int randomized_select(int *arr, int left, int right, int i)
{
if (left == right)
return arr[left];
int begin = left;
int end = right;
int key = arr[begin];
while (begin < end)
{
while (begin < end && arr[end] >= key)
end--;
arr[begin] = arr[end];
while (begin < end && arr[begin] <= key)
begin++;
arr[end] = arr[begin];
}
arr[begin] = key;
int n = begin - left + 1;
if (n == i)
return arr[begin];
else if (n < i)
{
return randomized_select(arr, begin+1, right, i - n);
}
else
return randomized_select(arr, left, begin - 1, i);
}
int randomized_select(int* arr, int s, int e, int i) {
if (s == e)
return arr[s];
int p = randomized_partition(arr, s, e);
int k = p-s+1; // +1 because, indexing starts at 0 while i starts at 1
if (k == i)
return arr[p];
else if (i < k)
return randomized_select(arr, s, p-1, i); // if it lies to the left, the required index is still i
else
return randomized_select(arr, p+1, e, i-k); // if it lies to the right, the required index is (i - k)
}
int randomized_select(int *arr, int start, int end, int i)
{
int randomized_partition(int*, int, int);
int partition = randomized_partition(arr, start, end);
int k = partition - start + 1;
if(k == i)
return arr[partition];
else
{
if(k < i)
return randomized_select(arr, partition+1, end, i-k);
else
return randomized_select(arr, start, partition-1, i);
}
}
// MARK: selection kth smallest element of the array A[p,r), k[0,1,...] [q,t)
int randomized_select(int A[], int p, int r, int k) {
pivot_t pivot, span;
if (p == r-1) {
return A[p];
}
pivot = randomized_partition_equal(A, p, r);
span.q = pivot.q - p;
span.t = pivot.t - p;
if (k >= span.q && k < span.t) {
return A[pivot.q];
} else if (k >= span.t) {
return randomized_select(A, pivot.t, r, k-span.t);
} else {
return randomized_select(A, p, pivot.q, k);
}
} //expected not worst ø(n) assuming that the elements are distinct, but here the elements can be equal because of pivot_t
double randomized_select(double *a, int p, int r, int i)
{
int q, k;
if (p == r)
return a[p];
q = randomized_partition(a, p, r);
/* number of elements in the first list */
k = q - p + 1;
if (i <= k)
return randomized_select(a, p, q, i);
else
return randomized_select(a, q+1, r, i-k);
}
int main(int argc, char const *argv[])
{
int arr[N] = {3, 4, 1, 7, 5, 8, 6};
int i = 4; // ith smallest element
int x = randomized_select(arr, 0, N-1, i);
printf("element #%d: %d\n", i, x);
return 0;
}
int randomized_select(vector<int>& nums,int p,int r, int i) {
if(p==r) {
return nums[p];
}
int x=nums[r], l=p;
for(int j=p; j<r; j++) {
if(nums[j]>x) {
swap(nums[l++],nums[j]);
}
}
swap(nums[l],nums[r]);
int q=l;
int k=q-p+1;
if(i==k)
return nums[q];
else if(i<k)
return randomized_select(nums,p,q-1,i);
else
return randomized_select(nums,q+1,r,i-k);
}
int median(int A[], int n)
{
return randomized_select(A, n, (1+n)/2);
}
int main(void)
{
int arr[10] = {23, 34, 21, 67, 89, 90, 6, 31, 16, 54};
printf("%d \n", randomized_select(arr, 0, 9, 5));
return 0;
}
// method 1 use quicksort partition
int findKthLargest(vector<int>& nums, int k) {
return randomized_select(nums,0,nums.size()-1,k);
}
