Given a matrix of characters and a pattern, find the orientation of pattern in the matrix. In other words, find if pattern appears in matrix in horizontal or vertical direction. Achieve this in minimum time possible.
Input:
mat[N][N] = { {'a', 'b', 'c', 'd', 'e'},
{'f', 'g', 'h', 'i', 'j'},
{'k', 'l', 'm', 'n', 'o'},
{'p', 'q', 'r', 's', 't'},
{'u', 'v', 'w', 'x', 'y'}};
pattern = "pqrs";
Output: Horizontal
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A simple solution is for each row and column, use Naive pattern searching algorithm to find the orientation of pattern in the matrix. The time complexity of Naive pattern searching algorithm for every row is O(NM) where N is size of the matrix and M is length of the pattern. So, the time complexity of this solution will be O(N*(NM)) as each of N rows and N columns takes O(NM) time.
Can we do better?Â
The idea is to use KMP pattern matching algorithm for each row and column. The KMP matching algorithm improves the worst case to O(N + M). The total cost of a KMP search is linear in the number of characters of string and pattern. For a N x N matrix and pattern of length M, complexity of this solution will be O(N*(N+M)) as each of N rows and N columns will take O(N + M) time.Â
Implementation:
C++
// C++ program for finding orientation of the pattern // using KMP pattern searching algorithm #include<bits/stdc++.h> using namespace std; #define N 5   // Used in KMP Search for preprocessing the pattern void computeLPSArray(char *pat, int M, int *lps) {     // length of the previous longest prefix suffix     int len = 0;     int i = 1;       lps[0] = 0; // lps[0] is always 0       // the loop calculates lps[i] for i = 1 to M-1     while (i < M)     {         if (pat[i] == pat[len])         {             len++;             lps[i++] = len;         }         else // (pat[i] != pat[len])         {             if (len != 0)             {                 // This is tricky. Consider the example                 // AAACAAAA and i = 7.                 len = lps[len - 1];                   // Also, note that we do not increment i here             }             else // if (len == 0)             {                 lps[i++] = 0;             }         }     } }   int KMPSearch(char *pat, char *txt) {     int M = strlen(pat);       // create lps[] that will hold the longest     // prefix suffix values for pattern     int *lps = (int *)malloc(sizeof(int)*M);     int j = 0; // index for pat[]       // Preprocess the pattern (calculate lps[] array)     computeLPSArray(pat, M, lps);       int i = 0; // index for txt[]     while (i < N)     {         if (pat[j] == txt[i])         {             j++;             i++;         }         if (j == M)         {             // return 1 is pattern is found             return 1;         }                   // mismatch after j matches         else if (i < N && pat[j] != txt[i])         {             // Do not match lps[0..lps[j-1]] characters,             // they will match anyway             if (j != 0)                 j = lps[j - 1];             else                i = i + 1;         }     }     free(lps); // to avoid memory leak           // return 0 is pattern is not found     return 0; }   // Function to find orientation of pattern in the matrix // It uses KMP pattern searching algorithm void findOrientation(char mat[][N], char *pat) {     // allocate memory for string containing cols     char *col = (char*) malloc(N);       for (int i = 0; i < N; i++)     {         // search in row i         if (KMPSearch(pat, mat[i]))         {             cout << "Horizontal" << endl;             return;         }           // Construct an array to store i'th column         for (int j = 0; j < N; j++)             col[j] = *(mat[j] + i);           // Search in column i         if (KMPSearch(pat, col))             cout << "Vertical" << endl;     }       // to avoid memory leak     free(col); }   // Driver Code int main() {     char mat[N][N] = {{'a', 'b', 'c', 'd', 'e'},                       {'f', 'g', 'h', 'i', 'j'},                        {'k', 'l', 'm', 'n', 'o'},                       {'p', 'q', 'r', 's', 't'},                       {'u', 'v', 'w', 'x', 'y'}};     char pat[] = "pqrs";       findOrientation(mat, pat);       return 0; }   // This code is contributed by kumar65 |
C
