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- #include <stdio.h>
- #include <stdlib.h>
- #include <math.h>
- void swap(int *a, int *b)
- {
- int t;
- t = *b;
- *b = *a;
- *a = t;
- }
- void insertion_sort(int A[], int from, int to) {
- for(int i = from; i < to; i++) {
- for(int j = i + 1; j > from && A[j] < A[j - 1]; j--) {
- int temp = A[j - 1];
- A[j - 1] = A[j];
- A[j] = temp;
- }
- }
- }
- int find_median(int A[],int p,int r)
- {
- int n = r-p+1;
- insertion_sort(A,p,r);
- return A[n+1/2];
- }
- int quick_select(int A[], int p, int r, int k);
- int median_of_medians(int A[],int p, int r)
- {
- int N = r-p+1;
- int copy[N+1];
- for (int i = 1; i<=N; i++)
- {
- copy[i] = A[i];
- }
- int groups_no = ceil(N/5);
- int medians[groups_no+1];
- for(int i = 0;i < groups_no;i++)
- {
- if(i == groups_no-1) //last group
- {
- insertion_sort(copy,(i*5)+1,N);
- int group_length = N - ((i*5)+1) + 1;
- int median_ind = (group_length+1)/2 - 1;
- medians[i] = copy[(i*5)+1+median_ind];
- }
- else
- {
- insertion_sort(copy,(i*5)+1,(i*5)+5);
- int group_length = ((i*5)+5) - ((i*5)+1) + 1;
- int median_ind = (group_length+1)/2 - 1;
- medians[i] = copy[(i*5)+1+median_ind];
- }
- }
- if(groups_no > 5)
- {
- return quick_select(medians,1,groups_no,(groups_no+1)/2);
- }
- else
- {
- return medians[(groups_no+1)/2];
- }
- }
- int partition(int A[], int p, int r){
- int M = (r-p)+1;
- int median = median_of_medians(A,p,r);
- int ind;
- for(int i = p;i<=r;i++)
- {
- if(A[i]== median)
- {
- ind = i;
- }
- }
- swap(&A[ind],&A[r]);
- int x = A[r];
- int i = p-1;
- for(int j = p;j<=(r-1);j++)
- {
- if(A[j] <= x)
- {
- i++;
- swap(&A[i],&A[j]);
- }
- }
- swap(&A[i+1],&A[r]);
- return i+1;
- }
- int quick_select(int A[], int p, int r, int rank){
- if(p == r)
- {
- return A[p];
- }
- int q = partition(A,p,r);
- int k = q-p+1;
- if(rank == k)
- {
- return A[q];
- }
- else if (rank < k)
- {
- return quick_select(A,p,q-1,rank);
- }
- else
- {
- return quick_select(A,q+1,r,rank-k);
- }
- }
- int main(){
- int T, M;
- scanf("%d", &T);
- while(T-- > 0){
- scanf("%d", &M);
- int arr[M+1];
- //read the elements of the input array
- for(int i=1; i<=M; i++){
- scanf("%d",&arr[i]);
- }
- int median_index = ((M+1)/2);
- printf("Median: %d\n", quick_select(arr, 1, M, median_index));
- }
- }
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