Given two strings A and B, the task is to split the string A into the minimum number of substrings such that each substring is in the string B.
Note: If there is no way to split the string, then print -1
Examples:
Input: A = “abcdab”, B = “dabc”
Output: 2
Explanation:
The two substrings of A which is also present in B are –
{“abc”, “dab”}Input: A = “abcde”, B = “edcb”
Output: -1
Explanation:
There is no way to split the string A into substring
Such that each string is also present in the B.
Approach:
- Construct a trie of every substring of B.
- After that, we’ll use Dynamic programming to find the minimum number of parts to break the string A such that every part is a substring of B.
Recurrence Relation in Dynamic Programming:
dp[i] = minimum number of parts to break the string A up to ith prefix.
dp[0] = 0 for i in {0, S1.length} for j in {i, S1.length} if(S1[i, ... j] is found in trie dp[j] = min(dp[j], dp[i] + 1); else break; dp[S1.length] is the minimum number of parts.
Below is the implementation of the above approach:
C++
// C++ implementation to split the // string into minimum number of // parts such that each part is also // present in the another string #include <bits/stdc++.h> using namespace std; const int INF = 1e9 + 9; // Node of Trie struct TrieNode { TrieNode* child[26] = { NULL }; }; // Function to insert a node in the // Trie Data Structure void insert( int idx, string& s, TrieNode* root) { TrieNode* temp = root; for ( int i = idx; i < s.length(); i++) { // Inserting every character from idx // till end to string into trie if (temp->child[s[i] - 'a' ] == NULL) // if there is no edge corresponding // to the ith character, // then make a new node temp->child[s[i] - 'a' ] = new TrieNode; temp = temp->child[s[i] - 'a' ]; } } // Function to find the minimum // number of parts such that each // part is present into another string int minCuts(string S1, string S2) { int n1 = S1.length(); int n2 = S2.length(); // Making a new trie TrieNode* root = new TrieNode; for ( int i = 0; i < n2; i++) { // Inserting every substring // of S2 in trie insert(i, S2, root); } // Creating dp array and // init it with infinity vector< int > dp(n1 + 1, INF); // Base Case dp[0] = 0; for ( int i = 0; i < n1; i++) { // Starting the cut from ith character // taking temporary node pointer // for checking whether the substring // [i, j) is present in trie of not TrieNode* temp = root; for ( int j = i + 1; j <= n1; j++) { if (temp->child[S1[j - 1] - 'a' ] == NULL) // if the jth character is not in trie // we'll break break ; // Updating the ending of // jth character with dp[i] + 1 dp[j] = min(dp[j], dp[i] + 1); // Descending the trie pointer temp = temp->child[S1[j - 1] - 'a' ]; } } // Answer not possible if (dp[n1] >= INF) return -1; else return dp[n1]; } // Driver Code int main() { string S1 = "abcdab" ; string S2 = "dabc" ; cout << minCuts(S1, S2); } |
Java
// Java implementation to split the // String into minimum number of // parts such that each part is also // present in the another String import java.util.*; class GFG{ static int INF = ( int )(1e9 + 9 ); // Node of Trie static class TrieNode { TrieNode []child = new TrieNode[ 26 ]; }; // Function to insert a node in the // Trie Data Structure static void insert( int idx, String s, TrieNode root) { TrieNode temp = root; for ( int i = idx; i < s.length(); i++) { // Inserting every character from idx // till end to String into trie if (temp.child[s.charAt(i) - 'a' ] == null ) // If there is no edge corresponding // to the ith character, // then make a new node temp.child[s.charAt(i) - 'a' ] = new TrieNode(); temp = temp.child[s.charAt(i) - 'a' ]; } } // Function to find the minimum // number of parts such that each // part is present into another String static int minCuts(String S1, String S2) { int n1 = S1.length(); int n2 = S2.length(); // Making a new trie TrieNode root = new TrieNode(); for ( int i = 0 ; i < n2; i++) { // Inserting every subString // of S2 in trie insert(i, S2, root); } // Creating dp array and // init it with infinity int []dp = new int [n1 + 1 ]; Arrays.fill(dp, INF); // Base Case dp[ 0 ] = 0 ; for ( int i = 0 ; i < n1; i++) { // Starting the cut from ith character // taking temporary node pointer // for checking whether the subString // [i, j) is present in trie of not TrieNode temp = root; for ( int j = i + 1 ; j <= n1; j++) { if (temp.child[S1.charAt(j - 1 ) - 'a' ] == null ) // If the jth character is not in trie // we'll break break ; // Updating the ending of // jth character with dp[i] + 1 dp[j] = Math.min(dp[j], dp[i] + 1 ); // Descending the trie pointer temp = temp.child[S1.charAt(j - 1 ) - 'a' ]; } } // Answer not possible if (dp[n1] >= INF) return - 1 ; else return dp[n1]; } // Driver Code public static void main(String[] args) { String S1 = "abcdab" ; String S2 = "dabc" ; System.out.print(minCuts(S1, S2)); } } // This code is contributed by Rajput-Ji |
Python3