// C program for finding orientation of the pattern // using KMP pattern searching algorithm #include<stdio.h> #include<string.h> #include<stdlib.h> #define N 5   // Used in KMP Search for preprocessing the pattern void computeLPSArray(char *pat, int M, int *lps) {     // length of the previous longest prefix suffix     int len = 0;     int i = 1;       lps[0] = 0; // lps[0] is always 0       // the loop calculates lps[i] for i = 1 to M-1     while (i < M)     {         if (pat[i] == pat[len])         {             len++;             lps[i++] = len;         }         else // (pat[i] != pat[len])         {             if (len != 0)             {                 // This is tricky. Consider the example                 // AAACAAAA and i = 7.                 len = lps[len-1];                   // Also, note that we do not increment i here             }             else // if (len == 0)             {                 lps[i++] = 0;             }         }     } }   int KMPSearch(char *pat, char *txt) {     int M = strlen(pat);       // create lps[] that will hold the longest prefix suffix     // values for pattern     int *lps = (int *)malloc(sizeof(int)*M);     int j = 0; // index for pat[]       // Preprocess the pattern (calculate lps[] array)     computeLPSArray(pat, M, lps);       int i = 0; // index for txt[]     while (i < N)     {         if (pat[j] == txt[i])         {             j++;             i++;         }         if (j == M)         {             // return 1 is pattern is found             return 1;         }         // mismatch after j matches         else if (i < N && pat[j] != txt[i])         {             // Do not match lps[0..lps[j-1]] characters,             // they will match anyway             if (j != 0)                 j = lps[j-1];             else                i = i+1;         }     }     free(lps); // to avoid memory leak     // return 0 is pattern is not found     return 0; }   // Function to find orientation of pattern in the matrix // It uses KMP pattern searching algorithm void findOrientation(char mat[][N], char *pat) {     // allocate memory for string containing cols     char *col = (char*) malloc(N);       for (int i = 0; i < N; i++)     {         // search in row i         if (KMPSearch(pat, mat[i]))         {             printf("Horizontal\n");             return;         }           // Construct an array to store i'th column         for (int j = 0; j < N; j++)             col[j] = *(mat[j] + i);           // Search in column i         if (KMPSearch(pat, col))             printf("Vertical\n");     }       // to avoid memory leak     free(col); }   // Driver program to test above function int main() {     char mat[N][N] =     {         {'a', 'b', 'c', 'd', 'e'},         {'f', 'g', 'h', 'i', 'j'},         {'k', 'l', 'm', 'n', 'o'},         {'p', 'q', 'r', 's', 't'},         {'u', 'v', 'w', 'x', 'y'}       };     char pat[] = "pqrs";       findOrientation(mat, pat);       return 0; } |
Java
// Java program for finding orientation of the pattern  // using KMP pattern searching algorithm import java.io.*; import java.util.*; class GFG {   public static int N = 5;     // Used in KMP Search for preprocessing the pattern    public static void computeLPSArray(char pat[],                                      int M, int lps[])   {       // length of the previous longest prefix suffix     int len = 0;      int i = 1;     lps[0] = 0; // lps[0] is always 0       // the loop calculates lps[i] for i = 1 to M-1     while(i < M)     {       if(pat[i] == pat[len])       {         len++;          lps[i++] = len;       }       else   // (pat[i] != pat[len])        {         if(len != 0)         {             // This is tricky. Consider the example            // AAACAAAA and i = 7.            len = lps[len - 1];             // Also, note that we do not increment i here         }         else   // if (len == 0)         {           lps[i++] = 0;         }       }     }     }   public static int KMPSearch(char pat[], char txt[])   {     int M = pat.length;       // create lps[] that will hold the longest      // prefix suffix values for pattern      int[] lps = new int[M];     int j = 0; // index for pat[]       // Preprocess the pattern (calculate lps[] array)      computeLPSArray(pat, M, lps);       int i = 0; // index for txt[]       while(i < N)     {       if(pat[j] == txt[i])       {         j++;         i++;       }       if(j == M)       {           // return 1 is pattern is found          return 1;       }         // mismatch after j matches        else if(i < N && pat[j] != txt[i])       {           // Do not match lps[0..lps[j-1]] characters,          // they will match anyway          if(j != 0)         {           j = lps[j - 1];           }         else        {           i = i + 1;         }       }     }       // return 0 is pattern is not found     return 0;   }     // Function to find orientation of pattern in the matrix    // It uses KMP pattern searching algorithm            public static void findOrientation(char mat[][], char pat[])   {       // allocate memory for string containing cols     char[] col = new char[N];     for(int i = 0; i < N; i++)     {         // search in row i       if(KMPSearch(pat, mat[i]) == 1)       {         System.out.println("Horizontal");         return;       }         // Construct an array to store i'th column        for(int j = 0; j < N; j++)       {         col[j] = mat[j][i];       }         // Search in column i        if(KMPSearch(pat, col) == 1)       {         System.out.println("Vertical");       }                }   }     // Driver Code   public static void main (String[] args)   {     char[][] mat = {       {'a', 'b', 'c', 'd', 'e'},{'f', 'g', 'h', 'i', 'j'},       {'k', 'l', 'm', 'n', 'o'},{'p', 'q', 'r', 's', 't'},       {'u', 'v', 'w', 'x', 'y'}};     char pat[] = {'p','q','r','s'};     findOrientation(mat, pat);   } }   // This code is contributed by avanitrachhadiya2155 |
