# First collision point of two series

• Difficulty Level : Medium
• Last Updated : 24 Jul, 2022

Given five numbers a, b, c, d and n (where a, b, c, d, n > 0). These values represent n terms of two series. The two series formed by these four numbers are b, b+a, b+2a….b+(n-1)a and d, d+c, d+2c, ….. d+(n-1)c
These two series will collide when at any single point summation values becomes exactly the same for both the series.Print the collision point.

```Example:
Input : a = 20, b = 2,
c = 9, d = 19,
n = 100
Output: 82
Explanation:
Series1 = (2, 22, 42, 62, 82, 102...)
Series2 = (28, 37, 46, 55, 64, 73, 82, 91..)
So the first collision point is 82.   ```

A naive approach is to calculate both the series in two different arrays, and then check for each element if it collides by running two nested loops
Time complexity: O(n * n)
Auxiliary Space: O(n)
An efficient Approach to the problem mentioned above is:
* Generate all elements of first series. Let current element be x.
* If x is also an element of second series, then following conditions should satisfy.
…..a) x should be greater than or equal to first element of second series.
…..a) Difference between x and first element should be divisible by c.
*If the above conditions are satisfied then the i-th value is the required meeting point.
Below is the implementation of the above problem :

## C++

 `// CPP program to calculate the colliding``// point of two series``#include``using` `namespace` `std;`  `void` `point(``int` `a, ``int` `b, ``int` `c, ``int` `d, ``int` `n)``{``    ``int` `x , flag = 0;` `    ``// Iterating through n terms of the``    ``// first series``    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ` `        ``// x is i-th term of first series``        ``x = b + i * a;    ``        ` `        ``// d is first element of second``        ``// series and c is common difference``        ``// for second series.``        ``if` `((x - d) % c == 0 and x - d >= 0)``        ``{``            ``cout << x << endl ;``            ``flag = 1;``            ``break``;``        ``}``    ` `    ``}` `    ``// If no term of first series is found    ``    ``if``(flag == 0)``    ``{``            ``cout << ``"No collision point"` `<< endl;``    ``}` `    ` `}``    `  `// Driver function``int` `main()``{``    ``int` `a = 20 ;``    ``int` `b = 2 ;``    ``int` `c = 9;``    ``int` `d = 19;``    ``int` `n = 20;``    ``point(a, b, c, d, n);``    ``return` `0;``}` `// This code is contributed by  'saloni1297'.`

## Java

 `// Java program to calculate the colliding``// point of two series``import` `java.io.*;` `class` `GFG``{``    ``static` `void` `point(``int` `a, ``int` `b, ``int` `c, ``int` `d, ``int` `n)``    ``{``        ``int` `x , flag = ``0``;` `        ``// Iterating through n terms of the``        ``// first series``        ``for` `(``int` `i = ``0``; i < n; i++)``        ``{``            ` `            ``// x is i-th term of first series``            ``x = b + i * a;``            ` `            ``// d is first element of second``            ``// series and c is common difference``            ``// for second series.``            ``if` `((x - d) % c == ``0` `&& x - d >= ``0``)``            ``{``                ``System.out.println( x ) ;``                ``flag = ``1``;``                ``break``;``            ``}``        ` `        ``}``    ` `        ``// If no term of first series is found``        ``if``(flag == ``0``)``        ``{``            ``System.out.println (``"No collision point"``);``        ``}``    ` `        ` `    ``}``        ` `    ` `    ``// Driver function``    ``public` `static` `void` `main (String[] args)``    ``{``        ``int` `a = ``20` `;``        ``int` `b = ``2` `;``        ``int` `c = ``9``;``        ``int` `d = ``19``;``        ``int` `n = ``20``;``        ``point(a, b, c, d, n);  ``    ` `    ``}``}``// This code is contributed by vt_m`

## Python

 `# Function to calculate the colliding point``# of two series``def` `point(a, b, c, d, n):` `    ``# Iterating through n terms of the``    ``# first series``    ``for` `i ``in` `range``(n):``        ` `        ``# x is i-th term of first series``        ``x ``=` `b ``+` `i``*``a    ``        ` `        ``# d is first element of second``        ``# series and c is common difference``        ``# for second series.``        ``if` `(x``-``d)``%``c ``=``=` `0` `and` `x``-``d >``=` `0``:``            ``print` `x``            ``return` `    ``# If no term of first series is found     ``    ``else``:``        ``print` `"No collision point"`   `   `  `# Driver code``a ``=` `20``b ``=` `2``c ``=` `9``d ``=` `19``n ``=` `20``point(a, b, c, d, n)`

## C#

 `// C# program to calculate the colliding``// point of two series``using` `System;` `class` `GFG {``    ` `    ``static` `void` `point(``int` `a, ``int` `b, ``int` `c,``                             ``int` `d, ``int` `n)``    ``{``        ``int` `x, flag = 0;` `        ``// Iterating through n terms of the``        ``// first series``        ``for` `(``int` `i = 0; i < n; i++) {` `            ``// x is i-th term of first series``            ``x = b + i * a;` `            ``// d is first element of second``            ``// series and c is common difference``            ``// for second series.``            ``if` `((x - d) % c == 0 && x - d >= 0) {``                ``Console.WriteLine(x);``                ``flag = 1;``                ``break``;``            ``}``        ``}` `        ``// If no term of first series is found``        ``if` `(flag == 0) {``            ``Console.WriteLine(``"No collision point"``);``        ``}``    ``}` `    ``// Driver function``    ``public` `static` `void` `Main()``    ``{``        ``int` `a = 20;``        ``int` `b = 2;``        ``int` `c = 9;``        ``int` `d = 19;``        ``int` `n = 20;``        ``point(a, b, c, d, n);``    ``}``}` `// This code is contributed by vt_m`

## PHP

 `= 0)``        ``{``            ``echo` `\$x``;``            ``\$flag` `= 1;``            ``break``;``        ``}``    ` `    ``}` `    ``// If no term of first``    ``// series is found``    ``if``(``\$flag` `== 0)``    ``{``            ``echo` `"No collision po\$"``;``    ``}` `    ` `}``    ` `    ``// Driver Code``    ``\$a` `= 20 ;``    ``\$b` `= 2 ;``    ``\$c` `= 9;``    ``\$d` `= 19;``    ``\$n` `= 20;``    ``point(``\$a``, ``\$b``, ``\$c``, ``\$d``, ``\$n``);` `// This code is contributed by anuj_67.``?>`

## Javascript

 ``

Output :

`82`

Time Complexity: O(n)

Auxiliary Space: O(1)
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