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1488. Avoid Flood in The City
Description
Your country has an infinite number of lakes. Initially, all the lakes are empty, but when it rains over the nth lake, the nth lake becomes full of water. If it rains over a lake that is full of water, there will be a flood. Your goal is to avoid floods in any lake.
Given an integer array rains where:
rains[i] > 0means there will be rains over therains[i]lake.rains[i] == 0means there are no rains this day and you can choose one lake this day and dry it.
Return an array ans where:
ans.length == rains.lengthans[i] == -1ifrains[i] > 0.ans[i]is the lake you choose to dry in theithday ifrains[i] == 0.
If there are multiple valid answers return any of them. If it is impossible to avoid flood return an empty array.
Notice that if you chose to dry a full lake, it becomes empty, but if you chose to dry an empty lake, nothing changes.
Example 1:
Input: rains = [1,2,3,4] Output: [-1,-1,-1,-1] Explanation: After the first day full lakes are [1] After the second day full lakes are [1,2] After the third day full lakes are [1,2,3] After the fourth day full lakes are [1,2,3,4] There's no day to dry any lake and there is no flood in any lake.
Example 2:
Input: rains = [1,2,0,0,2,1] Output: [-1,-1,2,1,-1,-1] Explanation: After the first day full lakes are [1] After the second day full lakes are [1,2] After the third day, we dry lake 2. Full lakes are [1] After the fourth day, we dry lake 1. There is no full lakes. After the fifth day, full lakes are [2]. After the sixth day, full lakes are [1,2]. It is easy that this scenario is flood-free. [-1,-1,1,2,-1,-1] is another acceptable scenario.
Example 3:
Input: rains = [1,2,0,1,2] Output: [] Explanation: After the second day, full lakes are [1,2]. We have to dry one lake in the third day. After that, it will rain over lakes [1,2]. It's easy to prove that no matter which lake you choose to dry in the 3rd day, the other one will flood.
Constraints:
1 <= rains.length <= 1050 <= rains[i] <= 109
Solutions
Solution 1: Greedy + Binary Search
We store all sunny days in the $sunny$ array or a sorted set, and use the hash table $rainy$ to record the last rainy day for each lake. We initialize the answer array $ans$ with each element set to $-1$.
Next, we traverse the $rains$ array. For each rainy day $i$, if $rainy[rains[i]]$ exists, it means that the lake has rained before, so we need to find the first date in the $sunny$ array that is greater than $rainy[rains[i]]$, and replace it with the rainy day. Otherwise, it means that the flood cannot be prevented, and we return an empty array. For each non-rainy day $i$, we store $i$ in the $sunny$ array and set $ans[i]$ to $1$.
After the traversal, we return the answer array.
The time complexity is $O(n \times \log n)$, and the space complexity is $O(n)$. Here, $n$ is the length of the $rains$ array.
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class Solution { public int[] avoidFlood(int[] rains) { int n = rains.length; int[] ans = new int[n]; Arrays.fill(ans, -1); TreeSet<Integer> sunny = new TreeSet<>(); Map<Integer, Integer> rainy = new HashMap<>(); for (int i = 0; i < n; ++i) { int v = rains[i]; if (v > 0) { if (rainy.containsKey(v)) { Integer t = sunny.higher(rainy.get(v)); if (t == null) { return new int[0]; } ans[t] = v; sunny.remove(t); } rainy.put(v, i); } else { sunny.add(i); ans[i] = 1; } } return ans; } } -
class Solution { public: vector<int> avoidFlood(vector<int>& rains) { int n = rains.size(); vector<int> ans(n, -1); set<int> sunny; unordered_map<int, int> rainy; for (int i = 0; i < n; ++i) { int v = rains[i]; if (v) { if (rainy.count(v)) { auto it = sunny.upper_bound(rainy[v]); if (it == sunny.end()) { return {}; } ans[*it] = v; sunny.erase(it); } rainy[v] = i; } else { sunny.insert(i); ans[i] = 1; } } return ans; } }; -
from sortedcontainers import SortedList class Solution: def avoidFlood(self, rains: List[int]) -> List[int]: n = len(rains) ans = [-1] * n sunny = SortedList() rainy = {} for i, v in enumerate(rains): if v: if v in rainy: idx = sunny.bisect_right(rainy[v]) if idx == len(sunny): return [] ans[sunny[idx]] = v sunny.discard(sunny[idx]) rainy[v] = i else: sunny.add(i) ans[i] = 1 return ans -
func avoidFlood(rains []int) []int { n := len(rains) ans := make([]int, n) for i := range ans { ans[i] = -1 } sunny := []int{} rainy := map[int]int{} for i, v := range rains { if v > 0 { if j, ok := rainy[v]; ok { idx := sort.SearchInts(sunny, j+1) if idx == len(sunny) { return []int{} } ans[sunny[idx]] = v sunny = append(sunny[:idx], sunny[idx+1:]...) } rainy[v] = i } else { sunny = append(sunny, i) ans[i] = 1 } } return ans } -
function avoidFlood(rains: number[]): number[] { const n = rains.length; const ans: number[] = new Array(n).fill(-1); const sunny: TreeSet<number> = new TreeSet<number>(); const rainy: Map<number, number> = new Map<number, number>(); for (let i = 0; i < n; ++i) { const v = rains[i]; if (v > 0) { if (rainy.has(v)) { const t = sunny.higher(rainy.get(v)!); if (t === undefined) { return []; } ans[t] = v; sunny.delete(t); } rainy.set(v, i); } else { sunny.add(i); ans[i] = 1; } } 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; } }