Python3
# Python3 program for finding orientation of the pattern # using KMP pattern searching algorithm N = 5  # Used in KMP Search for preprocessing the pattern def computeLPSArray(pat, M, lps):           # length of the previous longest prefix suffix     lenl = 0    i = 1      lps[0] = 0 # lps[0] is always 0       # the loop calculates lps[i] for i = 1 to M-1     while (i < M):         if (pat[i] == pat[lenl]):             lenl += 1            lps[i] = lenl             i += 1        else: # (pat[i] != pat[lenl])             if (lenl != 0) :                                   # This is tricky. Consider the example                 # AAACAAAA and i = 7.                 lenl = lps[lenl - 1]                   # Also, note that we do not increment i here                           # if (lenl == 0)             else:                 lps[i] = 0                i += 1  def KMPSearch(pat, txt):     M = len(pat)       # create lps[] that will hold the longest     # prefix suffix values for pattern     lps = [0] * M     j = 0 # index for pat[]       # Preprocess the pattern (calculate lps[] array)     computeLPSArray(pat, M, lps)       # index for txt[]     i = 0     while (i < N):         if (pat[j] == txt[i]):             j += 1            i += 1        if (j == M):                           # return 1 is pattern is found             return 1          # mismatch after j matches         elif (i < N and pat[j] != txt[i]):                           # Do not match lps[0..lps[j-1]] characters,             # they will match anyway             if (j != 0):                 j = lps[j - 1]             else:                 i = i + 1      # to amemory leak       # return 0 is pattern is not found     return 0  # Function to find orientation of pattern in the matrix # It uses KMP pattern searching algorithm def findOrientation(mat, pat):           # allocate memory for string containing cols     col = ['a'] * (N)       for i in range(N):                   # search in row i         if (KMPSearch(pat, mat[i])):             print("Horizontal")             return          # Construct an array to store i'th column         for j in range(N):             col[j] = mat[j][i]           # Search in column i         if (KMPSearch(pat, col)):             print("Vertical")   # Driver Code mat=[['a', 'b', 'c', 'd', 'e'],     ['f', 'g', 'h', 'i', 'j'],     ['k', 'l', 'm', 'n', 'o'],     ['p', 'q', 'r', 's', 't'],     ['u', 'v', 'w', 'x', 'y']] pat= "pqrs"  findOrientation(mat, pat)   # This code is contributed by Mohit kumar 29 |
C#
// C# program for finding orientation of // the pattern using KMP pattern searching // algorithm using System;   class GFG{       public static int N = 5;   // Used in KMP Search for preprocessing the pattern  public static void computeLPSArray(char[] pat,                                    int M, int[] lps) {           // Length of the previous longest     // prefix suffix     int len = 0;     int i = 1;           // lps[0] is always 0     lps[0] = 0;           // The loop calculates lps[i]     // for i = 1 to M-1     while (i < M)     {         if (pat[i] == pat[len])         {             len++;              lps[i++] = len;         }         else   // (pat[i] != pat[len])          {             if (len != 0)             {                                   // This is tricky. Consider the                 // example AAACAAAA and i = 7.                  len = lps[len - 1];                                   // Also, note that we do not                 // increment i here             }                           // If (len == 0)             else                 {                 lps[i++] = 0;             }         }     } }   public static int KMPSearch(char[] pat, char[] txt) {     int M = pat.Length;           // Create lps[] that will hold the longest      // prefix suffix values for pattern      int[] lps = new int[M];     int j = 0; // index for pat[]           // Preprocess the pattern     // (calculate lps[] array)      computeLPSArray(pat, M, lps);     int i = 0; // index for txt[]           while (i < N)     {         if (pat[j] == txt[i])         {             j++;             i++;         }         if (j == M)         {                           // Return 1 is pattern is found              return 1;         }                   // Mismatch after j matches         