题目
给定一个非空的整数数组，返回其中出现频率前 k 高的元素。
示例 1:
输入: nums = [1,1,1,2,2,3], k = 2
输出: [1,2]
示例 2:
输入: nums = [1], k = 1
输出: [1]
提示：
你可以假设给定的 k 总是合理的，且 1 ≤ k ≤ 数组中不相同的元素的个数。
你的算法的时间复杂度必须优于 O(n log n) , n 是数组的大小。
题目数据保证答案唯一，换句话说，数组中前 k 个高频元素的集合是唯一的。
你可以按任意顺序返回答案。
方法一 优先队列
Swift代码
final class FixedSizePriorityQueue<Element> {
let capacity: Int
fileprivate(set) var count: Int
var isEmpty: Bool { count == 0 }
private var pq, qp: [Int]
var elements: [Element?]
let comparator: ((Element, Element)-> Bool)
public init(_ capacity: Int, comparator: @escaping ((Element, Element)-> Bool)) {
self.capacity = capacity
count = 0
pq = Array(repeating: 0, count: capacity + 1)
qp = Array(repeating: -1, count: capacity + 1)
elements = Array(repeating: nil, count: capacity + 1)
self.comparator = comparator
}
public func contains(_ i: Int) -> Bool {
return qp[i] != -1
}
public func insert(_ i: Int, _ element: Element) {
count += 1
qp[i] = count
pq[count] = i
elements[i] = element
swim(count)
}
public func topIndex() -> Int {
return pq[1]
}
public func topElement() -> Element? {
return elementOf(topIndex())
}
public func deleteTop() -> Element? {
if isEmpty {
return nil
}
let element = topElement()
let min = pq[1]
exchange(1, count)
count -= 1
sink(1)
qp[min] = -1
elements[min] = nil
pq[count + 1] = -1
return element
}
public func elementOf(_ i: Int) -> Element? {
return elements[i]
}
public func changeKey(_ i: Int, _ key: Element) {
elements[i] = key
swim(qp[i])
sink(qp[i])
}
public func compare(_ i: Int, _ j: Int) -> Bool {
return comparator(elements[pq[i]]!, elements[pq[j]]!)
}
public func delete(_ i: Int) {
let index = qp[i]
exchange(index, count)
count -= 1
swim(index)
sink(index)
elements[i] = nil
qp[i] = -1
}
public func exchange(_ i: Int, _ j: Int) {
pq.swapAt(i, j)
qp[pq[i]] = i
qp[pq[j]] = j
}
private func swim(_ k: Int) {
var k = k
while k > 1 && compare(k >> 1, k) {
pq.swapAt(k >> 1, k)
k >>= 1
}
}
private func sink(_ k: Int) {
var k = k, j = k << 1
while j <= count {
if j < count && compare(j, j + 1) { j += 1 }
if !compare(k, j) { break }
pq.swapAt(k, j)
k = j
j = k << 1
}
}
}
class Solution {
func topKFrequent(_ nums: [Int], _ k: Int) -> [Int] {
var dic = [Int: Int]()
for item in nums {
if let value = dic[item] {
dic[item] = value + 1
} else {
dic[item] = 1
}
}
let queue = FixedSizePriorityQueue<(Int, Int)>(dic.count, comparator: { $0.1 < $1.1 })
for item in dic.enumerated() {
queue.insert(item.offset, item.element)
}
var result = [Int]()
while result.count < k && queue.count > 0 {
result.append(queue.deleteTop()!.0)
}
return result
}
}
方法二 红黑树
Swift代码
class RedBlackTree<Key: Comparable, Value> {
final class Node {
public var item: (Key, Value)
public var left: Node?
public var right: Node?
