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Iterative approach to print all combinations of an Array
• Last Updated : 15 Jan, 2020

Given an array arr[] of size N, the task is to generate and print all possible combinations of R elements in array.

Examples:

Input: arr[] = {0, 1, 2, 3}, R = 3
Output:
0 1 2
0 1 3
0 2 3
1 2 3

Input: arr[] = {1, 3, 4, 5, 6, 7}, R = 5
Output:
1 3 4 5 6
1 3 4 5 7
1 3 4 6 7
1 3 5 6 7
1 4 5 6 7
3 4 5 6 7

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Recursive methods are discussed here. In this post, an iterative method to output all combinations for a given array will be discussed.
The iterative method acts as a state machine. When the machine is called, it outputs a combination and move to the next one.
For a combination of r elements from an array of size n, a given element may be included or excluded from the combination.
Let’s have a Boolean array of size n to label whether the corresponding element in data array is included. If the ith element in the data array is included, then the ith element in the boolean array is true or false otherwise.
Then, r booleans in the boolean array will be labelled as true. We can initialize the boolean array to have r trues from index 0 to index r – 1. During the iteration, we scan the boolean array from left to right and find the first element which is true and whose previous one is false and the first element which is true and whose next one is false.
Then, we have the first continuous tract of trues in the Boolean array. Assume there are m trues in this tract, starting from index Start and ending at index End. The next iteration would be

1. Set index End + 1 of the boolean array to true.
2. Set index Start to index End – 1 of the boolean array to false.
3. Set index 0 to index k – 2 to true.

For example,
If the current boolean array is {0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0}, then k = 4, Start = 2, and End = 5. The next Boolean array would be {1, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0}. In case Start == End where there is only one true in the tract, we simply set index End to false and index End + 1 to true.
We also need to record the current Start and End and update Start and End during each iteration. When the last r booleans are set to true, we cannot move to the next combination and we stop.

The following image illustrates how the boolean array changes from one iteration to another. To output the combination, we just scan the boolean array. If its ith index is true, we print out the ith element of the data array.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach``#include ``using` `namespace` `std;`` ` `class` `Combination {``private``:``    ``// Data array for combination``    ``int``* Indices;`` ` `    ``// Length of the data array``    ``int` `N;`` ` `    ``// Number of elements in the combination``    ``int` `R;`` ` `    ``// The boolean array``    ``bool``* Flags;`` ` `    ``// Starting index of the 1st tract of trues``    ``int` `Start;`` ` `    ``// Ending index of the 1st tract of trues``    ``int` `End;`` ` `public``:``    ``// Constructor``    ``Combination(``int``* arr, ``int` `n, ``int` `r)``    ``{``        ``this``->Indices = arr;``        ``this``->N = n;``        ``this``->R = r;``        ``this``->Flags = nullptr;``    ``}``    ``~Combination()``    ``{``        ``if` `(``this``->Flags != nullptr) {``            ``delete``[] ``this``->Flags;``        ``}``    ``}`` ` `    ``// Set the 1st r Booleans to true,``    ``// initialize Start and End``    ``void` `GetFirst()``    ``{``        ``this``->Flags = ``new` `bool``[N];`` ` `        ``// Generate the very first combination``        ``for` `(``int` `i = 0; i < ``this``->N; ++i) {``            ``if` `(i < ``this``->R) {``                ``Flags[i] = ``true``;``            ``}``            ``else` `{``                ``Flags[i] = ``false``;``            ``}``        ``}`` ` `        ``// Update the starting ending indices``        ``// of trues in the boolean array``        ``this``->Start = 0;``        ``this``->End = ``this``->R - 1;``        ``this``->Output();``    ``}`` ` `    ``// Function that returns true if another``    ``// combination can still be generated``    ``bool` `HasNext()``    ``{``        ``return` `End < (``this``->N - 1);``    ``}`` ` `    ``// Function to generate the next combination``    ``void` `Next()``    ``{`` ` `        ``// Only one true in the tract``        ``if` `(``this``->Start == ``this``->End) {``            ``this``->Flags[``this``->End] = ``false``;``            ``this``->Flags[``this``->End + 1] = ``true``;``            ``this``->Start += 1;``            ``this``->End += 1;``            ``while` `(``this``->End + 1 < ``this``->N``                   ``&& ``this``->Flags[``this``->End + 1]) {``                ``++``this``->End;``            ``}``        ``}``        ``else` `{`` ` `            ``// Move the End and reset the End``            ``if` `(``this``->Start == 0) {``                ``Flags[``this``->End] = ``false``;``                ``Flags[``this``->End + 1] = ``true``;``                ``this``->End -= 1;``            ``}``            ``else` `{``                ``Flags[``this``->End + 1] = ``true``;`` ` `                ``// Set all the values to false starting from``                ``// index Start and ending at index End``                ``// in the boolean array``                ``for` `(``int` `i = ``this``->Start; i <= ``this``->End; ++i) {``                    ``Flags[i] = ``false``;``                ``}`` ` `                ``// Set the beginning elements to true``                ``for` `(``int` `i = 0; i < ``this``->End - ``this``->Start; ++i) {``                    ``Flags[i] = ``true``;``                ``}`` ` `                ``// Reset the End``                ``this``->End = ``this``->End - ``this``->Start - 1;``                ``this``->Start = 0;``            ``}``        ``}``        ``this``->Output();``    ``}`` ` `private``:``    ``// Function to print the combination generated previouslt``    ``void` `Output()``    ``{``        ``for` `(``int` `i = 0, count = 0; i < ``this``->N``                                   ``&& count < ``this``->R;``             ``++i) {`` ` `            ``// If current index is set to true in the boolean array``            ``// then element at current index in the original array``            ``// is part of the combination generated previously``            ``if` `(Flags[i]) {``                ``cout << Indices[i] << ``" "``;``                ``++count;``            ``}``        ``}``        ``cout << endl;``    ``}``};`` ` `// Driver code``int` `main()``{``    ``int` `arr[] = { 0, 1, 2, 3 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(``int``);``    ``int` `r = 3;``    ``Combination com(arr, n, r);``    ``com.GetFirst();``    ``while` `(com.HasNext()) {``        ``com.Next();``    ``}``    ``return` `0;``}`

