Find the i th largest number of numbers. (Use divide-and-conquer method)
#include <iostream>
using namespace std;
const int N = 1e6 + 10;
int a[N];
int ans[N];
void mergeSort(int a[], int l, int r)
{
if (l >=r) return;
int mid = (l + r) / 2;
mergeSort(a, l, mid );
mergeSort(a, mid + 1, r);
int k1=0, i = l, j = mid+1;
while (i <=mid&& j<=r)
{
if (a[i] >=a[j])
ans[k1++] = a[i++];
else
ans[k1++] = a[j++];
}
while(i<=mid)
ans[k1++] = a[i++];
while (j <= r)
ans[k1++] = a[j++];
for (int i = l, j=0; i <=r; i++,j++)
{
a[i] = ans[j];
}
}
int partition(int a[], int l, int r, int x)
{
int i = l - 1, j = r + 1;
while (i < j)
{
do i++;
while (a[i] > x);
do j--;
while (a[j] < x);
if (i < j)swap(a[i], a[j]);
}
return i;
}
int findK(int a[], int l, int r, int k)
{
if (r - l < 75)
return a[l + k - 1];
for (int i = 0; i < (r - l - 4) / 5; i += 5)
mergeSort(a, i, i + 4);
for (int i = 0; i < (r - l - 4) / 5; i++)
swap(a[i+l], a[l + 5 * i + 2]);
int x = findK(a, l, (r - l - 4) / 5, (r - l - 4) / 10);
int i = partition(a, l, r, x);
int j = i - l + 1;
if (k >= j)
findK(a, i+1, r, k - j);
else
findK(a, l, j, k);
}
int main()
{
int n;
cin >> n;
int k;
cout << "please enter the k to find the kth in the array" << endl;
cin >> k;
for (int i = 0; i < n; i++)
a[i]=rand();
int i = findK(a, 0, n-1, k);
cout << "The kth number is" << i << endl;
return 0;
}
//* 1.首先将数组分为五五一组,并且进行排序
//* 2.将每个组a[2]也就是中位数,挪到a[0]-a[(r-p-4)/5],也就是数组前几个,(r-p-4)/5代表五个组的个数
//* 3.递归找到中位数的中位数
//* 4.对整个数组进行排序,使中位数的中位数左边<中位数的中位数,右边>中位数的中位数,参考快排
//* 5.定位中位数的中位数的索引,分情况递归。