Iterative approach to print all permutations of an Array
Last Updated :
12 Jul, 2025
Given an array arr[] of size N, the task is to generate and print all permutations of the given array. Examples:
Input: arr[] = {1, 2} Output: 1 2 2 1 Input: {0, 1, 2} Output: 0 1 2 1 0 2 0 2 1 2 0 1 1 2 0 2 1 0
Approach: The recursive methods to solve the above problems are discussed here and here. In this post, an iterative method to output all permutations for a given array will be discussed. The iterative method acts as a state machine. When the machine is called, it outputs a permutation and move to the next one. To begin, we need an integer array Indexes to store all the indexes of the input array, and values in array Indexes are initialized to be 0 to n – 1. What we need to do is to permute the Indexes array. During the iteration, we find the smallest index Increase in the Indexes array such that Indexes[Increase] < Indexes[Increase + 1], which is the first "value increase". Then, we have Indexes[0] > Indexes[1] > Indexes[2] > ... > Indexes[Increase], which is a tract of decreasing values from index[0]. The next steps will be:
- Find the index mid such that Indexes[mid] is the greatest with the constraints that 0 ? mid ? Increase and Indexes[mid] < Indexes[Increase + 1]; since array Indexes is reversely sorted from 0 to Increase, this step can use binary search.
- Swap Indexes[Increase + 1] and Indexes[mid].
- Reverse Indexes[0] to Indexes[Increase].
When the values in Indexes become n - 1 to 0, there is no "value increase", and the algorithm terminates. To output the combination, we loop through the index array and the values of the integer array are the indexes of the input array. The following image illustrates the iteration in the algorithm. 
Below is the implementation of the above approach:
C++
// C++ implementation of the approach
#include <iostream>
using namespace std;
template <typename T>
class AllPermutation {
private:
// The input array for permutation
const T* Arr;
// Length of the input array
const int Length;
// Index array to store indexes of input array
int* Indexes;
// The index of the first "increase"
// in the Index array which is the smallest
// i such that Indexes[i] < Indexes[i + 1]
int Increase;
public:
// Constructor
AllPermutation(T* arr, int length)
: Arr(arr), Length(length)
{
this->Indexes = nullptr;
this->Increase = -1;
}
// Destructor
~AllPermutation()
{
if (this->Indexes != nullptr) {
delete[] this->Indexes;
}
}
// Initialize and output
// the first permutation
void GetFirst()
{
// Allocate memory for Indexes array
this->Indexes = new int[this->Length];
// Initialize the values in Index array
// from 0 to n - 1
for (int i = 0; i < this->Length; ++i) {
this->Indexes[i] = i;
}
// Set the Increase to 0
// since Indexes[0] = 0 < Indexes[1] = 1
this->Increase = 0;
// Output the first permutation
this->Output();
}
// Function that returns true if it is
// possible to generate the next permutation
bool HasNext()
{
// When Increase is in the end of the array,
// it is not possible to have next one
return this->Increase != (this->Length - 1);
}
// Output the next permutation
void GetNext()
{
// Increase is at the very beginning
if (this->Increase == 0) {
// Swap Index[0] and Index[1]
this->Swap(this->Increase, this->Increase + 1);
// Update Increase
this->Increase += 1;
while (this->Increase < this->Length - 1
&& this->Indexes[this->Increase]
> this->Indexes[this->Increase + 1]) {
++this->Increase;
}
}
else {
// Value at Indexes[Increase + 1] is greater than Indexes[0]
// no need for binary search,
// just swap Indexes[Increase + 1] and Indexes[0]
if (this->Indexes[this->Increase + 1] > this->Indexes[0]) {
this->Swap(this->Increase + 1, 0);
}
else {
// Binary search to find the greatest value
// which is less than Indexes[Increase + 1]
int start = 0;
int end = this->Increase;
int mid = (start + end) / 2;
int tVal = this->Indexes[this->Increase + 1];
while (!(this->Indexes[mid] < tVal
&& this->Indexes[mid - 1] > tVal)) {
if (this->Indexes[mid] < tVal) {
end = mid - 1;
