heap, heap-sort implementation in C++

heap.cpp

#include<iostream>
#include<vector>
#include<math.h>


using namespace std;

void display(vector<int> arr, std::FILE* stream=stdout) {
	for(auto it=arr.begin(); it!=arr.end(); it++) {
		fprintf(stream, "%d ", *it);
	}
	fprintf(stream, "\n");
}

void heapify(vector<int> &arr, int start, int end) {
	int offset = start;
	for(int i=end-start; i>=0; i--) {
		int key = arr[i+offset];

		if (2*i + offset < arr.size()) {
			// left child exists
			fprintf(stderr, "i: %d, p: %d, l: %d\n", i, key, arr[2*i + offset]);
			if (key > arr[2*i + offset]) {
				fprintf(stderr, "left child, swap\n");
				arr[i + offset] = arr[2*i + offset];
				arr[2*i + offset] = key;
				key = arr[i];
			}
		}

		if (2*i + 1 + offset< arr.size()) {
			// right child exists
			fprintf(stderr, "i: %d, p: %d, r: %d\n", i, key, arr[2*i + 1]);
			if (key > arr[2*i + 1 + offset]) {
				fprintf(stderr, "i: %d, right child, swap\n", i);
				arr[i + offset] = arr[2*i + 1 + offset];
				arr[2*i + 1 + offset] = key;
				key = arr[i + offset];
			}
		}
	}
}

void heapsort(vector<int> &arr) {
	for(int start=0; start<arr.size(); start++) {
		fprintf(stderr, "heapify:s=%d, e=%d\n", start, int(arr.size()/2 + 1));
		heapify(arr, start, arr.size());
	}
}


int main() {
	vector<int> arr = {33,2,27,5,7,13,9,6,11,1};

	// display(arr);
	// heapify(arr, 0, floor(arr.size()/2));
	heapsort(arr);
	display(arr);

	return 0;
}

Makefile

.PHONY: all

all: heap

heap: heap.cpp
	$(CXX) -std=c++11 heap.cpp