The Pattern

Joey is always fond of playing with patterns. So on his birthday, his uncle gave him a mat.  Mat is a rectangular grid

$(NM)$. i.e. there are $N$ rows and $M$ columns are drawn on the mat.  Each cell of this grid is filled with either dot$(.)$ or star$(\ast )$. Now Joey starts to fold this mat.  Firstly he folds the mat along the rows (top to down) until it transforms into a $(1\ast M)$ grid (Neglect width of mat on each fold). After that, he starts folding this along the columns (left to right) and finally transforms into a single cell. In the end Joey wants to know what will be on the top of that cell $($dot $(.)$or star$(\ast ))$.

When star$(\ast )$ come over dot$(.)$ it converted to dot$(.)$
When star$(\ast )$ come over star$(\ast )$, it remains the star$(\ast )$
When dot$(.)$ come over dot$(.)$, it remains dot$(.)$
When dot$(.)$ come over star$(\ast )$, it converted to star$(\ast )$

Example:

Input:  n = 5, m = 5 , pattern={{"*.***"},{".**.."},{".*.*."},{"*...*"},{"..*.*"}}
Output: *

Approach

C++

#include <bits/stdc++.h>
using namespace std;

void thePattern(vector<string> pattern, int n, int m)
{
    for (int i = 0; i < n - 1; i++)
    {
        for (int j = 0; j < m; j++)
        {
            if (pattern[i][j] == '.' && 
                  pattern[i + 1][j] == '*')
                pattern[i + 1][j] = '*';
            else if (pattern[i][j] == '*' &&
                      pattern[i + 1][j] == '.')
                pattern[i + 1][j] = '.';
        }
    }

    for (int j = 0; j < m - 1; j++)
    {
        if (pattern[n - 1][j] == '.' && 
                  pattern[n - 1][j + 1] == '*')
            pattern[n - 1][j + 1] = '*';
        else if (pattern[n - 1][j] == '*' &&
        pattern[n - 1][j + 1] == '.')
            pattern[n - 1][j + 1] = '.';
    }
    cout << pattern[n - 1][m - 1] << "\n";
}
int main()
{
    int n = 5, m = 5;

    vector<string> pattern = {{"*.***"},
                              {".**.."},
                              {".*.*."},
                              {"*...*"},
                              {"..*.*"}};

    thePattern(pattern, n, m);

    return 0;
}