}
else {
start = mid + 1;
}
mid = (start + end) / 2;
}
// Swap
this->Swap(this->Increase + 1, mid);
}
// Invert 0 to Increase
for (int i = 0; i <= this->Increase / 2; ++i) {
this->Swap(i, this->Increase - i);
}
// Reset Increase
this->Increase = 0;
}
this->Output();
}
private:
// Function to output the input array
void Output()
{
for (int i = 0; i < this->Length; ++i) {
// Indexes of the input array
// are at the Indexes array
cout << (this->Arr[this->Indexes[i]]) << " ";
}
cout << endl;
}
// Swap two values in the Indexes array
void Swap(int p, int q)
{
int tmp = this->Indexes[p];
this->Indexes[p] = this->Indexes[q];
this->Indexes[q] = tmp;
}
};
// Driver code
int main()
{
int arr[] = { 0, 1, 2 };
AllPermutation<int> perm(arr, sizeof(arr) / sizeof(int));
perm.GetFirst();
while (perm.HasNext()) {
perm.GetNext();
}
return 0;
}
// Java implementation of the approach
class AllPermutation
{
// The input array for permutation
private final int Arr[];
// Index array to store indexes of input array
private int Indexes[];
// The index of the first "increase"
// in the Index array which is the smallest
// i such that Indexes[i] < Indexes[i + 1]
private int Increase;
// Constructor
public AllPermutation(int arr[])
{
this.Arr = arr;
this.Increase = -1;
this.Indexes = new int[this.Arr.length];
}
// Initialize and output
// the first permutation
public void GetFirst()
{
// Allocate memory for Indexes array
this.Indexes = new int[this.Arr.length];
// Initialize the values in Index array
// from 0 to n - 1
for (int i = 0; i < Indexes.length; ++i)
{
this.Indexes[i] = i;
}
// Set the Increase to 0
// since Indexes[0] = 0 < Indexes[1] = 1
this.Increase = 0;
// Output the first permutation
this.Output();
}
// Function that returns true if it is
// possible to generate the next permutation
public boolean HasNext()
{
// When Increase is in the end of the array,
// it is not possible to have next one
return this.Increase != (this.Indexes.length - 1);
}
// Output the next permutation
public void GetNext()
{
// Increase is at the very beginning
if (this.Increase == 0)
{
// Swap Index[0] and Index[1]
this.Swap(this.Increase, this.Increase + 1);
// Update Increase
this.Increase += 1;
while (this.Increase < this.Indexes.length - 1
&& this.Indexes[this.Increase]
> this.Indexes[this.Increase + 1])
{
++this.Increase;
}
}
else
{
// Value at Indexes[Increase + 1] is greater than Indexes[0]
// no need for binary search,
// just swap Indexes[Increase + 1] and Indexes[0]
if (this.Indexes[this.Increase + 1] > this.Indexes[0])
{
this.Swap(this.Increase + 1, 0);
}
else
{
// Binary search to find the greatest value
// which is less than Indexes[Increase + 1]
int start = 0;
int end = this.Increase;
int mid = (start + end) / 2;
int tVal = this.Indexes[this.Increase + 1];
while (!(this.Indexes[mid]<tVal&& this.Indexes[mid - 1]> tVal))
{
if (this.Indexes[mid] < tVal)
{
end = mid - 1;
}
else
{
start = mid + 1;
}
mid = (start + end) / 2;
}
// Swap
this.Swap(this.Increase + 1, mid);
}
// Invert 0 to Increase
for (int i = 0; i <= this.Increase / 2; ++i)
{
this.Swap(i, this.Increase - i);
}
// Reset Increase
this.Increase = 0;
}
this.Output();
}
// Function to output the input array
private void Output()
{
for (int i = 0; i < this.Indexes.length; ++i)
{
// Indexes of the input array
// are at the Indexes array
System.out.print(this.Arr[this.Indexes[i]]);
System.out.print(" ");
}
System.out.println();
}
// Swap two values in the Indexes array
private void Swap(int p, int q)
{
int tmp = this.Indexes[p];
this.Indexes[p] = this.Indexes[q];
this.Indexes[q] = tmp;
}
}
// Driver code
class AppDriver
{
public static void main(String args[])
{
int[] arr = { 0, 1, 2 };
AllPermutation perm = new AllPermutation(arr);
perm.GetFirst();
while (perm.HasNext())
{
perm.GetNext();
}
}
}
// This code is contributed by ghanshyampandey
// C# implementation of the approach
using System;
namespace Permutation {
class AllPermutation<T> {
// The input array for permutation
private readonly T[] Arr;
// Index array to store indexes of input array
