Assume that we start with a random array of size n= 2k-1 and form a heap....
Assume that we start with a random array of size n= 2k-1 and form a heap.
a) What is the probability that the third largest element will be a child of the root? Justify
b) Before you form a heap, you notice that none of the three smallest elements are near the
top of the array, or more formally none of them are in any of the first (n-3)/4 locations
of the array. What is the probability that the third smallest element will be the parent of
a leaf? Justify
Homework Answers
#include <iostream> using namespace std; void MAX_HEAPIFY(int a[], int i, int n) { int l,r,largest,loc; l=2*i; r=(2*i+1); if((l<=n)&&a[l]>a[i]) largest=l; else largest=i; if((r<=n)&&(a[r]>a[largest])) largest=r; if(largest!=i) { loc=a[i]; a[i]=a[largest]; a[largest]=loc; MAX_HEAPIFY(a, largest,n); } } void BUILD_MAX_HEAP(int a[], int n) { for(int k = n/2; k >= 1; k--) { MAX_HEAPIFY(a, k, n); } } void HEAPSORT(int a[], int n) { BUILD_MAX_HEAP(a,n); int i, temp; for (i = n; i >= 2; i--) { temp = a[i]; a[i] = a[1]; a[1] = temp; MAX_HEAPIFY(a, 1, i - 1); } } int main() { int n; cout<<"Enter the size of the array"<<endl; cin>>n; int a[n]; cout<<"Enter the elements in the array"<<endl; for (int i = 1; i <= n; i++) { cin>>a[i]; } HEAPSORT(a, n); cout<<":::::::SORTED FORM::::::"<<endl; for (int i = 1; i <= n; i++) { cout<<a[i]<<endl; } }
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Assume that we start with a random array of size n=
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