# Probability of a random pair being the maximum weighted pair

Given two arrays A and B, a random pair is picked having an element from array A and another from array B. Output the probability of the pair being maximum weighted.

Examples:

```Input : A[] = 1 2 3
B[] = 1 3 3
Output : 0.222
Explanation : Possible pairs are : {1, 1},
{1, 3}, {1, 3}, {2, 1}, {2, 3}, {2, 3},
{3, 1}, {3, 3}, {3, 3} i.e. 9.
The pair with maximum weight is {3, 3} with
frequency 2. So, the probability of random
pair being maximum is 2/9 = 0.2222.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Brute Force Method : Generate all possible pairs in N^2 time complexity and count
maximum weighted pairs.

Better Method : Sort both the arrays and count the last (max) elements from A and B. No. of maximum weighted pairs will be product of both counts. The probability will be
(product of counts) / sizeof(A) * sizeof(B)

Best Method Best approach will be to traverse both the arrays and count the maximum element. No. of maximum weighted pairs will be product of both counts. The probability will be (product of counts) / sizeof(A) * sizeof(B)

Below is the implementation:

## C++

 `#include ` `using` `namespace` `std; ` ` `  `// Function to return probability ` `double` `probability(``int` `a[], ``int` `b[], ``int` `size1,  ` `                                     ``int` `size2) ` `{ ` `    ``// Count occurrences of maximum element  ` `    ``// in A[] ` `    ``int` `max1 = INT_MIN,  count1 = 0; ` `    ``for` `(``int` `i = 0; i < size1; i++) { ` `        ``if` `(a[i] > max1) { ` `            ``max1 = a[i]; ` `            ``count1 = 1; ` `        ``} ` `        ``else` `if` `(a[i] == max1) { ` `            ``count1++; ` `        ``} ` `    ``} ` ` `  `    ``// Count occurrences of maximum element  ` `    ``// in B[] ` `    ``int` `max2 = INT_MIN, count2 = 0; ` `    ``for` `(``int` `i = 0; i < size2; i++) { ` `        ``if` `(b[i] > max2) { ` `            ``max2 = b[i]; ` `            ``count2 = 1; ` `        ``} ` `        ``else` `if` `(b[i] == max2) { ` `            ``count2++; ` `        ``} ` `    ``} ` ` `  `    ``// Returning probability ` `    ``return` `(``double``)(count1 * count2) /  ` `                  ``(size1 * size2); ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `a[] = { 1, 2, 3 }; ` `    ``int` `b[] = { 1, 3, 3 }; ` ` `  `    ``int` `size1 = ``sizeof``(a) / ``sizeof``(a); ` `    ``int` `size2 = ``sizeof``(b) / ``sizeof``(b); ` ` `  `    ``cout << probability(a, b, size1, size2); ` `    ``return` `0; ` `} `

## Java

 `// Java program to find Probability  ` `// of a random pair being the maximum ` `// weighted pair ` `import` `java.io.*; ` ` `  `class` `GFG { ` `     `  `    ``// Function to return probability ` `    ``static` `double` `probability(``int` `a[], ``int` `b[],  ` `                            ``int` `size1,``int` `size2) ` `    ``{ ` `        ``// Count occurrences of maximum  ` `        ``// element in A[] ` `        ``int` `max1 = Integer.MIN_VALUE,  count1 = ``0``; ` `        ``for` `(``int` `i = ``0``; i < size1; i++) { ` `            ``if` `(a[i] > max1) { ` `                ``max1 = a[i]; ` `                ``count1 = ``1``; ` `            ``} ` `            ``else` `if` `(a[i] == max1) { ` `                ``count1++; ` `            ``} ` `        ``} ` `      `  `        ``// Count occurrences of maximum  ` `        ``// element in B[] ` `        ``int` `max2 = Integer.MIN_VALUE, count2 = ``0``; ` `        ``for` `(``int` `i = ``0``; i < size2; i++) { ` `            ``if` `(b[i] > max2) { ` `                ``max2 = b[i]; ` `                ``count2 = ``1``; ` `            ``} ` `            ``else` `if` `(b[i] == max2) { ` `                ``count2++; ` `            ``} ` `        ``} ` `      `  `        ``// Returning probability ` `        ``return` `(``double``)(count1 * count2) / (size1 * size2); ` `    ``} ` `      `  `    ``// Driver code ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``int` `a[] = { ``1``, ``2``, ``3` `}; ` `        ``int` `b[] = { ``1``, ``3``, ``3` `}; ` `      `  `        ``int` `size1 = a.length; ` `        ``int` `size2 = b.length; ` `      `  `        ``System.out.println(probability(a, b,  ` `                            ``size1, size2)); ` `    ``} ` `} ` ` `  `/*This code is contributed by Nikita Tiwari.*/`

