Recursively print all sentences that can be formed from list of word lists

Given a list of word lists How to print all sentences possible taking one word from a list at a time via recursion? 

Example: 

Input: {{"you", "we"},
        {"have", "are"},
        {"sleep", "eat", "drink"}}

Output:
  you have sleep
  you have eat
  you have drink
  you are sleep
  you are eat
  you are drink
  we have sleep
  we have eat
  we have drink
  we are sleep
  we are eat
  we are drink 

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The idea is based on a simple depth-first traversal. We start from every word of the first list as the first word of an output sentence, then recur for the remaining lists.

Below is the C++ implementation of the above idea. In the below implementation, the input list of the list is considered as a 2D array. If we take a closer look, we can observe that the code is very close to the DFS of graph.

C++

// C++ program to print all possible sentences from a list of word list
#include <iostream>
#include <string>

#define R 3
#define C 3
using namespace std;

// A recursive function to print all possible sentences that can be formed
// from a list of word list
void printUtil(string arr[R][C], int m, int n, string output[R])
{
    // Add current word to output array
    output[m] = arr[m][n];

    // If this is last word of current output sentence, then print
    // the output sentence
    if (m==R-1)
    {
        for (int i=0; i<R; i++)
           cout << output[i] << " ";
        cout << endl;
        return;
    }

    // Recur for next row
    for (int i=0; i<C; i++)
       if (arr[m+1][i] != "")
          printUtil(arr, m+1, i, output);
}

// A wrapper over printUtil()
void print(string arr[R][C])
{
   // Create an array to store sentence
   string output[R];

   // Consider all words for first row as starting points and
   // print all sentences
   for (int i=0; i<C; i++)
     if (arr[0][i] != "")
        printUtil(arr, 0, i, output);
}

// Driver program to test above functions
int main()
{
   string arr[R][C]  = {{"you", "we"},
                        {"have", "are"},
                        {"sleep", "eat", "drink"}};

   print(arr);

   return 0;
}

Java

// Java program to print
// all possible sentences
// from a list of word list
import java.io.*;
class GFG{

static final int R= 3;
static final int C =3;

// A recursive function to
// print all possible sentences
// that can be formed
// from a list of word list
static void printUtil(String [][]arr,
                      int m, int n,
                      String []output)
{
  // Add current word to output array
  output[m] = arr[m][n];

  // If this is last word of
  // current output sentence,
  // then print the output sentence
  if (m == R - 1)
  {
    for (int i = 0; i < R; i++)
      System.out.print(output[i] + " ");
    System.out.println();
    return;
  }

  // Recur for next row
  for (int i = 0; i < C; i++)
    if (arr[m + 1][i] != "" && m < C)
      printUtil(arr, m + 1, i, output);
}

// A wrapper over printUtil()
static void print(String [][]arr)
{
  // Create an array to store sentence
  String []output = new String[R];

  // Consider all words for first
  // row as starting points and
  // print all sentences
  for (int i = 0; i < C; i++)
    if (arr[0][i] != "")
      printUtil(arr, 0, i, output);
}

// Driver program to test above functions
public static void main(String[] args)
{
  String [][]arr  = {{"you", "we", ""},
                     {"have", "are", ""},
                     {"sleep", "eat", "drink"}};
  print(arr);
}
}

// This code is contributed by gauravrajput1

Python3

# Python program recursively print all sentences that can be
# formed from list of word lists
R = 3
C = 3

# A recursive function to print all possible sentences that can
# be formed from a list of word list
def printUtil(arr, m, n, output):

    # Add current word to output array
    output[m] = arr[m][n]

    # If this is last word of current output sentence, then print
    # the output sentence
    if m==R-1:
        for i in range(R):
            print (output[i],end= " ")
        print()
        return

    # Recur for next row
    for i in range(C):
        if arr[m+1][i] != "":
            printUtil(arr, m+1, i, output)

# A wrapper over printUtil
def printf(arr):

    # Create an array to store sentence
    output = [""] * R

    # Consider all words for first row as starting
    #  points and print all sentences
    for i in range(C):
        if arr[0][i] != "":
            printUtil(arr, 0, i, output)

# Driver program
arr = [ ["you", "we",""],
        ["have", "are",""],
        ["sleep", "eat", "drink"]]
printf(arr)
# This code is contributed by Bhavya Jain

C#

// C# program to print
// all possible sentences
// from a list of word list
using System;
class GFG{

static readonly int R= 3;
static readonly int C =3;

// A recursive function to
// print all possible sentences
// that can be formed
// from a list of word list
static void printUtil(String [,]arr,
                      int m, int n,
                      String []output)
{
  // Add current word to output array
  output[m] = arr[m, n];

  // If this is last word of
  // current output sentence,
  // then print the output sentence
  if (m == R - 1)
  {
    for (int i = 0; i < R; i++)
      Console.Write(output[i] + " ");
    Console.WriteLine();
    return;
  }

  // Recur for next row
  for (int i = 0; i < C; i++)
    if (arr[m + 1, i] != "" && m < C)
      printUtil(arr, m + 1, i, output);
}

// A wrapper over printUtil()
static void print(String [,]arr)
{
  // Create an array to store sentence
  String []output = new String[R];

  // Consider all words for first
  // row as starting points and
  // print all sentences
  for (int i = 0; i < C; i++)
    if (arr[0, i] != "")
      printUtil(arr, 0, i, output);
}

// Driver program to test above functions
public static void Main(String[] args)
{
  String [,]arr  = {{"you", "we", ""},
                    {"have", "are", ""},
                    {"sleep", "eat", "drink"}};
  print(arr);
}
}

// This code is contributed by gauravrajput1

Javascript

<script>

// JavaScript program recursively print all sentences that can be
// formed from list of word lists
const R = 3
const C = 3

// A recursive function to print all possible sentences that can
// be formed from a list of word list
function printUtil(arr, m, n, output){

    // Add current word to output array
    output[m] = arr[m][n]

    // If this is last word of current output sentence, then print
    // the output sentence
    if(m == R - 1){
        for(let i = 0; i < R; i++)
            document.write(output[i]," ")
        document.write("</br>")
        return
    }

    // Recur for next row
    for(let i = 0; i < C; i++){
        if(arr[m+1][i] != "")
            printUtil(arr, m+1, i, output)
    }
}

// A wrapper over printUtil
function printf(arr){

    // Create an array to store sentence
    let output = new Array(R).fill("")

    // Consider all words for first row as starting
    //  points and print all sentences
    for(let i = 0; i < C; i++){
        if(arr[0][i] != "")
            printUtil(arr, 0, i, output)
    }
}

// Driver program
let arr = [ ["you", "we",""],
        ["have", "are",""],
        ["sleep", "eat", "drink"]]
printf(arr)

// This code is contributed by shinjanpatra

</script>

Output

you have sleep 
you have eat 
you have drink 
you are sleep 
you are eat 
you are drink 
we have sleep 
we have eat 
we have drink 
we are sleep 
we are eat 
we are drink 

Time Complexity: O(n^m)

Where n is the number of words in the array and m is the number of rows.

Space Complexity: O(m)

Where m is the number of rows. We need an array of size m to store the output sentences.