Minimum Word Break - GeeksforGeeks

Given a string s, break s such that every substring of the partition can be found in the dictionary. Return the minimum break needed.
Examples:

Given a dictionary ["Cat", "Mat", "Ca", 
     "tM", "at", "C", "Dog", "og", "Do"]

Input :  Pattern "CatMat"
Output : 1 
Explanation: we can break the sentences
in three ways, as follows:
CatMat = [ Cat Mat ]  break 1
CatMat = [ Ca tM at ] break 2
CatMat = [ C at Mat ] break 2  so the 
         output is: 1

Input : Dogcat
Output : 1

Asked in: Facebook

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

Solution of this problem is based on the WordBreak Trie solution and level ordered graph. We start traversing given pattern and start finding a character of pattern in a trie. If we reach a node(leaf) of a trie from where we can traverse a new word of a trie(dictionary), we increment level by one and call search function for rest of the pattern character in a trie. In the end, we return minimum Break.

  MinBreak(Trie, key, level, start = 0 )
  ....  If start == key.length()
      ...update min_break
  for i = start to keylenght 
  ....If we found a leaf node in trie 
        MinBreak( Trie, key, level+1, i )

Below is the implementation of above idea

C++

// C++ program to find minimum breaks needed 
// to break a string in dictionary words. 
#include <bits/stdc++.h> 
using namespace std; 
  
const int ALPHABET_SIZE = 26; 
  
// trie node 
struct TrieNode { 
    struct TrieNode* children[ALPHABET_SIZE]; 
  
    // isEndOfWord is true if the node  
    // represents end of a word 
    bool isEndOfWord; 
}; 
  
// Returns new trie node (initialized to NULLs) 
struct TrieNode* getNode(void) 
{ 
    struct TrieNode* pNode = new TrieNode; 
  
    pNode->isEndOfWord = false; 
  
    for (int i = 0; i < ALPHABET_SIZE; i++) 
        pNode->children[i] = NULL; 
  
    return pNode; 
} 
  
// If not present, inserts the key into the trie 
// If the key is the prefix of trie node, just 
// marks leaf node 
void insert(struct TrieNode* root, string key) 
{ 
    struct TrieNode* pCrawl = root; 
  
    for (int i = 0; i < key.length(); i++) { 
        int index = key[i] - 'a'; 
        if (!pCrawl->children[index]) 
            pCrawl->children[index] = getNode(); 
  
        pCrawl = pCrawl->children[index]; 
    } 
  
    // mark last node as leaf 
    pCrawl->isEndOfWord = true; 
} 
  
// function break the string into minimum cut 
// such the every substring after breaking  
// in the dictionary. 
void minWordBreak(struct TrieNode* root,  
          string key, int start, int* min_Break,  
                                 int level = 0) 
{ 
    struct TrieNode* pCrawl = root; 
  
    // base case, update minimum Break 
    if (start == key.length()) {         
        *min_Break = min(*min_Break, level - 1); 
        return; 
    } 
  
    // traverse given key(pattern) 
    int minBreak = 0;    
    for (int i = start; i < key.length(); i++) { 
        int index = key[i] - 'a'; 
        if (!pCrawl->children[index]) 
            return; 
  
        // if we find a condition were we can  
        // move to the next word in a trie 
        // dictionary 
        if (pCrawl->children[index]->isEndOfWord) 
            minWordBreak(root, key, i + 1, 
                           min_Break, level + 1); 
  
        pCrawl = pCrawl->children[index]; 
    } 
} 
  
// Driver program to test above functions 
int main() 
{ 
    string dictionary[] = { "Cat", "Mat", 
   "Ca", "Ma", "at", "C", "Dog", "og", "Do" }; 
    int n = sizeof(dictionary) / sizeof(dictionary[0]); 
    struct TrieNode* root = getNode(); 
  
    // Construct trie 
    for (int i = 0; i < n; i++) 
        insert(root, dictionary[i]); 
    int min_Break = INT_MAX; 
  
    minWordBreak(root, "CatMatat", 0, &min_Break, 0); 
    cout << min_Break << endl; 
    return 0; 
} 

Java

// Java program to find minimum breaks needed 
// to break a string in dictionary words. 
public class Trie { 
  
TrieNode root = new TrieNode(); 
int minWordBreak = Integer.MAX_VALUE; 
  
    // Trie node 
    class TrieNode { 
        boolean endOfTree; 
        TrieNode children[] = new TrieNode[26]; 
        TrieNode(){ 
            endOfTree = false; 
            for(int i=0;i<26;i++){ 
                children[i]=null; 
            } 
        } 
    } 
  
    // If not present, inserts a key into the trie 
    // If the key is the prefix of trie node, just 
    // marks leaf node 
    void insert(String key){ 
        int length = key.length(); 
  
        int index; 
  
