How to match ASCII art segments within ASCII art?

Question

I am practising for a programming competition in which I will have the choice for each problem whether to use Python or C++, so I am open to a solution in either language – whatever language is best suited to this problem.

The URL to the past problem I am stuck on is http://progconz.elena.aut.ac.nz/attachments/article/74/10%20points%20Problem%20Set%202012.pdf, problem F ("Maps").

Basically it involves matching occurrences of a small piece of ASCII art within a big one. In C++ I can make a vector for each piece of ASCII art. The problem is how to match it when the smaller piece is multi-line.

I have no idea how to go about it. I don't want all the code written for me, just an idea of the logic needed for the problem.

Thanks for any help.

Here's what I've got so far:

#include <cstdlib>
#include <iostream>
#include <string>
#include <algorithm>
#include <vector>

using namespace std;

int main( int argc, char** argv )
{
    int nScenarios, areaWidth, areaHeight, patternWidth, patternHeight;

    cin >> nScenarios;

    for( int a = 0; a < nScenarios; a++ )
    {
        //get the pattern info and make a vector
        cin >> patternHeight >> patternWidth;
        vector< vector< bool > > patternIsBuilding( patternHeight, vector<bool>( patternWidth, false ) );

        //populate data
        for( int i = 0; i < patternHeight; i++ )
        {
            string temp;
            cin >> temp;
            for( int j = 0; j < patternWidth; j++ )
            {
                patternIsBuilding.at( i ).at( j ) = ( temp[ j ] == 'X' );
            }
        }

        //get the area info and make a vector
        cin >> areaHeight >> areaWidth;
        vector< vector< bool > > areaIsBuilding( areaHeight, vector<bool>( areaWidth, false ) );

        //populate data
        for( int i = 0; i < areaHeight; i++ )
        {
            string temp;
            cin >> temp;
            for( int j = 0; j < areaWidth; j++ )
            {
                areaIsBuilding.at( i ).at( j ) = ( temp[ j ] == 'X' );
            }
        }


        //now the vectors contain a `true` for a building and a `false` for snow
        //need to find the matches for patternIsBuilding inside areaIsBuilding
        //how?

    }


    return 0;
}

EDIT: From the comments below I've got a solution in Python from J.F. Sebastian. It works but I don't understand it all. I've commented what I could but need help understanding the return statement in the count_pattern function.

#function to read a matrix from stdin
def read_matrix():

    #get the width and height for this matrix
    nrows, ncols = map( int, raw_input().split() )

    #get the matrix from input
    matrix = [ raw_input() for _ in xrange( nrows ) ]

    #make sure that it all matches up
    assert all(len(row) == ncols for row in matrix)

    #return the matrix
    return matrix

#perform the check, given the pattern and area map
def count_pattern( pattern, area ):

    #get the number of rows, and the number of columns in the first row (cause it's the same for all of them)
    nrows = len( pattern )
    ncols = len( pattern[0] )

    #how does this work?
    return sum(
        pattern == [ row[ j:j + ncols ] for row in area[ i:i + nrows ] ]
        for i in xrange( len( area ) - nrows + 1 )
        for j in xrange( len( area[i] ) - ncols + 1 )
    )

#get a number of scenarios, and that many times, operate on the two inputted matrices, pattern and area
for _ in xrange( int( raw_input() ) ):
    print count_pattern( read_matrix(), read_matrix() )

Answer 1

Don't think in terms of lines. Read the entire page into a string and treat the end-of-line character(s) like any other.

(You may think this is a cryptic hint, but you did ask for just "an idea" how to do it.)

EDIT: Since you know the overall dimensions of the picture, you can count characters forward from the first line of the pattern you're trying to match in order to match the second line, and so on for subsequent lines.

Answer 2

#how does this work?
return sum(
    pattern == [ row[ j:j + ncols ] for row in area[ i:i + nrows ] ]
    for i in xrange( len( area ) - nrows + 1 )
    for j in xrange( len( area[i] ) - ncols + 1 )
)

The generator expression could be rewritten using explicit for-loop blocks:

count = 0
for i in xrange( len( area ) - nrows + 1 ):
    for j in xrange( len( area[i] ) - ncols + 1 ):
        count += (pattern == [ row[ j:j + ncols ]
                              for row in area[ i:i + nrows ] ])
return count

The comparison (pattern == ..) returns True/False that are equal to 1/0 in Python.

The list comprehension that builds submatrixes to compare with the pattern can be optimized to return earlier:

count += all(pattern_row == row[j:j + ncols]
             for pattern_row, row in zip(pattern, area[i:i + nrows]))

Or using explicit for-loop blocks:

for pattern_row, row in zip(pattern, area[i:i + nrows]):
    if pattern_row != row[j:j + ncols]:
       break # no match (the count stays the same)
else: # matched (no break)
    count += 1 # all rows are equal

Answer 3

#include <iostream>
#include <vector>

using namespace std;

int main(){

    int numOfRounds;
    cin >> numOfRounds;



    for(int round = 0; round < numOfRounds; round++){

        int out = 0;

        int linesToMatch;
        cin >> linesToMatch;

        int sizeToMatch;
        cin >> sizeToMatch;

        vector <string> v;
        string t;

        for (int i = 0; i < linesToMatch; i++){
            cin >> t;
            v.push_back(t);
        }

        string s = "";

        int rows;
        cin >> rows;

        int columns;
        cin >> columns;

        for (int j = 0; j < rows; j++){        //map->string
            cin >> t;
            s += t;
        }

        // main part of implementation
        // it's mainly basic algebra and index tracking
        for (int m = 0; m <= rows - linesToMatch; m++){
            for (int n = 0; n <= columns - sizeToMatch; n++){
                int x;
                for (x = 0; x < linesToMatch; x++){
                    int index = (m + x) * columns + n;
                    string newTemp(s.begin() + index, s.begin() + index + sizeToMatch);
                    if (newTemp != v.at(x)) break;
                }
                if (x == linesToMatch) out++;
            }
        }

        cout << out << endl;

    }

}