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# push_heap

Adds an element to a heap
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### Key Facts

Gyroscopic Couple: The rate of change of angular momentum ($\inline&space;\tau$) = $\inline&space;I\omega\Omega$ (In the limit).
• $\inline&space;I$ = Moment of Inertia.
• $\inline&space;\omega$ = Angular velocity
• $\inline&space;\Omega$ = Angular velocity of precession.

Blaise Pascal (1623-1662) was a French mathematician, physicist, inventor, writer and Catholic philosopher.

Leonhard Euler (1707-1783) was a pioneering Swiss mathematician and physicist.

## Definition

The push_heap() algorithm is defined in the standard header <algorithm> and in the nonstandard backward-compatibility header <algo.h>.

## Interface

#include <algorithm>
template < class RandomAccessIterator >
void push_heap(
RandomAccessIterator first,
RandomAccessIterator last
);
template < class RandomAccessIterator, class BinaryPredicate >
void push_heap(
RandomAccessIterator first,
RandomAccessIterator last,
BinaryPredicate comp
);

Parameters:
Parameter Description
first A random-access iterator addressing the position of the first element in the heap
last A random-access iterator addressing the position one past the final element in the range to be converted into a heap
comp User-defined predicate function object that defines sense in which one element is less than another. A binary predicate takes two arguments and returns true when satisfied and false when not satisfied

## Description

Push_heap inserts the element at the position last - 1 into the heap defined by the range [first, last-1).

The first version compares objects using operator< and the second compares objects using a function object comp.

None.

## Complexity

The complexity is linear; performs at most log(last - first) comparisons.

### References

Example:
##### Example - push_heap algorithm
Problem
This program illustrates the use of the STL push_heap() algorithm (default version) to add a value to a (maximum) heap of integers.
Workings
#include <iostream>
#include <vector>
#include <algorithm>

using namespace std;

int main()
{
int a[] = {36, 19, 25, 17, 3, 7, 1, 2,};
vector<int> v(a, a+8);

cout <<"\nHere are the values in the vector (the heap):\n";
for (vector<int>::size_type i=0; i<v.size(); i++)
cout <<v.at(i)<<" ";

cout <<"\nNow we add the value 100 to the heap.";
v.push_back(100);
push_heap(v.begin(), v.end());

cout <<"\nHere are the revised contents of the vector (the new heap):\n";
for (vector<int>::size_type i=0; i<v.size(); i++)
cout <<v.at(i)<<" ";

return 0;
}
Solution
Output:

Here are the values in the vector (the heap):
36 19 25 17 3 7 1 2

Now we add the value 100 to the heap.

Here are the revised contents of the vector (the new heap):
100 36 25 19 3 7 1 2 17
References