private int[] Indexes;
// The index of the first "increase"
// in the Index array which is the smallest
// i such that Indexes[i] < Indexes[i + 1]
private int Increase;
// Constructor
public AllPermutation(T[] arr)
{
this.Arr = arr;
this.Increase = -1;
}
// Initialize and output
// the first permutation
public void GetFirst()
{
// Allocate memory for Indexes array
this.Indexes = new int[this.Arr.Length];
// Initialize the values in Index array
// from 0 to n - 1
for (int i = 0; i < Indexes.Length; ++i) {
this.Indexes[i] = i;
}
// Set the Increase to 0
// since Indexes[0] = 0 < Indexes[1] = 1
this.Increase = 0;
// Output the first permutation
this.Output();
}
// Function that returns true if it is
// possible to generate the next permutation
public bool HasNext()
{
// When Increase is in the end of the array,
// it is not possible to have next one
return this.Increase != (this.Indexes.Length - 1);
}
// Output the next permutation
public void GetNext()
{
// Increase is at the very beginning
if (this.Increase == 0) {
// Swap Index[0] and Index[1]
this.Swap(this.Increase, this.Increase + 1);
// Update Increase
this.Increase += 1;
while (this.Increase < this.Indexes.Length - 1
&& this.Indexes[this.Increase]
> this.Indexes[this.Increase + 1]) {
++this.Increase;
}
}
else {
// Value at Indexes[Increase + 1] is greater than Indexes[0]
// no need for binary search,
// just swap Indexes[Increase + 1] and Indexes[0]
if (this.Indexes[this.Increase + 1] > this.Indexes[0]) {
this.Swap(this.Increase + 1, 0);
}
else {
// Binary search to find the greatest value
// which is less than Indexes[Increase + 1]
int start = 0;
int end = this.Increase;
int mid = (start + end) / 2;
int tVal = this.Indexes[this.Increase + 1];
while (!(this.Indexes[mid]<tVal&& this.Indexes[mid - 1]> tVal)) {
if (this.Indexes[mid] < tVal) {
end = mid - 1;
}
else {
start = mid + 1;
}
mid = (start + end) / 2;
}
// Swap
this.Swap(this.Increase + 1, mid);
}
// Invert 0 to Increase
for (int i = 0; i <= this.Increase / 2; ++i) {
this.Swap(i, this.Increase - i);
}
// Reset Increase
this.Increase = 0;
}
this.Output();
}
// Function to output the input array
private void Output()
{
for (int i = 0; i < this.Indexes.Length; ++i) {
// Indexes of the input array
// are at the Indexes array
Console.Write(this.Arr[this.Indexes[i]]);
Console.Write(" ");
}
Console.WriteLine();
}
// Swap two values in the Indexes array
private void Swap(int p, int q)
{
int tmp = this.Indexes[p];
this.Indexes[p] = this.Indexes[q];
this.Indexes[q] = tmp;
}
}
// Driver code
class AppDriver {
static void Main()
{
int[] arr = { 0, 1, 2 };
AllPermutation<int> perm = new AllPermutation<int>(arr);
perm.GetFirst();
while (perm.HasNext()) {
perm.GetNext();
}
}
}
}
# Python 3 implementation of the approach
class AllPermutation :
# The input array for permutation
Arr = None
# Index array to store indexes of input array
Indexes = None
# The index of the first "increase"
# in the Index array which is the smallest
# i such that Indexes[i] < Indexes[i + 1]
Increase = 0
# Constructor
def __init__(self, arr) :
self.Arr = arr
self.Increase = -1
self.Indexes = [0] * (len(self.Arr))
# Initialize and output
# the first permutation
def GetFirst(self) :
# Allocate memory for Indexes array
self.Indexes = [0] * (len(self.Arr))
# Initialize the values in Index array
# from 0 to n - 1
i = 0
while (i < len(self.Indexes)) :
self.Indexes[i] = i
i += 1
# Set the Increase to 0
# since Indexes[0] = 0 < Indexes[1] = 1
self.Increase = 0
# Output the first permutation
self.Output()
# Function that returns true if it is
# possible to generate the next permutation
def HasNext(self) :
# When Increase is in the end of the array,
# it is not possible to have next one
return self.Increase != (len(self.Indexes) - 1)
# Output the next permutation
def GetNext(self) :
# Increase is at the very beginning
if (self.Increase == 0) :
# Swap Index[0] and Index[1]
self.Swap(self.Increase, self.Increase + 1)
# Update Increase
self.Increase += 1
while (self.Increase < len(self.Indexes) - 1 and self.Indexes[self.Increase] > self.Indexes[self.Increase + 1]) :
