# Find maximum and minimum distance between magnets

Given coordinates of two pivot points (x0, y0) & (x1, y1) in coordinates plane. Along with each pivot, two different magnets are tied with the help of a string of length r1 and r2 respectively. Find the distance between both magnets when they repelling each other and when they are attracting each other.

**Examples :**

Input : x1=0, y1=0, x2=5, y2=0, r1=2, r2=2

Output : Distance while repulsion = 9, Distance while attraction = 1Input : x1=0, y1=0, x2=5, y2=0, r1=3, r2=3

Output : Distance while repulsion = 11, Distance while attraction = 0

As we all know about the properties of magnet that they repel each other when they are facing each other with the same pole and attract each other when they are facing each other with opposite pole. Also, the force of attraction, as well as repulsion, always work in a straight line.

We have two pivots points on coordinates, so distance between these points are **D = ((x1-x2) ^{2} +(y1-y2)^{2} )^{1/2}**.

Also, we can conclude that distance between magnet is maximum while repulsion and that too should be the distance between pivots + sum of the length of both strings.

In case of attraction we have two cases to take care of:

Either the minimum distance is the distance between pivots – the sum of the length of both strings

Or minimum distance should be zero in case if the sum of the length of strings is greater than the distance between pivot points.

Illustration with help of diagram:

## C++

`// C++ program for max and min distance ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function for finding distance between pivots ` `int` `pivotDis(` `int` `x0, ` `int` `y0, ` `int` `x1, ` `int` `y1) ` `{ ` ` ` `return` `sqrt` `((x1 - x0) * (x1 - x0) + ` ` ` `(y1 - y0) * (y1 - y0)); ` `} ` ` ` `// Function for minimum distance ` `int` `minDis(` `int` `D, ` `int` `r1, ` `int` `r2) ` `{ ` ` ` `return` `max((D - r1 - r2), 0); ` `} ` ` ` `// Function for maximum distance ` `int` `maxDis(` `int` `D, ` `int` `r1, ` `int` `r2) ` `{ ` ` ` `return` `D + r1 + r2; ` `} ` ` ` `// Drivers code ` `int` `main() ` `{ ` ` ` `int` `x0 = 0, y0 = 0, x1 = 8, y1 = 0, r1 = 4, r2 = 5; ` ` ` `int` `D = pivotDis(x0, y0, x1, y1); ` ` ` `cout << ` `"Distance while repulsion = "` `<< maxDis(D, r1, r2); ` ` ` `cout << ` `"\nDistance while attraction = "` `<< minDis(D, r1, r2); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program for max ` `// and min distance ` `import` `java.io.*; ` ` ` `class` `GFG ` `{ ` ` ` `// Function for finding ` `// distance between pivots ` `static` `int` `pivotDis(` `int` `x0, ` `int` `y0, ` ` ` `int` `x1, ` `int` `y1) ` `{ ` ` ` `return` `(` `int` `)Math.sqrt((x1 - x0) * ` ` ` `(x1 - x0) + ` ` ` `(y1 - y0) * ` ` ` `(y1 - y0)); ` `} ` ` ` `// Function for ` `// minimum distance ` `static` `int` `minDis(` `int` `D, ` `int` `r1, ` `int` `r2) ` `{ ` ` ` `return` `Math.max((D - r1 - r2), ` `0` `); ` `} ` ` ` `// Function for ` `// maximum distance ` `static` `int` `maxDis(` `int` `D, ` `int` `r1, ` `int` `r2) ` `{ ` ` ` `return` `D + r1 + r2; ` `} ` ` ` `// Driver Code ` `public` `static` `void` `main (String[] args) ` `{ ` `int` `x0 = ` `0` `, y0 = ` `0` `, x1 = ` `8` `, ` ` ` `y1 = ` `0` `, r1 = ` `4` `, r2 = ` `5` `; ` `int` `D = pivotDis(x0, y0, x1, y1); ` `System.out.print( ` `"Distance while "` `+ ` ` ` `"repulsion = "` `+ ` ` ` `maxDis(D, r1, r2)); ` `System.out.print(` `"\nDistance while "` `+ ` ` ` `"attraction = "` `+ ` ` ` `minDis(D, r1, r2)); ` `} ` `} ` ` ` `// This code is contributed by anuj_67. ` |

