In C++, count the number of integer points between two points
In this tutorial we will write a program that finds the number of integer points between given two points.
The number of points between two given points will be gcd(abs(x2), abs(y1-y2)) - 1.
If the connecting line is parallel to the x-axis, the number of integer points will be abs(y1 - y2) - 1.
If the connecting line is parallel to the y-axis, the number of integer points will be abs(x1 - x2) - 1.
If the x-coordinates of two points are equal, they are parallel to the x-axis. If the y-coordinates of two points are equal, they are parallel to the y-axis.
Let's look at an example.
Input
pointOne = [1, 5] pointTwo = [1, 3]
Output
1
Algorithm
- Initialize two points.
- Check if they are parallel to the x-axis.
- If they are parallel to the x-axis, use the formula abs(y1 - y2) - 1.
- Check if they are parallel to the y-axis.
- If they are parallel to the y-axis, use the formula abs(x1 - x2) - 1.
- If they are not parallel to any axis, use the formula gcd(abs(x1-x2), abs(y1- y2)) - 1.
- Calculate the result and print it.
Implementation
The following is the implementation of the above algorithm in C
#include <bits/stdc++.h> using namespace std; int gcd(int a, int b) { if (b == 0) { return a; } return gcd(b, a % b); } int getCount(int pointOne[], int pointTwo[]) { if (pointOne[0] == pointTwo[0]) { return abs(pointOne[1] - pointTwo[1]) - 1; } if (pointOne[1] == pointTwo[1]) { return abs(pointOne[0] - pointTwo[0]) - 1; } return gcd(abs(pointOne[0] - pointTwo[0]), abs(pointOne[1] - pointTwo[1])) - 1; } int main() { int pointOne[] = {1, 3}, pointTwo[] = {10, 12}; cout << getCount(pointOne, pointTwo) << endl; return 0; }
Output
If you run the above code, you will get the following results.
8
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