Find the cordinates of the fourth vertex of a rectangle with given 3 vertices

Given an N * M grid. It contains exactly three ‘*’ and every other cell is a ‘.’ where ‘*’ denotes a vertex of a rectangle. The task is to find the coordinates of the fourth (missing) vertex (1-based indexing).

Examples:

Input: grid[][] = {“*.*”, “*..”, “…”}
Output: 2 3
(1, 1), (1, 3) and (2, 1) are the given coordinates of the rectangle where (2, 3) is the missing coordinate.

Input: grid[][] = {“*.*”, “..*”}
Output: 2 1



Approach: Find the coordinates of the 3 vertices by iterating through the given grid. Since a rectangle consists of 2 X-coordinates and 2 Y-coordinates and 4 vertices, every X-coordinate and Y-coordinate should occur exactly twice. We can count how many times each X and Y coordinate occurs in the 3 given vertices and the 4th one will have coordinates that occur only once.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function that return the coordinates
// of the fourth vertex of the rectangle
pair<int, int> findFourthVertex(int n, int m, string s[])
{
    map<int, int> row, col;
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++)
  
            // Save the coordinates of the given
            // vertices of the rectangle
            if (s[i][j] == '*') {
                row[i]++;
                col[j]++;
            }
    int x, y;
    for (auto tm : row)
        if (tm.second == 1)
            x = tm.first;
    for (auto tm : col)
        if (tm.second == 1)
            y = tm.first;
  
    // 1-based indexing
    return make_pair(x + 1, y + 1);
}
  
// Driver code
int main()
{
    string s[] = { "*.*", "*..", "..." };
    int n = sizeof(s) / sizeof(s[0]);
    int m = s[0].length();
  
    auto rs = findFourthVertex(n, m, s);
    cout << rs.first << " " << rs.second;
}

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Java

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// Java implementation of the approach
import java.util.HashMap;
import java.util.Map;
  
class GfG
{
  
    // Function that return the coordinates 
    // of the fourth vertex of the rectangle 
    static Pair<Integer, Integer> findFourthVertex(int n, 
                                        int m, String s[]) 
    
        HashMap<Integer, Integer> row = new HashMap<>(); 
        HashMap<Integer, Integer> col = new HashMap<>(); 
          
        for (int i = 0; i < n; i++)
        
            for (int j = 0; j < m; j++)
            
      
                // Save the coordinates of the given 
                // vertices of the rectangle 
                if (s[i].charAt(j) == '*'
                
                      
                    if (row.containsKey(i))
                    {
                        row.put(i, row.get(i) + 1);
                    }
                    else
                    {
                        row.put(i, 1);
                    }
                      
                    if (col.containsKey(j))
                    {
                        col.put(j, col.get(j) + 1);
                    }
                    else
                    {
                        col.put(j, 1);
                    
                }
            }
        }
                  
        int x = 0, y = 0
        for (Map.Entry<Integer, Integer> entry : row.entrySet())
        
            if (entry.getValue() == 1
                x = entry.getKey();
        }
                  
        for (Map.Entry<Integer, Integer> entry : col.entrySet())
        
            if (entry.getValue() == 1
                y = entry.getKey();
        }
      
        // 1-based indexing
        Pair<Integer, Integer> ans = new Pair<>(x + 1, y + 1);
        return ans; 
    
  
    // Driver Code 
    public static void main(String []args)
    {
          
        String s[] = { "*.*", "*..", "..." }; 
        int n = s.length; 
        int m = s[0].length(); 
      
        Pair<Integer, Integer> rs = findFourthVertex(n, m, s); 
        System.out.println(rs.first + " " + rs.second);
    }
}
  
class Pair<A, B> 
{
    A first;
    B second;
  
    public Pair(A first, B second) 
    {
        this.first = first;
        this.second = second;
    }
}
      
// This code is contributed by Rituraj Jain 

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Python3

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# Python3 implementation of the approach 
  
# Function that return the coordinates 
# of the fourth vertex of the rectangle 
def findFourthVertex(n, m, s) :
  
    row = dict.fromkeys(range(n), 0)
    col = dict.fromkeys(range(m), 0)
      
    for i in range(n) :
        for j in range(m) : 
  
            # Save the coordinates of the given 
            # vertices of the rectangle 
            if (s[i][j] == '*') :
                row[i] += 1
                col[j] += 1
  
    for keys,values in row.items() : 
        if (values == 1) :
            x = keys; 
              
    for keys,values in col.items() : 
        if (values == 1) :
            y = keys; 
  
    # 1-based indexing 
    return (x + 1, y + 1) ;
  
# Driver code 
if __name__ == "__main__" :
      
    s = [ "*.*", "*..", "..."
    n = len(s);
    m = len(s[0]);
      
    rs = findFourthVertex(n, m, s); 
    print(rs[0], rs[1]) 
  
# This code is contributed by Ryuga

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Output:

2 3

Time Complexity: O(N * M)



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Improved By : AnkitRai01, rituraj_jain