# Python3 implementation to split the # string into minimum number of # parts such that each part is also # present in the another string INF = 1e9 + 9 # Node of Trie class TrieNode(): def __init__( self ): self .child = [ None ] * 26 # Function to insert a node in the # Trie Data Structure def insert(idx, s, root): temp = root for i in range (idx, len (s)): # Inserting every character from idx # till end to string into trie if temp.child[ ord (s[i]) - ord ( 'a' )] = = None : # If there is no edge corresponding # to the ith character, # then make a new node temp.child[ ord (s[i]) - ord ( 'a' )] = TrieNode() temp = temp.child[ ord (s[i]) - ord ( 'a' )] # Function to find the minimum # number of parts such that each # part is present into another string def minCuts(S1, S2): n1 = len (S1) n2 = len (S2) # Making a new trie root = TrieNode() for i in range (n2): # Inserting every substring # of S2 in trie insert(i, S2, root) # Creating dp array and # init it with infinity dp = [INF] * (n1 + 1 ) # Base Case dp[ 0 ] = 0 for i in range (n1): # Starting the cut from ith character # taking temporary node pointer # for checking whether the substring # [i, j) is present in trie of not temp = root for j in range (i + 1 , n1 + 1 ): if temp.child[ ord (S1[j - 1 ]) - ord ( 'a' )] = = None : # If the jth character is not # in trie we'll break break # Updating the ending of # jth character with dp[i] + 1 dp[j] = min (dp[j], dp[i] + 1 ) # Descending the trie pointer temp = temp.child[ ord (S1[j - 1 ]) - ord ( 'a' )] # Answer not possible if dp[n1] > = INF: return - 1 else : return dp[n1] # Driver Code S1 = "abcdab" S2 = "dabc" print (minCuts(S1, S2)) # This code is contributed by Shivam Singh |
C#
// C# implementation to split the // String into minimum number of // parts such that each part is also // present in the another String using System; class GFG{ static int INF = ( int )(1e9 + 9); // Node of Trie class TrieNode { public TrieNode []child = new TrieNode[26]; }; // Function to insert a node in the // Trie Data Structure static void insert( int idx, String s, TrieNode root) { TrieNode temp = root; for ( int i = idx; i < s.Length; i++) { // Inserting every character from idx // till end to String into trie if (temp.child[s[i] - 'a' ] == null ) // If there is no edge corresponding // to the ith character, // then make a new node temp.child[s[i] - 'a' ] = new TrieNode(); temp = temp.child[s[i] - 'a' ]; } } // Function to find the minimum // number of parts such that each // part is present into another String static int minCuts(String S1, String S2) { int n1 = S1.Length; int n2 = S2.Length; // Making a new trie TrieNode root = new TrieNode(); for ( int i = 0; i < n2; i++) { // Inserting every subString // of S2 in trie insert(i, S2, root); } // Creating dp array and // init it with infinity int []dp = new int [n1 + 1]; for ( int i = 0; i <= n1; i++) dp[i] = INF; // Base Case dp[0] = 0; for ( int i = 0; i < n1; i++) { // Starting the cut from ith character // taking temporary node pointer // for checking whether the subString // [i, j) is present in trie of not TrieNode temp = root; for ( int j = i + 1; j <= n1; j++) { if (temp.child[S1[j-1] - 'a' ] == null ) // If the jth character is not in trie // we'll break break ; // Updating the ending of // jth character with dp[i] + 1 dp[j] = Math.Min(dp[j], dp[i] + 1); // Descending the trie pointer temp = temp.child[S1[j - 1] - 'a' ]; } } // Answer not possible if (dp[n1] >= INF) return -1; else return dp[n1]; } // Driver Code public static void Main(String[] args) { String S1 = "abcdab" ; String S2 = "dabc" ; Console.Write(minCuts(S1, S2)); } } // This code is contributed by shikhasingrajput |
Javascript
<script> // Javascript implementation to split the // String into minimum number of // parts such that each part is also // present in the another String let INF = (1e9 + 9); // Node of Trie class Node { constructor() { } } function TrieNode() { let temp = new Node(); temp.child = new Node(26); for (let i = 0; i < 26; i++) { temp.child[i] = null ; } return temp; } // Function to insert a node in the // Trie Data Structure function insert(idx, s, root) { let temp = root; for (let i = idx; i < s.length; i++) { // Inserting every character from idx // till end to String into trie if (temp.child[s[i].charCodeAt() - 'a' .charCodeAt()] == null ) // If there is no edge corresponding // to the ith character, // then make a new node temp.child[s[i].charCodeAt() - 'a' .charCodeAt()] = new TrieNode(); temp = temp.child[s[i].charCodeAt() - 'a' .charCodeAt()]; } } // Function to find the minimum // number of parts such that each // part is present into another String function minCuts(S1, S2) { let n1 = S1.length; let n2 = S2.length; // Making a new trie let root = new TrieNode(); for (let i = 0; i < n2; i++) { // Inserting every subString // of S2 in trie insert(i, S2, root); } // Creating dp array and // init it with infinity let dp = new Array(n1 + 1); dp.fill(INF); // Base Case dp[0] = 0; for (let i = 0; i < n1; i++) { // Starting the cut from ith character // taking temporary node pointer // for checking whether the subString // [i, j) is present in trie of not let temp = root; for (let j = i + 1; j <= n1; j++) { if (temp.child[S1[j - 1].charCodeAt() - 'a' .charCodeAt()] == null ) // If the jth character is not in trie // we'll break break ; // Updating the ending of // jth character with dp[i] + 1 dp[j] = Math.min(dp[j], dp[i] + 1); // Descending the trie pointer temp = temp.child[S1[j - 1].charCodeAt() - 'a'.charCodeAt()]; } } // Answer not possible if (dp[n1] >= INF) return -1; else return dp[n1]; } let S1 = "abcdab" ; let S2 = "dabc" ; document.write(minCuts(S1, S2)); // This code is contributed by mukesh07. </script> |
2
Time complexity: O(|S1||S2|^2) where |S1| and |S2| are the lengths of S1 and S2, respectively.
Auxiliary Space: The space complexity of the program is dominated by the size of the Trie data structure. In the worst case, the size of the Trie will be proportional to the size of S2. So, the space complexity of the program is O(|S2|)
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