0347. Top K Frequent Elements (M)

Top K Frequent Elements (M)

题目

Given a non-empty array of integers, return the *k* most frequent elements.

Example 1:

Input: nums = [1,1,1,2,2,3], k = 2
Output: [1,2]

Example 2:

Input: nums = [1], k = 1
Output: [1]

Note:

• You may assume k is always valid, 1 ≤ k ≤ number of unique elements.
• Your algorithm's time complexity must be better than O(n log n), where n is the array's size.
• It's guaranteed that the answer is unique, in other words the set of the top k frequent elements is unique.
• You can return the answer in any order.

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题意

求一个数组中出现次数最多的前k个元素。要求时间复杂度小于\(O(NlogN)\)。

思路

最直接的方法是维护一个最大大小为k的小顶堆，向其中添加数组中的不重复元素，按照出现次数排序，如果添加后堆大小为k+1，则将堆顶元素去除，这样最终留下的就是k个出现次数最多的元素，复杂度为\(O(Nlogk)\)。

top k类型的问题还可以用 快速选择算法 来解决，平均复杂度为\(O(N)\)。

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代码实现

Java

优先队列

class Solution {
    public int[] topKFrequent(int[] nums, int k) {
        Map<Integer, Integer> record = new HashMap<>();
        Queue<Integer> q = new PriorityQueue<>((a, b) -> record.get(a) - record.get(b));
        for (int num : nums) {
            record.put(num, record.getOrDefault(num, 0) + 1);
        }
        for (int num : record.keySet()) {
            q.offer(num);
            if (q.size() > k) {
                q.poll();
            }
        }
        int[] res = new int[k];
        int i = 0;
        while (!q.isEmpty()) {
            res[i++] = q.poll();
        }
        return res;
    }
}

快速选择

class Solution {
    public int[] topKFrequent(int[] nums, int k) {
        Map<Integer, Integer> record = new HashMap<>();
        for (int num : nums) {
            record.put(num, record.getOrDefault(num, 0) + 1);
        }
        int[] arr = new int[record.size()];
        int i = 0;
        for (int num : record.keySet()) {
            arr[i++] = num;
        }

        int left = 0, right = arr.length - 1;
        int[] res = new int[k];
        while (left <= right) {
            int mid = partition(arr, left, right, record);
            if (k - 1 < mid) {
                right = mid - 1;
            } else if (k - 1 > mid) {
                left = mid + 1;
            } else {
                for (int j = 0; j < k; j++) {
                    res[j] = arr[j];
                }
                return res;
            }
        }
        return res;
    }

    private int partition(int[] arr, int left, int right, Map<Integer, Integer> record) {
        int tmp = arr[left];
        while (left < right) {
            while (left < right && record.get(arr[right]) < record.get(tmp)) {
                right--;
            }
            arr[left] = arr[right];
            while (left < right && record.get(arr[left]) >= record.get(tmp)) {
                left++;
            }
            arr[right] = arr[left];
        }
        arr[left] = tmp;
        return left;
    }
}