## Java

 `// Java implementation of the approach``class` `Combination ``{`` ` `    ``// Data array for combination``    ``private` `int``[] Indices;`` ` `    ``// Number of elements in the combination``    ``private` `int` `R;`` ` `    ``// The boolean array``    ``private` `boolean``[] Flags;`` ` `    ``// Starting index of the 1st tract of trues``    ``private` `int` `Start;`` ` `    ``// Ending index of the 1st tract of trues``    ``private` `int` `End;`` ` `    ``// Constructor``    ``public` `Combination(``int``[] arr, ``int` `r)``    ``{``        ``this``.Indices = arr;``        ``this``.R = r;``    ``}`` ` `    ``// Set the 1st r Booleans to true,``    ``// initialize Start and End``    ``public` `void` `GetFirst()``    ``{``        ``Flags = ``new` `boolean``[``this``.Indices.length];`` ` `        ``// Generate the very first combination``        ``for` `(``int` `i = ``0``; i < ``this``.R; ++i) ``        ``{``            ``Flags[i] = ``true``;``        ``}`` ` `        ``// Update the starting ending indices``        ``// of trues in the boolean array``        ``this``.Start = ``0``;``        ``this``.End = ``this``.R - ``1``;``        ``this``.Output();``    ``}`` ` `    ``// Function that returns true if another``    ``// combination can still be generated``    ``public` `boolean` `HasNext()``    ``{``        ``return` `End < (``this``.Indices.length - ``1``);``    ``}`` ` `    ``// Function to generate the next combination``    ``public` `void` `Next()``    ``{`` ` `        ``// Only one true in the tract``        ``if` `(``this``.Start == ``this``.End)``        ``{``            ``this``.Flags[``this``.End] = ``false``;``            ``this``.Flags[``this``.End + ``1``] = ``true``;``            ``this``.Start += ``1``;``            ``this``.End += ``1``;``            ``while` `(``this``.End + ``1` `< ``this``.Indices.length``                ``&& ``this``.Flags[``this``.End + ``1``]) ``            ``{``                ``++``this``.End;``            ``}``        ``}``        ``else` `        ``{`` ` `            ``// Move the End and reset the End``            ``if` `(``this``.Start == ``0``)``            ``{``                ``Flags[``this``.End] = ``false``;``                ``Flags[``this``.End + ``1``] = ``true``;``                ``this``.End -= ``1``;``            ``}``            ``else` `            ``{``                ``Flags[``this``.End + ``1``] = ``true``;`` ` `                ``// Set all the values to false starting from``                ``// index Start and ending at index End``                ``// in the boolean array``                ``for` `(``int` `i = ``this``.Start; i <= ``this``.End; ++i)``                ``{``                    ``Flags[i] = ``false``;``                ``}`` ` `                ``// Set the beginning elements to true``                ``for` `(``int` `i = ``0``; i < ``this``.End - ``this``.Start; ++i) ``                ``{``                    ``Flags[i] = ``true``;``                ``}`` ` `                ``// Reset the End``                ``this``.End = ``this``.End - ``this``.Start - ``1``;``                ``this``.Start = ``0``;``            ``}``        ``}``        ``this``.Output();``    ``}`` ` `    ``// Function to print the combination generated previouslt``    ``private` `void` `Output()``    ``{``        ``for` `(``int` `i = ``0``, count = ``0``; i < Indices.length``                                ``&& count < ``this``.R; ++i)``        ``{`` ` `            ``// If current index is set to true in the boolean array``            ``// then element at current index in the original array``            ``// is part of the combination generated previously``            ``if` `(Flags[i]) ``            ``{``                ``System.out.print(Indices[i]);``                ``System.out.print(``" "``);``                ``++count;``            ``}``        ``}``        ``System.out.println();``    ``}``}`` ` `// Driver code``class` `GFG ``{``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int``[] arr = { ``0``, ``1``, ``2``, ``3` `};``        ``int` `r = ``3``;``        ``Combination com = ``new` `Combination(arr, r);``        ``com.GetFirst();``        ``while` `(com.HasNext())``        ``{``            ``com.Next();``        ``}``    ``}``}`` ` `// This code is contributed by Rajput-Ji`

