利用快速排序中的切分函数寻找数组主元素

最新推荐文章于 2021-05-23 01:46:48 发布

原创最新推荐文章于 2021-05-23 01:46:48 发布 · 698 阅读

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本文介绍了一种用于查找数组中是否存在主元素（超过一半元素相同）的算法，并提供了完整的C语言实现代码。通过查找中位数并验证其是否为数组的主元素来解决问题。

如果一个数组A[1..n]中超过半数的元素都相同时，该数组被称为含有主元素。

算法：利用切分函数查找中位数，遍历数组如果与中位数相等的元素个数大于数组长度一半，那么则存在主元素，这个中位数即主元素。

代码：

#include <stdio.h>

void swap(int *a,int *b)
{
	int	temp = *a;
	*a = *b;
	*b = temp;
}

int hoare_partition(int a[],int left,int right)
{
	int i,j,pivot;
	pivot = a[left];
	i = left - 1;
	j = right + 1;
	while(1)
	{
		do
		{
			j--;
		}while(a[j]>pivot);

		do
		{
			i++;
		}while(a[i]<pivot);

		if(i<j)
			swap(a+i,a+j);
		else
			return j;
	}	
}

int partition(int a[],int left,int right)
{
	int i,j;
	int pivot = a[right];
	i = left - 1;
	for(j=left;j<right;j++)
	{
		if(a[j]<=pivot)
		{
			i++;
			swap(a+i,a+j);
		}
	}
	swap(a+i+1,a+right);
	return i+1;
}
int selectKth(int a[],int left,int right,int K)
{
	int idx = partition(a,left,right);
	if(idx-left+1 == K)
		return idx;
	else if (idx-left+1 < K)
		return selectKth(a,idx+1,right,K-(idx-left+1));
	else
		return selectKth(a,left,idx-1,K);
}

void qSort(int a[],int left,int right)
{
	if(left<right){
		int idx = partition(a,left,right);
		qSort(a,left,idx-1);
		qSort(a,idx+1,right);
	}
}
int major_element(int a[],int left,int right)
{
	/* major element exist if non-negative is returned. */
	if(left<=right){
		int mid = selectKth(a,left,right,(right-left+2)>>1);

		int cnt = 0;
		for(int i=left;i<=right;i++){
			if(a[i] == a[mid])
			cnt++;
		}
		if(cnt>(right-left+1)>>1)
			return mid;
	} 
	return -1;
}

void showArray(int a[],int l,int r)
{
	for(int i=l;i<=r;i++)
		printf("%-3d",a[i]);
	printf("\n");
}
int main(){
	int a[] = {1,4,2,3,4,5,4,4,4};
	int b[] = {1,3,2};
	int c[] = {2};
	int d[] = {4,4,4,4,1,2,3,5};
	showArray(a,0,8);
	showArray(b,0,2);
	showArray(c,0,0);
	showArray(d,0,7);

	int m = major_element(a,0,8);
	printf("Major element exist in List a? %s \n",m>-1?"Yes!":"No!");
	
	printf("%-3d\n",a[m]);
	showArray(a,0,8);
	
	m = major_element(b,0,2);
	printf("Major element exist in List b? %s \n",m>-1?"Yes!":"No!");
	
	m = major_element(c,0,0);
	printf("Major element exist in List c? %s \n",m>-1?"Yes!":"No!");
	
	m = major_element(d,0,7);
	printf("Major element exist in List d? %s \n",m>-1?"Yes!":"No!");

	qSort(a,0,8);
	qSort(b,0,2);
	qSort(c,0,0);
	qSort(d,0,7);
	showArray(a,0,8);
	showArray(b,0,2);
	showArray(c,0,0);
	showArray(d,0,7);
}

测试结果：

1  4  2  3  4  5  4  4  4  (Array a)
1  3  2                    (Array b)
2  			   (Array c)	
4  4  4  4  1  2  3  5     (Array d)
Major element exist in List a? Yes! 
4  
1  4  2  3  4  4  4  4  5  
Major element exist in List b? No! 
Major element exist in List c? Yes! 
Major element exist in List d? No! 
1  2  3  4  4  4  4  4  5  
1  2  3  
2  
1  2  3  4  4  4  4  5