public var count: Int
public var color: Color
public init(
key: Key,
value: Value,
left: Node? = nil,
right: Node? = nil,
count: Int = 1,
color: Color = .red
) {
self.item = (key, value)
self.left = left
self.right = right
self.count = count
self.color = color
}
public func rotateLeft() -> Node? {
guard let x = right else {
return nil
}
right = x.left
x.left = self
x.color = x.left?.color ?? .black
x.left?.color = .red
x.count = count
count = (left?.count ?? 0) + (right?.count ?? 0) + 1
return x
}
public func rotateRight() -> Node? {
guard let x = left else {
return nil
}
left = x.right
x.right = self
x.color = x.right?.color ?? .black
x.right?.color = .red
x.count = count
count = (left?.count ?? 0) + (right?.count ?? 0) + 1
return x
}
public func flipColors() {
color.toggle()
left?.color.toggle()
right?.color.toggle()
}
private var stop = false
func reverseMiddleOrder(_ block: @escaping ((Key, Value), inout Bool) -> Void) {
stop = false
right?.reverseMiddleOrder(block)
block(item, &stop)
if !stop {
left?.reverseMiddleOrder(block)
}
}
}
var root: Node? = nil
var count: Int { size(root) }
subscript(key: Key) -> Value? {
set {
put(key, newValue)
}
get {
get(key)
}
}
private func isRed(_ node: Node?) -> Bool {
node?.color == .red
}
private func size(_ node: Node?) -> Int {
node?.count ?? 0
}
public var isEmpty: Bool {
root == nil
}
public func get(_ key: Key) -> Value? {
return get(root, key)
}
private func get(_ node: Node?, _ key: Key) -> Value? {
var node = node
while node != nil {
if key < node!.item.0 {
node = node?.left
} else if key > node!.item.0 {
node = node?.right
} else {
return node?.item.1
}
}
return nil
}
public func contains(_ key: Key) -> Bool {
get(key) != nil
}
public func put(_ key: Key, _ value: Value?) {
if value == nil {
return
}
root = put(root, key, value!)
root?.color = .black
}
private func put(_ node: Node?, _ key: Key, _ value: Value) -> Node? {
guard node != nil else {
return Node(key: key, value: value)
}
var node = node
if key < node!.item.0 {
node?.left = put(node?.left, key, value)
} else if key > node!.item.0 {
node?.right = put(node?.right, key, value)
} else {
node?.item.1 = value
}
if isRed(node?.right) && !isRed(node?.left) {
node = node?.rotateLeft()
}
if isRed(node?.left) && isRed(node?.left?.left) {
node = node?.rotateRight()
}
if isRed(node?.left) && isRed(node?.right) {
node?.flipColors()
}
node?.count = size(node?.left) + size(node?.right) + 1
return node
}
func balance(_ node: Node?) -> Node? {
var node = node
if isRed(node?.right) {
node = node?.rotateLeft()
}
if isRed(node?.left) && isRed(node?.left?.left) {
node = node?.rotateRight()
}
if isRed(node?.left) && isRed(node?.right) {
node?.flipColors()
}
node?.count = size(node?.left) + size(node?.right) + 1
return node
}
enum Color {
case red
case black
mutating func toggle() {
switch self {
case .red:
self = .black
case .black:
self = .red
}
}
}
}
class Solution {
func topKFrequent(_ nums: [Int], _ k: Int) -> [Int] {
var counter = Dictionary<Int, Int>()
for item in nums {
if let value = counter[item] {
counter[item] = value + 1
} else {
counter[item] = 1
}
}
let tree = RedBlackTree<Int, [Int]>()
for item in counter {
var items = tree[item.1]
if items == nil {
items = [item.0]
} else {
items?.append(item.0)
}
tree[item.1] = items
}
var items = [Int]()
tree.root?.reverseMiddleOrder { (item, stop) in
if items.count < k {
for element in item.1 {
items.append(element)
if items.count == k { break }
}
} else {
stop = true
}
}
return items
}
}
方法三 排序
排序并选取前k元素。该版本的快速排序比系统排序快一些。
extension Int {
mutating func increasing() -> Int {
self += 1
return self
}
mutating func decreasing() -> Int {
self -= 1
return self
}
}
extension Array {
mutating func quickSort(by comparator: @escaping (Element, Element) -> Bool ) {
quickSort(low: 0, high: count - 1, by: comparator)
}
mutating func quickSort(low: Int, high: Int, by comparator: @escaping (Element, Element) -> Bool ) {
if high <= low { return }
let j = partition(low: low, high:high, by: comparator)
quickSort(low: low, high: j - 1, by: comparator)
quickSort(low: j + 1, high: high, by: comparator)
}
mutating func partition(low: Int, high: Int, by comparator: @escaping (Element, Element) -> Bool) -> Int {
var i = low
var j = high + 1
let v = self[low]
while true {
while comparator(self[i.increasing()], v) && i != high {}
while comparator(v, self[j.decreasing()]) && i != low {}
if i >= j { break }
swapAt(i, j)
}
swapAt(low, j)
return j
}
}
class Solution {
func topKFrequent(_ nums: [Int], _ k: Int) -> [Int] {
var items = nums.reduce(into: [Int: Int]()) { (counter, item) in
counter[item] = (counter[item] ?? 0) + 1
}.map { $0 }
items.quickSort {
$0.1 > $1.1
}
return items[0..<k].map { $0.0 }
}
}
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