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Word Break Problem | DP-32 | Set – 2

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  • Difficulty Level : Hard
  • Last Updated : 22 Jun, 2022

Given a non-empty sequence S and a dictionary dict[] containing a list of non-empty words, print all possible ways to break the sentence in individual dictionary words.
Examples: 
 

Input: S = “catsanddog” 
dict[] = {“cat”, “cats”, “and”, “sand”, “dog”} 
Output: 
“cats and dog” 
“cat sand dog”
Input: S = “pineapplepenapple” 
dict[] = {“apple”, “pen”, “applepen”, “pine”, “pineapple”} 
Output: 
“pine apple pen apple” 
“pineapple pen apple” 
“pine applepen apple” 
 

 

A similar problem to this is discussed in this article, where the task is to check that is there any solution such that the sequence can be broken into the dictionary words.
Approach: The idea is to check for every substring starting from any position I , such that it ends at the length of the string which is present in the dictionary then simply recurse for the substring [0, I]. Meanwhile, store the overlapping subproblems for each substring to avoid the computation of the subproblem again. Overlapping subproblems can be shown as follows – 
 

Below is the implementation of the above approach: 
 

C++




// C++ implementation to break
// a sequence into the words of
// the dictionary
 
#include <bits/stdc++.h>
 
using namespace std;
 
// Unordered_map used for storing
// the sentences the key string
// can be broken into
unordered_map<string,
            vector<string> > mp;
 
// Unordered_set used
// to store the dictionary.
unordered_set<string> dict;
 
// Utility function used for
// printing the obtained result
void printResult(vector<string> A)
{
    for (int i = 0; i < A.size(); i++)
        cout << A[i] << '\n';
}
 
// Utility function for
// appending new words
// to already existing strings
vector<string> combine(
     vector<string> prev, string word){
     
    // Loop to find the append string
    // which can be broken into
    for (int i = 0; i < prev.size(); i++) {
        prev[i] += " " + word;
    }
    return prev;
}
 
// Utility function for word Break
vector<string> wordBreakUtil(string s)
{  
    // Condition to check if the
    // subproblem is already computed
    if (mp.find(s) != mp.end())
        return mp[s];
    vector<string> res;
     
    // If the whole word is a dictionary
    // word then directly append into
    // the result array for the string
    if (dict.find(s) != dict.end())
        res.push_back(s);
     
    // Loop to iterate over the substring
    for (int i = 1; i < s.length(); i++) {
        string word = s.substr(i);
         
        // If the substring is present into
        // the dictionary then recurse for
        // other substring of the string
        if (dict.find(word) != dict.end()) {
            string rem = s.substr(0, i);
            vector<string> prev =
             combine(wordBreakUtil(rem), word);
            res.insert(res.end(),
                 prev.begin(), prev.end());
        }
    }
     
    // Store the subproblem
    // into the map
    mp[s] = res;
    return res;
}
 
// Master wordBreak function converts
// the string vector to unordered_set
vector<string> wordBreak(string s,
             vector<string>& wordDict)
{
    // Clear the previous stored data
    mp.clear();
    dict.clear();
    dict.insert(wordDict.begin(), wordDict.end());
    return wordBreakUtil(s);
}
 
// Driver Code
int main()
{
    vector<string> wordDict1 = {
        "cat", "cats", "and", "sand", "dog" };
    printResult(wordBreak("catsanddog", wordDict1));
    return 0;
}

Java




import java.util.*;
import java.io.*;
 
// Java program for the above approach
class GFG{
 
  // Unordered_map used for storing
  // the sentences the key String
  // can be broken into
  static TreeMap<String, ArrayList<String>> mp =
    new TreeMap<String, ArrayList<String>>();
 
  // Unordered_set used
  // to store the dictionary.
  static TreeSet<String> dict = new TreeSet<String>();
 
  // Utility function used for
  // printing the obtained result
  static void printResult(ArrayList<String> A)
  {
    for (int i = 0 ; i < A.size() ; i++){
      System.out.println(A.get(i));
    }
  }
 
  // Utility function for
  // appending new words
  // to already existing strings
  static ArrayList<String> combine(ArrayList<String> prev, String word){
 
    // Loop to find the append String
    // which can be broken into
    for (int i = 0 ; i < prev.size() ; i++) {
      prev.set(i, prev.get(i) + " " + word);
    }
    return prev;
  }
 
  // Utility function for word Break
  static ArrayList<String> wordBreakUtil(String s)
  {
 
    // Condition to check if the
    // subproblem is already computed
    if (mp.containsKey(s)){
      return mp.get(s);
    }
    ArrayList<String> res = new ArrayList<String>();
 
    // If the whole word is a dictionary
    // word then directly append into
    // the result array for the String
    if (dict.contains(s))
      res.add(s);
 
    // Loop to iterate over the substring
    for (int i = 1 ; i < s.length() ; i++) {
      String word = s.substring(i);
 
      // If the substring is present into
      // the dictionary then recurse for
      // other substring of the String
      if (dict.contains(word)) {
        String rem = s.substring(0, i);
        ArrayList<String> prev =  combine(wordBreakUtil(rem), word);
        for(int j = 0 ; j < prev.size() ; j++){
          res.add(prev.get(j));
        }
      }
    }
 
    // Store the subproblem
    // into the map
    mp.put(s, res);
    return res;
  }
 
  // Master wordBreak function converts
  // the String vector to unordered_set
  static ArrayList<String> wordBreak(String s, ArrayList<String> wordDict)
  {
    // Clear the previous stored data
    mp.clear();
    dict.clear();
    dict.addAll(wordDict);
    return wordBreakUtil(s);
  }
 
  // Driver Code
  public static void main(String args[])
  {
    ArrayList<String> wordDict1 = new ArrayList<String>(
      List.of("cat", "cats", "and", "sand", "dog")
    );
    printResult(wordBreak("catsanddog", wordDict1));
  }
}
 
// This code is contributed by subhamgoyal2014.

