# Number of ordered points pair satisfying line equation in C++

The line equation that should be satisfied is y = mx + c. Given an array, m, and c, we have to find the number of order points satisfying the line equation. Let's see an example.

Input

arr = [1, 2, 3]
m = 1
c = 1

Output

2

The pairs satisfying the line equation are

2 1
3 2

## Algorithm

• Initialise the array, m, and c.
• Write two loops to get all pairs from the array.
• Check whether the pair is satisfying the line equation or not.
• We can check the whether the equation is satisfied or not by substituting the values into the line equation.
• If the pair satisfies the line equation, then increment the count.
• Return the count.

## Implementation

Following is the implementation of the above algorithm in C++

#include <bits/stdc++.h>
using namespace std;
bool isSatisfyingLineEquation(int arr[], int i, int j, int m, int c) {
if (i == j) {
return false;
}
return arr[j] == m * arr[i] + c;
}
int getOrderedPointsPairCount(int arr[], int n, int m, int c) {
int count = 0;
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
if (isSatisfyingLineEquation(arr, i, j, m, c)) {
count++;
}
}
}
return count;
}
int main() {
int arr[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 };
int n = 10;
int m = 1, c = 1;
cout << getOrderedPointsPairCount(arr, n, m, c) << endl;
return 0;
}

## Output

If you run the above code, then you will get the following result.

9

Updated on: 26-Oct-2021

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