# Minimum Word Break

• Difficulty Level : Expert
• Last Updated : 09 Jul, 2021

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```

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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 ``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);``    ``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

## 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;``        ``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`

## Javascript

 ``
Output:
`2`

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