Quick select

最新推荐文章于 2024-08-26 09:08:17 发布

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Quick select是一种在未排序数组中查找第k小/大元素的算法，它借鉴了快速排序的思想，但避免了不必要的递归。通过选取pivot将数组分区，然后仅关注目标元素所在的部分，减少了平均时间复杂度到O(n)。

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https://zhuanlan.zhihu.com/p/64627590

Quick select算法通常用来在未排序的数组中寻找第k小/第k大的元素

总体而言，Quick select采用和Quick sort类似的步骤。首先选定一个pivot，然后根据每个数字与该pivot的大小关系将整个数组分为两部分。那么与Quick sort不同的是，Quick select只考虑所寻找的目标所在的那一部分子数组，而非像Quick sort一样分别再对两边进行分割。正是因为如此，Quick select将平均时间复杂度从O(nlogn)降到了O(n)。

public class Solution {
    public int findKthSmallest(int[] nums, int k) {
        if (nums == null || nums.length == 0) {
            return Integer.MIN_VALUE;
        }

        int len = nums.length;

        return quickSelect(nums, k, 0, len - 1);
    }

    private int quickSelect(int[] nums, int k, int start, int end) {

        //Choose a pivot randomly
        Random rand = new Random();
        int index = rand.nextInt(end - start + 1) + start;
        int pivot = nums[index];
        swap(nums, index, end);

        int left = start, right = end;

        while(left < right) {
            if (nums[left++] >= pivot) {
                swap(nums, --left, --right);
            }
        }
        //left is now pointing to the first number that is greater than or equal to the pivot
        swap(nums, left, end);

        //m is the number of numbers that is smaller than pivot
        int m = left - start;

        if (m == k - 1) { //in order to find the kth smallest number, there must be k - 1 number smaller than it 
            return pivot;
        }
        else if (k <= m) { //target is in the left subarray
            return quickSelect(nums, k, start, left - 1);
        }
        else { 
            //target is in the right subarray, but need to update k 
            //Since we have discarded m numbers smaller than it which is in the right subarray
            return quickSelect(nums, k - m, left, end);
        }
    }

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