self.Increase += 1
else :
# Value at Indexes[Increase + 1] is greater than Indexes[0]
# no need for binary search,
# just swap Indexes[Increase + 1] and Indexes[0]
if (self.Indexes[self.Increase + 1] > self.Indexes[0]) :
self.Swap(self.Increase + 1, 0)
else :
# Binary search to find the greatest value
# which is less than Indexes[Increase + 1]
start = 0
end = self.Increase
mid = int((start + end) / 2)
tVal = self.Indexes[self.Increase + 1]
while (not (self.Indexes[mid] < tVal and self.Indexes[mid - 1] > tVal)) :
if (self.Indexes[mid] < tVal) :
end = mid - 1
else :
start = mid + 1
mid = int((start + end) / 2)
# Swap
self.Swap(self.Increase + 1, mid)
# Invert 0 to Increase
i = 0
while (i <= int(self.Increase / 2)) :
self.Swap(i, self.Increase - i)
i += 1
# Reset Increase
self.Increase = 0
self.Output()
# Function to output the input array
def Output(self) :
i = 0
while (i < len(self.Indexes)) :
# Indexes of the input array
# are at the Indexes array
print(self.Arr[self.Indexes[i]], end ="")
print(" ", end ="")
i += 1
print()
# Swap two values in the Indexes array
def Swap(self, p, q) :
tmp = self.Indexes[p]
self.Indexes[p] = self.Indexes[q]
self.Indexes[q] = tmp
# Driver code
class AppDriver :
@staticmethod
def main( args) :
arr = [0, 1, 2]
perm = AllPermutation(arr)
perm.GetFirst()
while (perm.HasNext()) :
perm.GetNext()
if __name__=="__main__":
AppDriver.main([])
# This code is contributed by aadityaburujwale.
// JavaScript implementation of the approach
class AllPermutation {
// The input array for permutation
constructor(arr) {
this.Arr = arr;
this.Increase = -1;
this.Indexes = new Array(this.Arr.length);
}
// Initialize and output the first permutation
GetFirst() {
// Allocate memory for Indexes array
this.Indexes = new Array(this.Arr.length);
// Initialize the values in Index array from 0 to n - 1
for (let i = 0; i < this.Indexes.length; i++) {
this.Indexes[i] = i;
}
// Set the Increase to 0
// since Indexes[0] = 0 < Indexes[1] = 1
this.Increase = 0;
// Output the first permutation
this.Output();
}
// Function that returns true if it is possible to generate the next permutation
HasNext() {
// When Increase is in the end of the array, it is not possible to have next one
return this.Increase !== this.Indexes.length - 1;
}
// Output the next permutation
GetNext() {
// Increase is at the very beginning
if (this.Increase === 0) {
// Swap Index[0] and Index[1]
this.Swap(this.Increase, this.Increase + 1);
// Update Increase
this.Increase++;
while (
this.Increase < this.Indexes.length - 1 &&
this.Indexes[this.Increase] > this.Indexes[this.Increase + 1]
) {
this.Increase++;
}
} else {
// Value at Indexes[Increase + 1] is greater than Indexes[0]
// no need for binary search, just swap Indexes[Increase + 1] and Indexes[0]
if (this.Indexes[this.Increase + 1] > this.Indexes[0]) {
this.Swap(this.Increase + 1, 0);
} else {
// Binary search to find the greatest value which is less than Indexes[Increase + 1]
let start = 0;
let end = this.Increase;
let mid = Math.floor((start + end) / 2);
let tVal = this.Indexes[this.Increase + 1];
while (!(this.Indexes[mid] < tVal && this.Indexes[mid - 1] > tVal)) {
if (this.Indexes[mid] < tVal) {
end = mid - 1;
} else {
start = mid + 1;
}
mid = Math.floor((start + end) / 2);
}
// Swap
this.Swap(this.Increase + 1, mid);
}
// Invert 0 to Increase
for (let i = 0; i <= this.Increase / 2; i++) {
this.Swap(i, this.Increase - i);
}
// Reset Increase
this.Increase = 0;
}
this.Output();
}
Output() {
let temp = "";
for (var i = 0; i < this.Indexes.length; i++) {
temp += this.Indexes[i]+" ";
//console.log(this.Arr[this.Indexes[i]] + " ");
}
console.log(temp);
}
Swap(p, q) {
var tmp = this.Indexes[p];
this.Indexes[p] = this.Indexes[q];
this.Indexes[q] = tmp;
}
}
let arr = [0, 1, 2];
let perm = new AllPermutation(arr);
perm.GetFirst();
while (perm.HasNext()) {
perm.GetNext();
}
// This code is contributed by abn95knd1.
Output:0 1 2
1 0 2
0 2 1
2 0 1
1 2 0
2 1 0
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