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

Last Updated : 31 May, 2022

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[])` `{` `    ``unordered_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), as we are using a loop to traverse N*M times.
Auxiliary Space: O(N + M), as we are using extra space for map.

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