# Maximum integral co-ordinates with non-integer distances

Given a maximum limit of x – coordinate and y – coordinate, we want to calculate a set of coordinates such that the distance between any two points is a non-integer number. The coordinates (i, j) chosen should be of range 0<=i<=x and 0<=j<=y. Also, we have to maximize the set. Examples:

Input : 4 4 Output : 0 4 1 3 2 2 3 1 4 0 Explanation : Distance between any two points mentioned in output is not integer.

Firstly, we want to create a set, that means our set cannot contain any other point with same x’s or y’s which are used before. Well, the reason behind it is that such points which either have same x-coordinate or y-coordinate would cancel that coordinate, resulting an integral distance between them.

Example, consider points (1, 4) and (1, 5), the x-coordinate would cancel and thus, we will get and integral distance.

Secondly, we can observe that, we have only x+1 distinct i-coordinates and y+1 distinct j-coordinates. Thus, the size of the set cannot exceed min(x, y)+1.

Third observation is that we know that the diagonal elements are |i-j|* distance apart, thus, we take evaluate along the diagonal element of i-coordinate and calculate the j-coordinate by formula min(i, j)-i.

`// C++ program to find maximum integral points ` `// such that distances between any two is not ` `// integer. ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Making set of coordinates such that ` `// any two points are non-integral distance apart ` `void` `printSet(` `int` `x, ` `int` `y) ` `{ ` ` ` `// used to avoid duplicates in result ` ` ` `set<pair<` `int` `, ` `int` `> > arr; ` ` ` ` ` `for` `(` `int` `i = 0; i <= min(x, y); i++) { ` ` ` ` ` `pair<` `int` `, ` `int` `> pq; ` ` ` `pq = make_pair(i, min(x, y) - i); ` ` ` `arr.insert(pq); ` ` ` `} ` ` ` ` ` `for` `(` `auto` `it = arr.begin(); it != arr.end(); it++) ` ` ` `cout << (*it).first << ` `" "` `<< (*it).second << endl; ` `} ` ` ` `// Driver function ` `int` `main() ` `{ ` ` ` `int` `x = 4, y = 4; ` ` ` `printSet(x, y); ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

Output:

0 4 1 3 2 2 3 1 4 0

## Recommended Posts:

- Find the original coordinates whose Manhattan distances are given
- Sum of Manhattan distances between all pairs of points
- Find a point such that sum of the Manhattan distances is minimized
- Find all possible coordinates of parallelogram
- Count Integral points inside a Triangle
- Coordinates of rectangle with given points lie inside
- Minimum length of square to contain at least half of the given Coordinates
- Find whether only two parallel lines contain all coordinates points or not
- Number of Integral Points between Two Points
- Maximum area of quadrilateral
- Maximum points of intersection n circles
- Maximum number of pieces in N cuts
- Maximum number of segments that can contain the given points
- Maximum area of rectangle possible with given perimeter
- Maximum points of intersection n lines

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.