# C++ Program to Implement Heap’s Algorithm for Permutation of N Numbers

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This is a C++ to implement Heap’s Algorithm for the permutation of N numbers.

Problem Description

1. This algorithm print the permutation using heap algorithm.
2. The time complexity of this algorithm is O(n!).

Problem Solution

1. This algorithm takes the input of ‘N’ distinct numbers.
2. It fixes an element at the end of the array and permutes the remaining numbers.
3. Exit.

Program/Source Code

C++ Program to implement Heap’s Algorithm for permutation of N numbers
This program is successfully run on Dev-C++ using TDM-GCC 4.9.2 MinGW compiler on a Windows system.

```#include<iostream>
#include<iomanip>

using namespace std;

// A function swapping values using references.
void swap(int *x, int *y)
{
int temp;
temp = *x;
*x = *y;
*y = temp;
}

// A function to implement Heap’s Algorithm for the permutation of N numbers.
void print(const int *v)
{
int i;
int size = sizeof(v)/sizeof(int)+1;

// Loop to print the sequence.
cout<<"\t";
for ( i = 0; i < size; i++)
cout<<setw(4)<<v[i];
cout<<"\n";
}
void HeapPermute(int v[], int n)
{
int i;
// Print the sequence if the heap top reaches to the 1.
if (n == 1)
print(v);
else
{
// Fix a number at the heap top until only two one element remaining and permute remaining.
for (i = 0; i < n; i++)
{
HeapPermute(v, n-1);
// If odd then swap the value at the start index with the n-1.
if(n%2 == 1)
swap(&v, &v[n-1]);
// If even then swap the value at the 'i' index with the n-1.
else
swap(&v[i], &v[n-1]);
}
}
}

int main()
{
int  i, n, count = 1;
cout<<"How many numbers do you want to enter: ";
cin>>n;
int num[n];

// Take the input.
cout<<"\nEnter the numbers: ";
for (i = 0; i < n; i++)
{
cin>>num[i];
count *= (i+1);
}

// Print the permutation's count.
cout<<"\nThe number of permutations possible is: "<<count<<"\n";

// Calling Function to print all the permutation.
HeapPermute(num, n);
return 0;
}```
Program Explanation

1. Take the input of ‘n’ element of the array.
2. Compute the factorial of ‘n’, which will be the total number of permutation possible.
3. Call HeapPermute(), with array ‘num’, ‘n’ be the number of element remained to permute.
4. In HeapPermute(), recursively call HeapPermute() with decremented value of ‘n’.
5. If n equals to 1 then a complete permutation is generated so print it.
6. Otherwise, swap values according to n value to be even or odd.
7. Exit.

Runtime Test Cases
```Case 1:
How many numbers you want to enter: 3

Enter the numbers: 1
9
4

The number of permutations possible is: 6
1   9   4
9   1   4
4   1   9
1   4   9
9   4   1
4   9   1

Case 2:
How many numbers you want to enter: 4

Enter the numbers: 11
23
95
31

The number of permutations possible is: 24
11  23  95
23  11  95
95  11  23
11  95  23
23  95  11
95  23  11
31  23  95
23  31  95
95  31  23
31  95  23
23  95  31
95  23  31
31  11  95
11  31  95
95  31  11
31  95  11
11  95  31
95  11  31
31  11  23
11  31  23
23  31  11
31  23  11
11  23  31
23  11  31```

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