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## Python3

`# Python 3 program for max and min ` `# distance ` `import` `math ` ` ` `# Function for finding distance between ` `# pivots ` `def` `pivotDis(x0, y0, x1, y1): ` ` ` ` ` `return` `math.sqrt((x1 ` `-` `x0) ` `*` `(x1 ` `-` `x0) ` ` ` `+` `(y1 ` `-` `y0) ` `*` `(y1 ` `-` `y0)) ` ` ` `# Function for minimum distance ` `def` `minDis( D, r1, r2): ` ` ` ` ` `return` `max` `((D ` `-` `r1 ` `-` `r2), ` `0` `) ` ` ` `# Function for maximum distance ` `def` `maxDis( D, r1, r2): ` ` ` ` ` `return` `D ` `+` `r1 ` `+` `r2 ` ` ` `# Drivers code ` `x0 ` `=` `0` `y0 ` `=` `0` `x1 ` `=` `8` `y1 ` `=` `0` `r1 ` `=` `4` `r2 ` `=` `5` `D ` `=` `pivotDis(x0, y0, x1, y1) ` `print` `(` `"Distance while repulsion = "` `, ` ` ` `int` `(maxDis(D, r1, r2))) ` ` ` `print` `(` `"Distance while attraction = "` `, ` ` ` `minDis(D, r1, r2)) ` ` ` `# This code is contributed by Smitha ` |

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## C#

`// C# program for max and min distance ` `using` `System; ` ` ` `class` `GFG { ` ` ` ` ` `// Function for finding ` ` ` `// distance between pivots ` ` ` `static` `int` `pivotDis(` `int` `x0, ` `int` `y0, ` ` ` `int` `x1, ` `int` `y1) ` ` ` `{ ` ` ` `return` `(` `int` `)Math.Sqrt((x1 - x0) * ` ` ` `(x1 - x0) + ` ` ` `(y1 - y0) * ` ` ` `(y1 - y0)); ` ` ` `} ` ` ` ` ` `// Function for ` ` ` `// minimum distance ` ` ` `static` `int` `minDis(` `int` `D, ` `int` `r1, ` `int` `r2) ` ` ` `{ ` ` ` `return` `Math.Max((D - r1 - r2), 0); ` ` ` `} ` ` ` ` ` `// Function for ` ` ` `// maximum distance ` ` ` `static` `int` `maxDis(` `int` `D, ` `int` `r1, ` `int` `r2) ` ` ` `{ ` ` ` `return` `D + r1 + r2; ` ` ` `} ` ` ` ` ` `// Driver Code ` ` ` `public` `static` `void` `Main () ` ` ` `{ ` ` ` `int` `x0 = 0, y0 = 0, x1 = 8, ` ` ` `y1 = 0, r1 = 4, r2 = 5; ` ` ` `int` `D = pivotDis(x0, y0, x1, y1); ` ` ` ` ` `Console.WriteLine( ` `"Distance while "` `+ ` ` ` `"repulsion = "` `+ ` ` ` `maxDis(D, r1, r2)); ` ` ` `Console.WriteLine(` `"Distance while "` `+ ` ` ` `"attraction = "` `+ ` ` ` `minDis(D, r1, r2)); ` ` ` `} ` `} ` ` ` `// This code is contributed by anuj_67. ` |

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## PHP

`<?php ` `// PHP program for max and ` `// min distance ` ` ` `// Function for finding ` `// distance between pivots ` `function` `pivotDis(` `$x0` `, ` `$y0` `, ` ` ` `$x1` `, ` `$y1` `) ` `{ ` ` ` `return` `sqrt((` `$x1` `- ` `$x0` `) * ` ` ` `(` `$x1` `- ` `$x0` `) + ` ` ` `(` `$y1` `- ` `$y0` `) * ` ` ` `(` `$y1` `- ` `$y0` `)); ` `} ` ` ` `// Function for minimum distance ` `function` `minDis( ` `$D` `, ` `$r1` `, ` `$r2` `) ` `{ ` ` ` `return` `max((` `$D` `- ` `$r1` `- ` `$r2` `), 0); ` `} ` ` ` `// Function for maximum distance ` `function` `maxDis( ` `$D` `, ` `$r1` `, ` `$r2` `) ` `{ ` ` ` `return` `$D` `+ ` `$r1` `+ ` `$r2` `; ` `} ` ` ` ` ` `// Driver code ` ` ` `$x0` `= 0; ` `$y0` `= 0; ` ` ` `$x1` `= 8; ` `$y1` `= 0; ` ` ` `$r1` `= 4; ` `$r2` `= 5; ` ` ` `$D` `= pivotDis(` `$x0` `, ` `$y0` `, ` ` ` `$x1` `, ` `$y1` `); ` ` ` `echo` `"Distance while repulsion = "` ` ` `, maxDis(` `$D` `, ` `$r1` `, ` `$r2` `); ` ` ` `echo` `"\nDistance while attraction = "` ` ` `, minDis(` `$D` `, ` `$r1` `, ` `$r2` `); ` ` ` `// This code is contributed by anuj_67. ` `?> ` |

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**Output:**

Distance while repulsion = 17 Distance while attraction = 0

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