        TrieNode pcrawl = root; 
  
        for(int i = 0; i < length; i++) 
        { 
            index = key.charAt(i)- 'a'; 
  
            if(pcrawl.children[index] == null) 
                pcrawl.children[index] = new TrieNode(); 
  
            pcrawl = pcrawl.children[index]; 
        } 
          
        // mark last node as leaf 
        pcrawl.endOfTree = true; 
  
    } 
  
    // function break the string into minimum cut 
    // such the every substring after breaking  
    // in the dictionary. 
    void minWordBreak(String key) 
    { 
        minWordBreak = Integer.MAX_VALUE; 
          
        minWordBreakUtil(root, key, 0, Integer.MAX_VALUE, 0); 
    } 
      
    void minWordBreakUtil(TrieNode node, String key, 
                int start, int min_Break, int level) 
    { 
        TrieNode pCrawl = node; 
  
        // base case, update minimum Break 
        if (start == key.length()) { 
            min_Break = Math.min(min_Break, level - 1); 
            if(min_Break<minWordBreak){ 
                minWordBreak = min_Break; 
            } 
            return; 
        } 
  
        // traverse given key(pattern) 
        for (int i = start; i < key.length(); i++) { 
            int index = key.charAt(i) - 'a'; 
            if (pCrawl.children[index]==null) 
                return; 
  
            // if we find a condition were we can 
            // move to the next word in a trie 
            // dictionary 
            if (pCrawl.children[index].endOfTree) { 
                minWordBreakUtil(root, key, i + 1, 
                        min_Break, level + 1); 
  
            } 
            pCrawl = pCrawl.children[index]; 
        } 
    } 
  
    // Driver code 
    public static void main(String[] args) 
    { 
        String keys[] = {"cat", "mat", "ca", "ma", 
                    "at", "c", "dog", "og", "do" }; 
  
        Trie trie = new Trie(); 
  
        // Construct trie 
          
        int i; 
        for (i = 0; i < keys.length ; i++) 
            trie.insert(keys[i]); 
          
        trie.minWordBreak("catmatat"); 
  
        System.out.println(trie.minWordBreak); 
    } 
} 
  
// This code is contributed by Pavan Koli. 

C#

// C# program to find minimum breaks needed  
// to break a string in dictionary words. 
using System;  
  
class Trie 
{  
  
    TrieNode root = new TrieNode();  
    int minWordBreak = int.MaxValue ;  
  
    // Trie node  
    public class TrieNode  
    {  
        public bool endOfTree;  
        public TrieNode []children = new TrieNode[26];  
        public TrieNode() 
        {  
            endOfTree = false;  
            for(int i = 0; i < 26; i++) 
            {  
                children[i] = null;  
            }  
        }  
    }  
  
    // If not present, inserts a key  
    // into the trie If the key is the  
    // prefix of trie node, just marks leaf node  
    void insert(String key) 
    {  
        int length = key.Length;  
  
        int index;  
  
        TrieNode pcrawl = root;  
  
        for(int i = 0; i < length; i++)  
        {  
            index = key[i]- 'a';  
  
            if(pcrawl.children[index] == null)  
                pcrawl.children[index] = new TrieNode();  
  
            pcrawl = pcrawl.children[index];  
        }  
          
        // mark last node as leaf  
        pcrawl.endOfTree = true;  
  
    }  
  
    // function break the string into minimum cut  
    // such the every substring after breaking  
    // in the dictionary.  
    void minWordBreaks(String key)  
    {  
        minWordBreak = int.MaxValue;  
        minWordBreakUtil(root, key, 0, int.MaxValue, 0);  
    }  
      
    void minWordBreakUtil(TrieNode node, String key,  
                int start, int min_Break, int level)  
    {  
        TrieNode pCrawl = node;  
  
        // base case, update minimum Break  
        if (start == key.Length)  
        {  
            min_Break = Math.Min(min_Break, level - 1);  
            if(min_Break < minWordBreak) 
            {  
                minWordBreak = min_Break;  
            }  
            return;  
        }  
  
        // traverse given key(pattern)  
        for (int i = start; i < key.Length; i++)  
        {  
            int index = key[i] - 'a';  
            if (pCrawl.children[index]==null)  
                return;  
  
            // if we find a condition were we can  
            // move to the next word in a trie  
            // dictionary  
            if (pCrawl.children[index].endOfTree)  
            {  
                minWordBreakUtil(root, key, i + 1,  
                        min_Break, level + 1);  
            }  
            pCrawl = pCrawl.children[index];  
        }  
    }  
  
    // Driver code  
    public static void Main(String[] args)  
    {  
        String []keys = {"cat", "mat", "ca", "ma",  
                    "at", "c", "dog", "og", "do" };  
  
        Trie trie = new Trie();  
  
        // Construct trie  
        int i;  
        for (i = 0; i < keys.Length ; i++)  
            trie.insert(keys[i]);  
          
        trie.minWordBreaks("catmatat");  
        Console.WriteLine(trie.minWordBreak);  
    }  
}  
  
// This code is contributed by 29AjayKumar 

Output:

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C++

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