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# Find the coordinates of the fourth vertex of a rectangle with given 3 vertices

• Difficulty Level : Basic
• Last Updated : 02 Aug, 2021

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++

 `// C++ implementation of the approach``#include ``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;``}`

## Java

 `// 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 findFourthVertex(``int` `n,``                                        ``int` `m, String s[])``    ``{``        ``HashMap row = ``new` `HashMap<>();``        ``HashMap 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 entry : row.entrySet())``        ``{``            ``if` `(entry.getValue() == ``1``)``                ``x = entry.getKey();``        ``}``                ` `        ``for` `(Map.Entry entry : col.entrySet())``        ``{``            ``if` `(entry.getValue() == ``1``)``                ``y = entry.getKey();``        ``}``    ` `        ``// 1-based indexing``        ``Pair 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 rs = findFourthVertex(n, m, s);``        ``System.out.println(rs.first + ``" "` `+ rs.second);``    ``}``}` `class` `Pair``{``    ``A first;``    ``B second;` `    ``public` `Pair(A first, B second)``    ``{``        ``this``.first = first;``        ``this``.second = second;``    ``}``}``    ` `// This code is contributed by Rituraj Jain`

## Python3

 `# 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`

## C#

 `// C# implementation of the approach``using` `System;``using` `System.Collections.Generic;` `class` `GfG``{` `    ``// Function that return the coordinates``    ``// of the fourth vertex of the rectangle``    ``static` `Pair<``int``, ``int``> findFourthVertex(``int` `n,``                                        ``int` `m, String []s)``    ``{``        ``Dictionary<``int``, ``int``> row = ``new` `Dictionary<``int``, ``int``>();``        ``Dictionary<``int``, ``int``> col = ``new` `Dictionary<``int``, ``int``>();``        ` `        ``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] == ``'*'``)``                ``{``                    ` `                    ``if` `(row.ContainsKey(i))``                    ``{``                        ``row[i] = row[i] + 1;``                    ``}``                    ``else``                    ``{``                        ``row.Add(i, 1);``                    ``}``                    ` `                    ``if` `(col.ContainsKey(j))``                    ``{``                        ``col[j] = col[j] + 1;``                    ``}``                    ``else``                    ``{``                        ``col.Add(j, 1);``                    ``}``                ``}``            ``}``        ``}``                ` `        ``int` `x = 0, y = 0;``        ``foreach``(KeyValuePair<``int``, ``int``> entry ``in` `row)``        ``{``            ``if` `(entry.Value == 1)``                ``x = entry.Key;``        ``}``                ` `        ``foreach``(KeyValuePair<``int``, ``int``> entry ``in` `col)``        ``{``            ``if` `(entry.Value == 1)``                ``y = entry.Key;``        ``}``    ` `        ``// 1-based indexing``        ``Pair<``int``, ``int``> ans = ``new` `Pair<``int``, ``int``>(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<``int``, ``int``> rs = findFourthVertex(n, m, s);``        ``Console.WriteLine(rs.first + ``" "` `+ rs.second);``    ``}``}` `class` `Pair``{``    ``public` `A first;``    ``public` `B second;` `    ``public` `Pair(A first, B second)``    ``{``        ``this``.first = first;``        ``this``.second = second;``    ``}``}` `// This code is contributed by 29AjayKumar`

## Javascript

 ``
Output:

`2 3`

Time Complexity: O(N * M)
Auxiliary Space: O(N + M)

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