else if (i < N && pat[j] != txt[i])         {                           // Do not match lps[0..lps[j-1]]             // characters, they will match anyway             if (j != 0)             {                 j = lps[j - 1];             }             else            {                 i = i + 1;             }         }     }           // Return 0 is pattern is not found     return 0; }   // Function to find orientation of pattern // in the matrix. It uses KMP pattern // searching algorithm public static void findOrientation(char[,] mat,                                    char[] pat) {           // Allocate memory for string     // containing cols     char[] col = new char[N];     for(int i = 0; i < N; i++)     {                   // Allocate memory for string         // containing rows         char[] row = new char[(mat.GetLength(1))];         for(int j = 0; j < mat.GetLength(1); j++)         {             row[j] = mat[i, j];         }                   // Search in row i         if (KMPSearch(pat, row) == 1)         {             Console.WriteLine("Horizontal");             return;         }                   // Construct an array to store         // i'th column         for(int j = 0; j < N; j++)         {             col[j] = mat[j,i];         }                   // Search in column i          if (KMPSearch(pat, col) == 1)         {             Console.WriteLine("Vertical");         }     } }   // Driver Code static public void Main() {     char[,] mat = { { 'a', 'b', 'c', 'd', 'e' },                     { 'f', 'g', 'h', 'i', 'j' },                     { 'k', 'l', 'm', 'n', 'o' },                     { 'p', 'q', 'r', 's', 't' },                     { 'u', 'v', 'w', 'x', 'y' } };     char[] pat = {'p','q','r','s'};           findOrientation(mat, pat); } }   // This code is contributed by rag2127 |
Javascript
<script> // Javascript program for finding orientation of the pattern // using KMP pattern searching algorithm           let N = 5;            // Used in KMP Search for preprocessing the pattern     function computeLPSArray(pat,M,lps)     {         // length of the previous longest prefix suffix     let len = 0;     let i = 1;     lps[0] = 0; // lps[0] is always 0        // the loop calculates lps[i] for i = 1 to M-1     while(i < M)     {       if(pat[i] == pat[len])       {         len++;         lps[i++] = len;       }       else   // (pat[i] != pat[len])       {         if(len != 0)         {              // This is tricky. Consider the example           // AAACAAAA and i = 7.           len = lps[len - 1];              // Also, note that we do not increment i here         }         else   // if (len == 0)         {           lps[i++] = 0;         }       }     }     }           function KMPSearch(pat,txt)     {         let M = pat.length;        // create lps[] that will hold the longest     // prefix suffix values for pattern     let lps = new Array(M);     let j = 0; // index for pat[]        // Preprocess the pattern (calculate lps[] array)     computeLPSArray(pat, M, lps);        let i = 0; // index for txt[]        while(i < N)     {       if(pat[j] == txt[i])       {         j++;         i++;       }       if(j == M)       {            // return 1 is pattern is found         return 1;       }          // mismatch after j matches       else if(i < N && pat[j] != txt[i])       {            // Do not match lps[0..lps[j-1]] characters,         // they will match anyway         if(j != 0)         {           j = lps[j - 1];            }         else        {           i = i + 1;         }       }     }        // return 0 is pattern is not found     return 0;     }           // Function to find orientation of pattern in the matrix   // It uses KMP pattern searching algorithm        function findOrientation(mat,pat)     {         // allocate memory for string containing cols     let col = new Array(N);     for(let i = 0; i < N; i++)     {          // search in row i       if(KMPSearch(pat, mat[i]) == 1)       {         document.write("Horizontal");         return;       }          // Construct an array to store i'th column       for(let j = 0; j < N; j++)       {         col[j] = mat[j][i];       }          // Search in column i       if(KMPSearch(pat, col) == 1)       {         document.write("Vertical");       }               }     }           // Driver Code     let mat=[['a', 'b', 'c', 'd', 'e'],     ['f', 'g', 'h', 'i', 'j'],     ['k', 'l', 'm', 'n', 'o'],     ['p', 'q', 'r', 's', 't'],     ['u', 'v', 'w', 'x', 'y']];              let pat= "pqrs";     findOrientation(mat, pat);           // This code is contributed by unknown2108 </script> |
Output
Horizontal
Time complexity: O(n2).
Auxiliary Space: O(m)
This article is contributed by Aarti_Rathi and Aditya Goel. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
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