Python3




# Python3 implementation to break
# a sequence into the words of
# the dictionary
  
# Unordered_map used for storing
# the sentences the key string
# can be broken into
mp = dict()
  
# Unordered_set used
# to store the dictionary.
dict_t = set()
  
# Utility function used for
# printing the obtained result
def printResult(A):
 
    for i in range(len(A)):
        print(A[i])
  
# Utility function for
# appending new words
# to already existing strings
def combine( prev, word):
      
    # Loop to find the append string
    # which can be broken into
    for i in range(len(prev)):
     
        prev[i] += " " + word;
     
    return prev;
 
# Utility function for word Break
def wordBreakUtil(s):
 
    # Condition to check if the
    # subproblem is already computed
    if (s in mp):
        return mp[s];
     
    res = []
      
    # If the whole word is a dictionary
    # word then directly append into
    # the result array for the string
    if (s in dict_t):
        res.append(s);
      
    # Loop to iterate over the substring
    for i in range(1, len(s)):
         
        word = s[i:];
          
        # If the substring is present into
        # the dictionary then recurse for
        # other substring of the string
        if (word in dict_t):
             
            rem = s[:i]
            prev = combine(wordBreakUtil(rem), word);
            for i in prev:
                res.append(i)
      
    # Store the subproblem
    # into the map
    #res is an reference so we need to assign an reference to something if its keep on changing
    #res values changes after it start going through combine method
    #you can check if you had a doubt so here we just clone res
    x=[]
    for i in res:
      x.append(i)
    mp[s] = x;
    return res;
  
# Master wordBreak function converts
# the string vector to unordered_set
def wordBreak(s,  wordDict):
 
    # Clear the previous stored data
    mp.clear();
    dict_t.clear();
    for i in wordDict:
        dict_t.add(i)
    return wordBreakUtil(s);
 
# Driver Code
if __name__=='__main__':
 
    wordDict1 = ["cat", "cats", "and", "sand", "dog" ]
    printResult(wordBreak("catsanddog", wordDict1));
 
# This code is contributed by rutvik_56

Javascript




<script>
 
// JavaScript implementation to break
// a sequence into the words of
// the dictionary
 
// Unordered_map used for storing
// the sentences the key string
// can be broken into
let mp = new Map()
 
// Unordered_set used
// to store the dictionary.
let dict_t = new Set()
 
// Utility function used for
// printing the obtained result
function printResult(A){
 
    for(let i=0;i<A.length;i++)
        document.write(A[i],"</br>")
}
// Utility function for
// pushing new words
// to already existing strings
function combine(prev, word){
     
    // Loop to find the push string
    // which can be broken into
    for (let i=0;i<prev.length;i++)
     
        prev[i] += " " + word;
     
    return prev;
}
// Utility function for word Break
function wordBreakUtil(s){
 
    // Condition to check if the
    // subproblem is already computed
    if (mp.has(s))
        return mp.get(s)
     
    let res = []
     
    // If the whole word is a dictionary
    // word then directly push into
    // the result array for the string
    if (dict_t.has(s))
        res.push(s);
     
    // Loop to iterate over the substring
    for(let i=1;i<s.length;i++){
         
        let word = s.substring(i,)
         
        // If the substring is present into
        // the dictionary then recurse for
        // other substring of the string
        if (dict_t.has(word)){
             
            let rem = s.substring(0,i)
            let prev = combine(wordBreakUtil(rem), word);
            for(let i of prev)
                res.push(i)
        }
    }
     
    // Store the subproblem
    // into the map
    // res is an reference so we need to assign an reference to something if its keep on changing
    // res values changes after it start going through combine method
    // you can check if you had a doubt so here we just clone res
    let x=[]
    for(let i of res)
        x.push(i)
    mp.set(s, x)
    return res
}
 
// Master wordBreak function converts
// the string vector to unordered_set
function wordBreak(s, wordDict){
 
    // Clear the previous stored data
    mp.clear();
    dict_t.clear();
    for(let i of wordDict)
        dict_t.add(i)
    return wordBreakUtil(s);
}
 
// Driver Code
 
let wordDict1 = ["cat", "cats", "and", "sand", "dog" ];
printResult(wordBreak("catsanddog", wordDict1));
 
// This code is contributed by shinjanpatra
 
</script>

Output: 

cat sand dog
cats and dog

 

Time Complexity: O(2^N), where N is the length of the given string.
Auxiliary Space: O(S + N). where S is the sum of all characters of wordDict1.


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