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For a given array, generate all possible permutations of the array. Given an array of N elements, there will be N! permutations provided all N elements are unique. C++ provides a function in Standard Template Library to accomplish this
Algorithm using C++ STL
We can generate all permutations of an array by making use of the STL function next_permutation. A call of next_permutation returns the next lexicographically smallest permutation. If the sequence is lexicographically largest, the function returns false.
Syntax:
// a is an array
next_permutation(a.begin(), a.end())
Note:
- It will modify the array passed (a in the above example)
- It will generate a is the smallest lexicographic permutation of a that is larger than a
- It will return false in a is the largest permutation possible otherwise it will return true
The steps involved can be described as follows:
- Sort the array to get lexicographically smallest sequence.
- Print the array.
- Generate the next lexicographically smallest sequence.
Implementation
#include <bits/stdc++.h>
using namespace std;
//Display elements of the array
void display(vector<int> a, int n){
for(int i=0;i<n;i++) cout << a[i] << " ";
cout << endl;
}
int main()
{
//Obtaining length of array
int n;
cin >> n;
//Declaring a vector of integers
vector<int> a(n);
//Taking input of array of integers
for(int i=0; i<n; i++){
cin >> a[i];
}
do{
//Display the current permutation
display(a, n);
}while(next_permutation(a.begin(), a.end())); //Generate next permutation till it is not lexicographically largest
return 0;
}
Example
//Console input
5
1 2 3 4 5
//Console output
1 2 3 4 5
1 2 3 5 4
1 2 4 3 5
1 2 4 5 3
1 2 5 3 4
1 2 5 4 3
1 3 2 4 5
1 3 2 5 4
1 3 4 2 5
1 3 4 5 2
1 3 5 2 4
1 3 5 4 2
1 4 2 3 5
1 4 2 5 3
1 4 3 2 5
1 4 3 5 2
1 4 5 2 3
1 4 5 3 2
1 5 2 3 4
1 5 2 4 3
1 5 3 2 4
1 5 3 4 2
1 5 4 2 3
1 5 4 3 2
2 1 3 4 5
2 1 3 5 4
2 1 4 3 5
2 1 4 5 3
2 1 5 3 4
2 1 5 4 3
2 3 1 4 5
2 3 1 5 4
2 3 4 1 5
2 3 4 5 1
2 3 5 1 4
2 3 5 4 1
2 4 1 3 5
2 4 1 5 3
2 4 3 1 5
2 4 3 5 1
2 4 5 1 3
2 4 5 3 1
2 5 1 3 4
2 5 1 4 3
2 5 3 1 4
2 5 3 4 1
2 5 4 1 3
2 5 4 3 1
3 1 2 4 5
3 1 2 5 4
3 1 4 2 5
3 1 4 5 2
3 1 5 2 4
3 1 5 4 2
3 2 1 4 5
3 2 1 5 4
3 2 4 1 5
3 2 4 5 1
3 2 5 1 4
3 2 5 4 1
3 4 1 2 5
3 4 1 5 2
3 4 2 1 5
3 4 2 5 1
3 4 5 1 2
3 4 5 2 1
3 5 1 2 4
3 5 1 4 2
3 5 2 1 4
3 5 2 4 1
3 5 4 1 2
3 5 4 2 1
4 1 2 3 5
4 1 2 5 3
4 1 3 2 5
4 1 3 5 2
4 1 5 2 3
4 1 5 3 2
4 2 1 3 5
4 2 1 5 3
4 2 3 1 5
4 2 3 5 1
4 2 5 1 3
4 2 5 3 1
4 3 1 2 5
4 3 1 5 2
4 3 2 1 5
4 3 2 5 1
4 3 5 1 2
4 3 5 2 1
4 5 1 2 3
4 5 1 3 2
4 5 2 1 3
4 5 2 3 1
4 5 3 1 2
4 5 3 2 1
5 1 2 3 4
5 1 2 4 3
5 1 3 2 4
5 1 3 4 2
5 1 4 2 3
5 1 4 3 2
5 2 1 3 4
5 2 1 4 3
5 2 3 1 4
5 2 3 4 1
5 2 4 1 3
5 2 4 3 1
5 3 1 2 4
5 3 1 4 2
5 3 2 1 4
5 3 2 4 1
5 3 4 1 2
5 3 4 2 1
5 4 1 2 3
5 4 1 3 2
5 4 2 1 3
5 4 2 3 1
5 4 3 1 2
5 4 3 2 1
Complexity
The next_permutation call is "Up to linear in half the distance between first and last (in terms of actual swaps)."
Note
This method always generates all permutations in the lexicographic order.