使用堆的优先级队列

Question

I have written this code after studying from Introduction to Algorithm . I am unable to find out what is the problem with the code. I have written the code for heapsort and it runs well. heap_extract_max() will return the maximum value. heap_increase_key() increase the priority of an element. Here I have written program for priority queue using singly linked list which runs well.

#include <iostream>
#include <vector>
#include <algorithm>

template<typename T>
void max_heapify(std::vector<T>& array, size_t index)
{
  size_t largest;
  size_t left  = (2*index) + 1;
  size_t right = left + 1;

  if(left < array.size() && array[left] > array[index])
    largest = left;
  else
    largest = index;

  if(right < array.size() && array[right] > array[largest])
    largest = right;

  if(largest != index)
  {
    int tmp = array[index];
    array[index] = array[largest];
    array[largest] = tmp;
    max_heapify(array, largest);
  }
}

template<typename T>
void build_max_heap(std::vector<T>& array)
{
  for(size_t i = (array.size()/2) - 1; i >= 0; i--)
  max_heapify(array, i);
}

template<typename T>
T heap_maximum(std::vector<T>& array)
{
  return array[0];
}

template<typename T>
T heap_extract_max(std::vector<T>& array)
{
  if(array.size() < 0)
  {
    std::cerr << "Heap Underflow \n";
  }
  else
  {
    T max = array[0];
    array[0] = array[array.size() - 1];
    //array.size() = array.size() - 1;
    max_heapify(array, 1);
    return max;
  }
}

template<typename T>
void heap_increase_key(std::vector<T>& array, size_t index, T value)
{
  if(value < array[index])
  {
    std::cerr <<"New value is smaller than the current value\n";
    return;
  }
  else
  {
    array[index] = value;
    while(index > 0 && array[(index/2) - 1] < array[index])
    {
      std::swap(array[index], array[(index/2) - 1]);
      index = (index/2) - 1;
    }
  }
}

template<typename T>
void max_heap_insert(std::vector<T>& array, T value)
{
  array[array.size()] = -1;
  heap_increase_key(array, array.size(), value);
}

int main()
{
std::vector<int> v({1, 2, 6, 3, 7});
build_max_heap(v);
std::cout << heap_extract_max(v)<<"\n";
for(size_t i = 0; i < v.size(); i++)
{
  std::cout << v[i] << " ";
}
std::cout << "\n";
}

It is not showing any output. I am writing commands

$ g++ -std=c++11 priorityqueue.cpp -o priorityqueue
$ ./priorityqueue

Answer 1

Problem is with the below function what will be return for if case because of that

Control may reach end of non-void function

template<typename T>
T heap_extract_max(std::vector<T>& array)
{
    if(array.size() < 0)
    {
        std::cerr << "Heap Underflow \n";
    }
    else
    {
        T max = array[0];
        array[0] = array[array.size() - 1];
        //array.size() = array.size() - 1;
        max_heapify(array, 1);
        return max;
    }
}

Add return -1 or anything else for if case

if(array.size() < 0)
{
    std::cerr << "Heap Underflow \n";
    return -1;
}

second problem

for(size_t i = (array.size()/2) - 1; i >= 0; i--)

Comparison of unsigned expression >= 0 is always true

Try changing to:(as suggested by Serge Rogatch)

for(int64_t i = (int64_t(array.size())/2) - 1; i >= 0; i--)

As well as there is problem with extracting it Before change result was

7
2 3 6 1 2 
Program ended with exit code: 0

Because of wrong handling of remove .Handled removed properly in below code

template<typename T>
T heap_extract_max(std::vector<T>& array)
{
    if(array.size() < 0)
    {
        std::cerr << "Heap Underflow \n";
        return -1;
    }
    else
    {
        T max = array[0];
        array[0] = array[array.size() - 1];
        array.erase(std::remove(array.begin(), array.end(), array[0]),
                   array.end());
        array.shrink_to_fit();
        max_heapify(array, 0);
        return max;
    }
}

After change

7
6 3 1 2 
Program ended with exit code: 0

Answer 2

It seems your program enters an infinite loop or crashes. I see a problem here:

for(size_t i = (array.size()/2) - 1; i >= 0; i--)

Because i is unsigned, it is always i >= 0 . Also, for array.size() <= 1 , you initialize it with some large positive integer, because i tries to go negative, but size_t is never negative, so the number wraps.

Try changing to:

for(int64_t i = (int64_t(array.size())/2) - 1; i >= 0; i--)

Also you seem to confuse 0 - and 1 -based array indexing, and you should do array.pop_back() in place of //array.size() = array.size() - 1; . Furthermore, it seems you intended array[1] instead of array[0] here:

T max = array[0];
array[0] = array[array.size() - 1];

If you stick with 1 -based indexing, you should place and keep a dummy element at index 0 in your array:

std::vector<int> v({/*dummy*/-1, 1, 2, 6, 3, 7});

Array size is never negative, so you don't need if(array.size() < 0) and what's in then clause.

Though 0 -based indexing is more natural in C++ and heap can be implemented with it too. For this you would need to revise all the index arithmetic like:

size_t left  = (2*index) + 1;
size_t right = left + 1;

and

array[(index/2) - 1]