215. Kth Largest Element in an Array (M)

Kth Largest Element in an Array (M)

Find the kth largest element in an unsorted array. Note that it is the kth largest element in the sorted order, not the kth distinct element.

Example 1:

Input: [3,2,1,5,6,4] and k = 2
Output: 5

Example 2:

Input: [3,2,3,1,2,4,5,5,6] and k = 4
Output: 4

Note:
You may assume k is always valid, 1 ≤ k ≤ array’s length.

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题意

找到数组中第K大的数。

思路

最简单的方法是直接排序，再取第K大的数。

更高效的方法是分治法，利用快速排序的partition来选出第K大。

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代码实现 - 排序

class Solution {
    public int findKthLargest(int[] nums, int k) {
        Arrays.sort(nums);
        return nums[nums.length - k];
    }
}

代码实现 - 分治法(二路快排)

class Solution {
    public int findKthLargest(int[] nums, int k) {
        int left = 0, right = nums.length - 1;
        while (left < right) {
            int p = partition(nums, left, right);
            if (p < k - 1) {
                left = p + 1;
            } else if (p > k - 1) {
                right = p - 1;
            } else {
                return nums[p];
            }
        }
        return nums[k - 1];
    }

    private int partition(int[] nums, int left, int right) {
        int i = left, j = right + 1;
        // 随机选择一个元素当作参考标准(这一步很重要)
        int r = new Random().nextInt(right - left + 1) + left;
        swap(nums, left, r);
        int temp = nums[left];
        while (true) {
            while (nums[++i] > temp) {
                if (i == right) break;
            }
            while (nums[--j] < temp) {
                if (j == left) break;
            }
            if (i >= j) break;
            swap(nums, i, j);
        }
        swap(nums, left, j);
        return j;
    }

    private void swap(int[] nums, int i, int j) {
        int temp = nums[i];
        nums[i] = nums[j];
        nums[j] = temp;
    }
}

代码实现 - 分治法(三路快排)

class Solution {
    public int findKthLargest(int[] nums, int k) {
        return partition(nums, 0, nums.length - 1, k);
    }

    private int partition(int[] nums, int left, int right, int k) {
        int i = left, p = left, q = right;
        int temp = nums[new Random().nextInt(right - left + 1) + left];		// 随机化很重要
        // 将指定范围数组分为三个区域
        while (i <= q) {
            if (nums[i] > temp) {
                swap(nums, i++, p++);
            } else if (nums[i] < temp) {
                swap(nums, i, q--);
            } else {
                i++;
            }
        }
        // 判断第K大在哪个区域，并对应处理
        if (k < p - left + 1) {
            return partition(nums, left, p - 1, k);
        } else if (k > q - left + 1) {
            return partition(nums, q + 1, right, k - q + left - 1);
        } else {
            return nums[p];
        }
    }

    private void swap(int[] nums, int i, int j) {
        int temp = nums[i];
        nums[i] = nums[j];
        nums[j] = temp;
    }
}