find Kth smallest

最新推荐文章于 2018-06-29 00:03:36 发布

转载最新推荐文章于 2018-06-29 00:03:36 发布 · 648 阅读

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本文介绍了一种基于快速排序的高效算法，用于找到数组中第K小的元素。该算法利用了随机化分区过程来优化查找过程，并通过递归方式实现对目标元素的精确定位。

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public class KthSmallest {

	// This function returns k'th smallest element in arr[l..r]
    // using QuickSort based method.  ASSUMPTION: ALL ELEMENTS
    // IN ARR[] ARE DISTINCT
    int kthSmallest(int arr[], int l, int r, int k)
    {
        // If k is smaller than number of elements in array
        if (k > 0 && k <= r - l + 1)
        {
            // Partition the array around a random element and
            // get position of pivot element in sorted array
            int pos = randomPartition(arr, l, r);
 
            // If position is same as k
            if (pos-l == k-1)
                return arr[pos];
 
            // If position is more, recur for left subarray
            if (pos-l > k-1)
                return kthSmallest(arr, l, pos-1, k);
 
            // Else recur for right subarray
            return kthSmallest(arr, pos+1, r, k-pos+l-1);
        }
 
        // If k is more than number of elements in array
        return Integer.MAX_VALUE;
    }
 
    // Utility method to swap arr[i] and arr[j]
    void swap(int arr[], int i, int j)
    {
        int temp = arr[i];
        arr[i] = arr[j];
        arr[j] = temp;
    }
 
    // Standard partition process of QuickSort().  It considers
    // the last element as pivot and moves all smaller element 
    // to left of it and greater elements to right. This function
    // is used by randomPartition()
    int partition(int arr[], int l, int r)
    {
        int x = arr[r], i = l;
        for (int j = l; j <= r - 1; j++)
        {
            if (arr[j] <= x)
            {
                swap(arr, i, j);
                i++;
            }
        }
        swap(arr, i, r);
        return i;
    }
 
    // Picks a random pivot element between l and r and 
    // partitions arr[l..r] arount the randomly picked 
    // element using partition()
    int randomPartition(int arr[], int l, int r)
    {
        int n = r-l+1;
        int pivot = (int)(Math.random()) % n;
        swap(arr, l + pivot, r);
        return partition(arr, l, r);
    }
 
    // Driver method to test above
    public static void main(String args[])
    {
    	KthSmallest ob = new KthSmallest();
        int arr[] = {12, 3, 5, 7, 4, 19, 26};
        int n = arr.length,k = 3;
        System.out.println("K'th smallest element is "+
                           ob.kthSmallest(arr, 0, n-1, k));
    }
}