A full permutation is list of all variation for given items (usually numbers). For example, the full permutation of 3 elements are:

1 2 3

1 3 2

2 1 3

2 3 1

3 1 2

3 2 1

**Also Read: C program to find factorial of any number using recursion**

**Also Read: C++ program to enter a number and print it into words**

As we can easily calculate, the total number of iterations is n! (factorial). How do we get this number? The most simple way is to think of the number of different items we can choose for each position. For example, for the first place, we have n choices, and we have n-1 choices for the second place, and etc. Thus we have n*(n-1)*(n-2)*…1 that gives a total number n!.

So how to emulate this for the whole process? First, we can define a recursive function that ends printing one solution by checking if we have reached the end. For each iteration, we can simply swap the current item with the rest of the items and try the next position recursive. As we use a global array variable nums to keep the items, we need to swap the items back after each recursion call. The source code is pretty straight forward. Open Visual Studio, choose the ‘Console Application’ from ‘C++’ language projects.

*#include <iostream>*

*using namespace std;*

*// helper dynamic array*

*int *nums;*

*// exchange two integers*

*inline void swap(int &i, int &j)*

*{*

*int t = i;*

*i = j;*

*j = t;*

*}*

*// full permutation*

*void*

*perm(int n, int i)*

*{*

*if (i == n – 1) //*

check if reach the end of iteration

check if reach the end of iteration

*{*

*// print out*

the iteration

the iteration

*for (int j =*

0; j < n; j ++)

0; j < n; j ++)

*{*

*cout*

<< nums[j];

<< nums[j];

*}*

*cout <<*

endl;

endl;

*}*

*else*

*{*

*for (int j =*

i; j < n; j ++)

i; j < n; j ++)

*{*

*swap(nums[i],*

nums[j]); // swap

nums[j]); // swap

*perm(n,*

i + 1); // recursive

i + 1); // recursive

*swap(nums[i],*

nums[j]); // swap it back

nums[j]); // swap it back

*}*

*}*

*}*

*// main entry*

*int*

*main()*

*{*

*int n;*

*cin >> n;*

*nums = new int[n]; //*

declare a dynamic array

declare a dynamic array

*for (int i = 0; i*

< n; i ++)

< n; i ++)

*{*

*// and fill it*

with numbers as 1, 2, 3, … n

with numbers as 1, 2, 3, … n

*nums[i] = i +*

1;

1;

*}*

*perm(n, 0);*

*cin >> n; //*

pause

pause

*return 0;*

*}*

**Also Read: C++ Program to calculate roots of quadratic equation ax^2+bx+c=0**

**Also Read: C++ program to find sum of elements above and below the main digonal of a matrix**

**Author’s bio:**

*Zhihua Lai is now a Marie Curie Experienced Researcher at University of Sheffield. At his spare time, he writes blogs and programs just for fun. He is also an ACMer where he is keen on fast and efficient algorithms. His blog can be found at http://helloacm.com/*

Hi, I'm sort of a beginner at programming. I've used VS2012, opened a new project for VC++ and select Console Application. Copy and paste the program and when I press F5, VS says me that there an error.

error C1033: cannot open program database ''

Could someone help me?