: number): number { const ts = new TreapMultiSet<number>(); let ans = 0; let j = 0; for (let i = 0; i < nums.length; ++i) { ts.add(nums[i]); while (ts.last() - ts.first() > limit) { ts.delete(nums[j++]); } ans = Math.max(ans, i - j + 1); } return ans; } type CompareFunction<T, R extends 'number' | 'boolean'> = ( a: T, b: T, ) => R extends 'number' ? number : boolean; interface ITreapMultiSet<T> extends Iterable<T> { add: (...value: T[]) => this; has: (value: T) => boolean; delete: (value: T) => void; bisectLeft: (value: T) => number; bisectRight: (value: T) => number; indexOf: (value: T) => number; lastIndexOf: (value: T) => number; at: (index: number) => T | undefined; first: () => T | undefined; last: () => T | undefined; lower: (value: T) => T | undefined; higher: (value: T) => T | undefined; floor: (value: T) => T | undefined; ceil: (value: T) => T | undefined; shift: () => T | undefined; pop: (index?: number) => T | undefined; count: (value: T) => number; keys: () => IterableIterator<T>; values: () => IterableIterator<T>; rvalues: () => IterableIterator<T>; entries: () => IterableIterator<[number, T]>; readonly size: number; } class TreapNode<T = number> { value: T; count: number; size: number; priority: number; left: TreapNode<T> | null; right: TreapNode<T> | null; constructor(value: T) { this.value = value; this.count = 1; this.size = 1; this.priority = Math.random(); this.left = null; this.right = null; } static getSize(node: TreapNode<any> | null): number { return node?.size ?? 0; } static getFac(node: TreapNode<any> | null): number { return node?.priority ?? 0; } pushUp(): void { let tmp = this.count; tmp += TreapNode.getSize(this.left); tmp += TreapNode.getSize(this.right); this.size = tmp; } rotateRight(): TreapNode<T> { // eslint-disable-next-line @typescript-eslint/no-this-alias let node: TreapNode<T> = this; const left = node.left; node.left = left?.right ?? null; left && (left.right = node); left && (node = left); node.right?.pushUp(); node.pushUp(); return node; } rotateLeft(): TreapNode<T> { // eslint-disable-next-line @typescript-eslint/no-this-alias let node: TreapNode<T> = this; const right = node.right; node.right = right?.left ?? null; right && (right.left = node); right && (node = right); node.left?.pushUp(); node.pushUp(); return node; } } class TreapMultiSet<T = number> implements ITreapMultiSet<T> { private readonly root: TreapNode<T>; private readonly compareFn: CompareFunction<T, 'number'>; private readonly leftBound: T; private readonly rightBound: T; constructor(compareFn?: CompareFunction<T, 'number'>); constructor(compareFn: CompareFunction<T, 'number'>, leftBound: T, rightBound: T); constructor( compareFn: CompareFunction<T, any> = (a: any, b: any) => a - b, leftBound: any = -Infinity, rightBound: any = Infinity, ) { this.root = new TreapNode<T>(rightBound); this.root.priority = Infinity; this.root.left = new TreapNode<T>(leftBound); this.root.left.priority = -Infinity; this.root.pushUp(); this.leftBound = leftBound; this.rightBound = rightBound; this.compareFn = compareFn; } get size(): number { return this.root.size - 2; } get height(): number { const getHeight = (node: TreapNode<T> | null): number => { if (node == null) return 0; return 1 + Math.max(getHeight(node.left), getHeight(node.right)); }; return getHeight(this.root); } /** * * @complexity `O(logn)` * @description Returns true if value is a member. */ has(value: T): boolean { const compare = this.compareFn; const dfs = (node: TreapNode<T> | null, value: T): boolean => { if (node == null) return false; if (compare(node.value, value) === 0) return true; if (compare(node.value, value) < 0) return dfs(node.right, value); return dfs(node.left, value); }; return dfs(this.root, value); } /** * * @complexity `O(logn)` * @description Add value to sorted set. */ add(...values: T[]): this { const compare = this.compareFn; const dfs = ( node: TreapNode<T> | null, value: T, parent: TreapNode<T>, direction: 'left' | 'right', ): void => { if (node == null) return; if (compare(node.value, value) === 0) { node.count++; node.pushUp(); } else if (compare(node.value, value) > 0) { if (node.left) { dfs(node.left, value, node, 'left'); } else { node.left = new TreapNode(value); node.pushUp(); } if (TreapNode.getFac(node.left) > node.priority) { parent[direction] = node.rotateRight(); } } else if (compare(node.value, value) < 0) { if (node.right) { dfs(node.right, value, node, 'right'); } else { node.right = new TreapNode(value); node.pushUp(); } if (TreapNode.getFac(node.right) > node.priority) { parent[direction] = node.rotateLeft(); } } parent.pushUp(); }; values.forEach(value => dfs(this.root.left, value, this.root, 'left')); return this; } /** * * @complexity `O(logn)` * @description Remove value from sorted set if it is a member. * If value is not a member, do nothing. */ delete(value: T): void { const compare = this.compareFn; const dfs = ( node: TreapNode<T> | null, value: T, parent: TreapNode<T>, direction: 'left' | 'right', ): void => { if (node == null) return; if (compare(node.value, value) === 0) { if (node.count > 1) { node.count--; node?.pushUp(); } else if (node.left == null && node.right == null) { parent[direction] = null; } else { // 旋到根节点 if ( node.right == null || TreapNode.getFac(node.left) > TreapNode.getFac(node.right) ) { parent[direction] = node.rotateRight(); dfs(parent[direction]?.right ?? null, value, parent[direction]!, 'right'); } else { parent[direction] = node.rotateLeft(); dfs(parent[direction]?.left ?? null, value, parent[direction]!, 'left'); } } } else if (compare(node.value, value) > 0) { dfs(node.left, value, node, 'left'); } else if (compare(node.value, value) < 0) { dfs(node.right, value, node, 'right'); } parent?.pushUp(); }; dfs(this.root.left, value, this.root, 'left'); } /** * * @complexity `O(logn)` * @description Returns an index to insert value in the sorted set. * If the value is already present, the insertion point will be before (to the left of) any existing values. */ bisectLeft(value: T): number { const compare = this.compareFn; const dfs = (node: TreapNode<T> | null, value: T): number => { if (node == null) return 0; if (compare(node.value, value) === 0) { return TreapNode.getSize(node.left); } else if (compare(node.value, value) > 0) { return dfs(node.left, value); } else if (compare(node.value, value) < 0) { return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count; } return 0; }; return dfs(this.root, value) - 1; } /** * * @complexity `O(logn)` * @description Returns an index to insert value in the sorted set. * If the value is already present, the insertion point will be before (to the right of) any existing values. */ bisectRight(value: T): number { const compare = this.compareFn; const dfs = (node: TreapNode<T> | null, value: T): number => { if (node == null) return 0; if (compare(node.value, value) === 0) { return TreapNode.getSize(node.left) + node.count; } else if (compare(node.value, value) > 0) { return dfs(node.left, value); } else if (compare(node.value, value) < 0) { return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count; } return 0; }; return dfs(this.root, value) - 1; } /** * * @complexity `O(logn)` * @description Returns the index of the first occurrence of a value in the set, or -1 if it is not present. */ indexOf(value: T): number { const compare = this.compareFn; let isExist = false; const dfs = (node: TreapNode<T> | null, value: T): number => { if (node == null) return 0; if (compare(node.value, value) === 0) { isExist = true; return TreapNode.getSize(node.left); } else if (compare(node.value, value) > 0) { return dfs(node.left, value); } else if (compare(node.value, value) < 0) { return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count; } return 0; }; const res = dfs(this.root, value) - 1; return isExist ? res : -1; } /** * * @complexity `O(logn)` * @description Returns the index of the last occurrence of a value in the set, or -1 if it is not present. */ lastIndexOf(value: T): number { const compare = this.compareFn; let isExist = false; const dfs = (node: TreapNode<T> | null, value: T): number => { if (node == null) return 0; if (compare(node.value, value) === 0) { isExist = true; return TreapNode.getSize(node.left) + node.count - 1; } else if (compare(node.value, value) > 0) { return dfs(node.left, value); } else if (compare(node.value, value) < 0) { return dfs(node.right, value) + TreapNode.getSize(node.left) + node.count; } return 0; }; const res = dfs(this.root, value) - 1; return isExist ? res : -1; } /** * * @complexity `O(logn)` * @description Returns the item located at the specified index. * @param index The zero-based index of the desired code unit. A negative index will count back from the last item. */ at(index: number): T | undefined { if (index < 0) index += this.size; if (index < 0 || index >= this.size) return undefined; const dfs = (node: TreapNode<T> | null, rank: number): T | undefined => { if (node == null) return undefined; if (TreapNode.getSize(node.left) >= rank) { return dfs(node.left, rank); } else if (TreapNode.getSize(node.left) + node.count >= rank) { return node.value; } else { return dfs(node.right, rank - TreapNode.getSize(node.left) - node.count); } }; const res = dfs(this.root, index + 2); return ([this.leftBound, this.rightBound] as any[]).includes(res) ? undefined : res; } /** * * @complexity `O(logn)` * @description Find and return the element less than `val`, return `undefined` if no such element found. */ lower(value: T): T | undefined { const compare = this.compareFn; const dfs = (node: TreapNode<T> | null, value: T): T | undefined => { if (node == null) return undefined; if (compare(node.value, value) >= 0) return dfs(node.left, value); const tmp = dfs(node.right, value); if (tmp == null || compare(node.value, tmp) > 0) { return node.value; } else { return tmp; } }; const res = dfs(this.root, value) as any; return res === this.leftBound ? undefined : res; } /** * * @complexity `O(logn)` * @description Find and return the element greater than `val`, return `undefined` if no such element found. */ higher(value: T): T | undefined { const compare = this.compareFn; const dfs = (node: TreapNode<T> | null, value: T): T | undefined => { if (node == null) return undefined; if (compare(node.value, value) <= 0) return dfs(node.right, value); const tmp = dfs(node.left, value); if (tmp == null || compare(node.value, tmp) < 0) { return node.value; } else { return tmp; } }; const res = dfs(this.root, value) as any; return res === this.rightBound ? undefined : res; } /** * * @complexity `O(logn)` * @description Find and return the element less than or equal to `val`, return `undefined` if no such element found. */ floor(value: T): T | undefined { const compare = this.compareFn; const dfs = (node: TreapNode<T> | null, value: T): T | undefined => { if (node == null) return undefined; if (compare(node.value, value) === 0) return node.value; if (compare(node.value, value) >= 0) return dfs(node.left, value); const tmp = dfs(node.right, value); if (tmp == null || compare(node.value, tmp) > 0) { return node.value; } else { return tmp; } }; const res = dfs(this.root, value) as any; return res === this.leftBound ? undefined : res; } /** * * @complexity `O(logn)` * @description Find and return the element greater than or equal to `val`, return `undefined` if no such element found. */ ceil(value: T): T | undefined { const compare = this.compareFn; const dfs = (node: TreapNode<T> | null, value: T): T | undefined => { if (node == null) return undefined; if (compare(node.value, value) === 0) return node.value; if (compare(node.value, value) <= 0) return dfs(node.right, value); const tmp = dfs(node.left, value); if (tmp == null || compare(node.value, tmp) < 0) { return node.value; } else { return tmp; } }; const res = dfs(this.root, value) as any; return res === this.rightBound ? undefined : res; } /** * @complexity `O(logn)` * @description * Returns the last element from set. * If the set is empty, undefined is returned. */ first(): T | undefined { const iter = this.inOrder(); iter.next(); const res = iter.next().value; return res === this.rightBound ? undefined : res; } /** * @complexity `O(logn)` * @description * Returns the last element from set. * If the set is empty, undefined is returned . */ last(): T | undefined { const iter = this.reverseInOrder(); iter.next(); const res = iter.next().value; return res === this.leftBound ? undefined : res; } /** * @complexity `O(logn)` * @description * Removes the first element from an set and returns it. * If the set is empty, undefined is returned and the set is not modified. */ shift(): T | undefined { const first = this.first(); if (first === undefined) return undefined; this.delete(first); return first; } /** * @complexity `O(logn)` * @description * Removes the last element from an set and returns it. * If the set is empty, undefined is returned and the set is not modified. */ pop(index?: number): T | undefined { if (index == null) { const last = this.last(); if (last === undefined) return undefined; this.delete(last); return last; } const toDelete = this.at(index); if (toDelete == null) return; this.delete(toDelete); return toDelete; } /** * * @complexity `O(logn)` * @description * Returns number of occurrences of value in the sorted set. */ count(value: T): number { const compare = this.compareFn; const dfs = (node: TreapNode<T> | null, value: T): number => { if (node == null) return 0; if (compare(node.value, value) === 0) return node.count; if (compare(node.value, value) < 0) return dfs(node.right, value); return dfs(node.left, value); }; return dfs(this.root, value); } *[Symbol.iterator](): Generator<T, any, any> { yield* this.values(); } /** * @description * Returns an iterable of keys in the set. */ *keys(): Generator<T, any, any> { yield* this.values(); } /** * @description * Returns an iterable of values in the set. */ *values(): Generator<T, any, any> { const iter = this.inOrder(); iter.next(); const steps = this.size; for (let _ = 0; _ < steps; _++) { yield iter.next().value; } } /** * @description * Returns a generator for reversed order traversing the set. */ *rvalues(): Generator<T, any, any> { const iter = this.reverseInOrder(); iter.next(); const steps = this.size; for (let _ = 0; _ < steps; _++) { yield iter.next().value; } } /** * @description * Returns an iterable of key, value pairs for every entry in the set. */ *entries(): IterableIterator<[number, T]> { const iter = this.inOrder(); iter.next(); const steps = this.size; for (let i = 0; i < steps; i++) { yield [i, iter.next().value]; } } private *inOrder(root: TreapNode<T> | null = this.root): Generator<T, any, any> { if (root == null) return; yield* this.inOrder(root.left); const count = root.count; for (let _ = 0; _ < count; _++) { yield root.value; } yield* this.inOrder(root.right); } private *reverseInOrder(root: TreapNode<T> | null = this.root): Generator<T, any, any> { if (root == null) return; yield* this.reverseInOrder(root.right); const count = root.count; for (let _ = 0; _ < count; _++) { yield root.value; } yield* this.reverseInOrder(root.left); } }