## Python3

 `import` `sys ` ` `  `# Function to return probability  ` `def` `probability(a, b, size1, size2): ` ` `  `    ``# Count occurrences of maximum ` `    ``# element in A[]  ` `    ``max1 ``=` `-``(sys.maxsize ``-` `1``) ` `    ``count1 ``=` `0` `    ``for` `i ``in` `range``(size1): ` `        ``if` `a[i] > max1: ` `            ``count1 ``=` `1` `        ``elif` `a[i] ``=``=` `max1: ` `            ``count1 ``+``=` `1` ` `  `    ``# Count occurrences of maximum  ` `    ``# element in B[]  ` `    ``max2 ``=` `-``(sys.maxsize ``-` `1``) ` `    ``count2 ``=` `0` `    ``for` `i ``in` `range``(size2): ` `        ``if` `b[i] > max2: ` `            ``max2 ``=` `b[i] ` `            ``count2 ``=` `1` `        ``elif` `b[i] ``=``=` `max2: ` `            ``count2 ``+``=` `1` ` `  `    ``# Returning probability  ` `    ``return` `round``((count1 ``*` `count2) ``/`  `                 ``(size1 ``*` `size2), ``6``) ` ` `  `# Driver code ` `a ``=` `[``1``, ``2``, ``3``] ` `b ``=` `[``1``, ``3``, ``3``] ` `size1 ``=` `len``(a) ` `size2 ``=` `len``(b) ` `print``(probability(a, b, size1, size2)) ` ` `  `# This code is contributed  ` `# by Shrikant13 `

## C#

 `// C# program to find Probability of a random  ` `// pair being the maximum weighted pair ` `using` `System; ` ` `  `class` `GFG { ` `     `  `    ``// Function to return probability ` `    ``static` `float` `probability(``int` `[]a, ``int` `[]b,  ` `                          ``int` `size1,``int` `size2) ` `    ``{ ` `         `  `        ``// Count occurrences of maximum  ` `        ``// element in A[] ` `        ``int` `max1 = ``int``.MinValue, count1 = 0; ` `         `  `        ``for` `(``int` `i = 0; i < size1; i++) { ` `            ``if` `(a[i] > max1) { ` `                ``max1 = a[i]; ` `                ``count1 = 1; ` `            ``} ` `            ``else` `if` `(a[i] == max1) { ` `                ``count1++; ` `            ``} ` `        ``} ` `     `  `        ``// Count occurrences of maximum  ` `        ``// element in B[] ` `        ``int` `max2 = ``int``.MinValue, count2 = 0; ` `         `  `        ``for` `(``int` `i = 0; i < size2; i++) { ` `            ``if` `(b[i] > max2) { ` `                ``max2 = b[i]; ` `                ``count2 = 1; ` `            ``} ` `            ``else` `if` `(b[i] == max2) { ` `                ``count2++; ` `            ``} ` `        ``} ` `     `  `        ``// Returning probability ` `        ``return` `(``float``)(count1 * count2) /  ` `                            ``(size1 * size2); ` `    ``} ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int` `[]a = { 1, 2, 3 }; ` `        ``int` `[]b = { 1, 3, 3 }; ` `     `  `        ``int` `size1 = a.Length; ` `        ``int` `size2 = b.Length; ` `     `  `        ``Console.WriteLine(probability(a, b,  ` `                            ``size1, size2)); ` `    ``} ` `} ` ` `  `/* This code is contributed by vt_m.*/`

## PHP

 ` ``\$max1``) ` `        ``{ ` `            ``\$max1` `= ``\$a``[``\$i``]; ` `            ``\$count1` `= 1; ` `        ``} ` `        ``else` `if` `(``\$a``[``\$i``] == ``\$max1``) ` `        ``{ ` `            ``\$count1``++; ` `        ``} ` `    ``} ` ` `  `    ``// Count occurrences of maximum  ` `    ``// element in B[] ` `    ``\$max2` `= PHP_INT_MIN; ``\$count2` `= 0; ` `    ``for` `(``\$i` `= 0; ``\$i` `< ``\$size2``; ``\$i``++)  ` `    ``{ ` `        ``if` `(``\$b``[``\$i``] > ``\$max2``)  ` `        ``{ ` `            ``\$max2` `= ``\$b``[``\$i``]; ` `            ``\$count2` `= 1; ` `        ``} ` `        ``else` `if` `(``\$b``[``\$i``] == ``\$max2``)  ` `        ``{ ` `            ``\$count2``++; ` `        ``} ` `    ``} ` ` `  `    ``// Returning probability ` `    ``return` `(double)(``\$count1` `* ``\$count2``) /  ` `                     ``(``\$size1` `* ``\$size2``); ` `} ` ` `  `    ``// Driver code ` `    ``\$a` `= ``array``(1, 2, 3); ` `    ``\$b` `= ``array``(1, 3, 3); ` `    ``\$size1` `= sizeof(``\$a``); ` `    ``\$size2` `= sizeof(``\$b``); ` `    ``echo` `probability(``\$a``, ``\$b``,  ` `            ``\$size1``, ``\$size2``); ` `     `  `// This code is contributed by ajit ` `?> `

Output:

```0.222222
```

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Improved By : jit_t, shrikanth13