## C#

 `// C# implementation of the approach``using` `System;``namespace` `IterativeCombination {``class` `Combination {`` ` `    ``// Data array for combination``    ``private` `int``[] Indices;`` ` `    ``// Number of elements in the combination``    ``private` `int` `R;`` ` `    ``// The boolean array``    ``private` `bool``[] Flags;`` ` `    ``// Starting index of the 1st tract of trues``    ``private` `int` `Start;`` ` `    ``// Ending index of the 1st tract of trues``    ``private` `int` `End;`` ` `    ``// Constructor``    ``public` `Combination(``int``[] arr, ``int` `r)``    ``{``        ``this``.Indices = arr;``        ``this``.R = r;``    ``}`` ` `    ``// Set the 1st r Booleans to true,``    ``// initialize Start and End``    ``public` `void` `GetFirst()``    ``{``        ``Flags = ``new` `bool``[``this``.Indices.Length];`` ` `        ``// Generate the very first combination``        ``for` `(``int` `i = 0; i < ``this``.R; ++i) {``            ``Flags[i] = ``true``;``        ``}`` ` `        ``// Update the starting ending indices``        ``// of trues in the boolean array``        ``this``.Start = 0;``        ``this``.End = ``this``.R - 1;``        ``this``.Output();``    ``}`` ` `    ``// Function that returns true if another``    ``// combination can still be generated``    ``public` `bool` `HasNext()``    ``{``        ``return` `End < (``this``.Indices.Length - 1);``    ``}`` ` `    ``// Function to generate the next combination``    ``public` `void` `Next()``    ``{`` ` `        ``// Only one true in the tract``        ``if` `(``this``.Start == ``this``.End) {``            ``this``.Flags[``this``.End] = ``false``;``            ``this``.Flags[``this``.End + 1] = ``true``;``            ``this``.Start += 1;``            ``this``.End += 1;``            ``while` `(``this``.End + 1 < ``this``.Indices.Length``                   ``&& ``this``.Flags[``this``.End + 1]) {``                ``++``this``.End;``            ``}``        ``}``        ``else` `{`` ` `            ``// Move the End and reset the End``            ``if` `(``this``.Start == 0) {``                ``Flags[``this``.End] = ``false``;``                ``Flags[``this``.End + 1] = ``true``;``                ``this``.End -= 1;``            ``}``            ``else` `{``                ``Flags[``this``.End + 1] = ``true``;`` ` `                ``// Set all the values to false starting from``                ``// index Start and ending at index End``                ``// in the boolean array``                ``for` `(``int` `i = ``this``.Start; i <= ``this``.End; ++i) {``                    ``Flags[i] = ``false``;``                ``}`` ` `                ``// Set the beginning elements to true``                ``for` `(``int` `i = 0; i < ``this``.End - ``this``.Start; ++i) {``                    ``Flags[i] = ``true``;``                ``}`` ` `                ``// Reset the End``                ``this``.End = ``this``.End - ``this``.Start - 1;``                ``this``.Start = 0;``            ``}``        ``}``        ``this``.Output();``    ``}`` ` `    ``// Function to print the combination generated previouslt``    ``private` `void` `Output()``    ``{``        ``for` `(``int` `i = 0, count = 0; i < Indices.Length``                                   ``&& count < ``this``.R;``             ``++i) {`` ` `            ``// If current index is set to true in the boolean array``            ``// then element at current index in the original array``            ``// is part of the combination generated previously``            ``if` `(Flags[i]) {``                ``Console.Write(Indices[i]);``                ``Console.Write(``" "``);``                ``++count;``            ``}``        ``}``        ``Console.WriteLine();``    ``}``}`` ` `// Driver code``class` `AppDriver {``    ``static` `void` `Main()``    ``{``        ``int``[] arr = { 0, 1, 2, 3 };``        ``int` `r = 3;``        ``Combination com = ``new` `Combination(arr, r);``        ``com.GetFirst();``        ``while` `(com.HasNext()) {``            ``com.Next();``        ``}``    ``}``}``}`
Output:
```0 1 2
0 1 3
0 2 3
1 2 3
```

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