Given an array of n elements. The task is to find number of sextuplets that satisfy the below equation such that a, b, c, d, e and f belong to the given array:
a * b + c - e = f
d
Examples:
Input : arr[] = { 1 }.
Output : 1
a = b = c = d = e = f = 1 satisfy
the equation.
Input : arr[] = { 2, 3 }
Output : 4
Input : arr[] = { 1, -1 }
Output : 24
First, reorder the equation, a * b + c = (f + e) * d.
Now, make two arrays, one for LHS (Left Hand Side) of the equation and one for the RHS (Right Hand Side) of the equation. Search each element of RHS’s array in the LHS’s array. Whenever you find a value of RHS in LHS, check how many times it is repeated in LHS and add that count to the total. Searching can be done using binary search, by sorting the LHS array.
Below is the implementation of this approach:
C++
#include<bits/stdc++.h>
using namespace std;
int findSextuplets( int arr[], int n)
{
int index = 0;
int RHS[n*n*n + 1];
for ( int i = 0; i < n; i++)
if (arr[i])
for ( int j = 0; j < n; j++)
for ( int k = 0; k < n; k++)
RHS[index++] = arr[i] * (arr[j] + arr[k]);
sort(RHS, RHS + n);
int result = 0;
for ( int i = 0; i < n; i++)
{
for ( int j = 0; j < n; j++)
{
for ( int k = 0; k < n; k++)
{
int val = arr[i] * arr[j] + arr[k];
result += (upper_bound(RHS, RHS + index, val) -
lower_bound(RHS, RHS + index, val));
}
}
}
return result;
}
int main()
{
int arr[] = {2, 3};
int n = sizeof (arr)/ sizeof (arr[0]);
cout << findSextuplets(arr, n) << endl;
return 0;
}
|
Java
import java.util.Arrays;
class GFG{
static int upper_bound( int [] array, int length, int value) {
int low = 0 ;
int high = length;
while (low < high) {
final int mid = (low + high) / 2 ;
if (value >= array[mid]) {
low = mid + 1 ;
} else {
high = mid;
}
}
return low;
}
static int lower_bound( int [] array, int length, int value) {
int low = 0 ;
int high = length;
while (low < high) {
final int mid = (low + high) / 2 ;
if (value <= array[mid]) {
high = mid;
} else {
low = mid + 1 ;
}
}
return low;
}
static int findSextuplets( int [] arr, int n)
{
int index = 0 ;
int [] RHS = new int [n * n * n + 1 ];
for ( int i = 0 ; i < n; i++)
{
if (arr[i] != 0 )
{
for ( int j = 0 ; j < n; j++)
{
for ( int k = 0 ; k < n; k++)
{
RHS[index++] = arr[i] * (arr[j] + arr[k]);
}
}
}
}
Arrays.sort(RHS);
int result = 0 ;
for ( int i = 0 ; i < n; i++)
{
for ( int j = 0 ; j < n; j++)
{
for ( int k = 0 ; k < n; k++)
{
int val = arr[i] * arr[j] + arr[k];
result += (upper_bound(RHS, index, val)-lower_bound(RHS, index, val));
}
}
}
return result;
}
public static void main(String[] args)
{
int [] arr = { 2 , 3 };
int n = arr.length;
System.out.println(findSextuplets(arr, n));
}
}
|
Python3
def upper_bound(array, length, value):
low = 0 ;
high = length;
while (low < high):
mid = int ((low + high) / 2 );
if (value > = array[mid]):
low = mid + 1 ;
else :
high = mid;
return low;
def lower_bound(array, length, value):
low = 0 ;
high = length;
while (low < high):
mid = int ((low + high) / 2 );
if (value < = array[mid]):
high = mid;
else :
low = mid + 1 ;
return low;
def findSextuplets(arr, n):
index = 0 ;
RHS = [ 0 ] * (n * n * n + 1 );
for i in range (n):
if (arr[i] ! = 0 ):
for j in range (n):
for k in range (n):
RHS[index] = arr[i] * (arr[j] +
arr[k]);
index + = 1 ;
RHS.sort();
result = 0 ;
for i in range (n):
for j in range (n):
for k in range (n):
val = arr[i] * arr[j] + arr[k];
result + = (upper_bound(RHS, index, val) -
lower_bound(RHS, index, val));
return result;
arr = [ 2 , 3 ];
n = len (arr);
print (findSextuplets(arr, n));
|
C#
using System;
using System.Collections;
class GFG{
static int upper_bound( int [] array, int length, int value) {
int low = 0;
int high = length;
while (low < high) {
int mid = (low + high) / 2;
if (value >= array[mid]) {
low = mid + 1;
} else {
high = mid;
}
}
return low;
}
static int lower_bound( int [] array, int length, int value) {
int low = 0;
int high = length;
while (low < high) {
int mid = (low + high) / 2;
if (value <= array[mid]) {
high = mid;
} else {
low = mid + 1;
}
}
return low;
}
static int findSextuplets( int [] arr, int n)
{
int index = 0;
int [] RHS = new int [n * n * n + 1];
for ( int i = 0; i < n; i++)
{
if (arr[i] != 0)
{
for ( int j = 0; j < n; j++)
{
for ( int k = 0; k < n; k++)
{
RHS[index++] = arr[i] * (arr[j] + arr[k]);
}
}
}
}
Array.Sort(RHS);
int result = 0;
for ( int i = 0; i < n; i++)
{
for ( int j = 0; j < n; j++)
{
for ( int k = 0; k < n; k++)
{
int val = arr[i] * arr[j] + arr[k];
result += (upper_bound(RHS, index, val)-lower_bound(RHS, index, val));
}
}
}
return result;
}
static void Main()
{
int [] arr = {2, 3};
int n = arr.Length;
Console.WriteLine(findSextuplets(arr, n));
}
}
|
PHP
<?php
function upper_bound( $array , $length , $value )
{
$low = 0;
$high = $length ;
while ( $low < $high )
{
$mid = (int)(( $low + $high ) / 2);
if ( $value >= $array [ $mid ])
$low = $mid + 1;
else
$high = $mid ;
}
return $low ;
}
function lower_bound( $array , $length , $value )
{
$low = 0;
$high = $length ;
while ( $low < $high )
{
$mid = (int)(( $low + $high ) / 2);
if ( $value <= $array [ $mid ])
$high = $mid ;
else
$low = $mid + 1;
}
return $low ;
}
function findSextuplets( $arr , $n )
{
$index = 0;
$RHS = array_fill (0, $n * $n * $n + 1, 0);
for ( $i = 0; $i < $n ; $i ++)
if ( $arr [ $i ] != 0)
for ( $j = 0; $j < $n ; $j ++)
for ( $k = 0; $k < $n ; $k ++)
$RHS [ $index ++] = $arr [ $i ] *
( $arr [ $j ] + $arr [ $k ]);
sort( $RHS );
$result = 0;
for ( $i = 0; $i < $n ; $i ++)
for ( $j = 0; $j < $n ; $j ++)
for ( $k = 0; $k < $n ; $k ++)
{
$val = $arr [ $i ] * $arr [ $j ] + $arr [ $k ];
$result += (upper_bound( $RHS , $index , $val ) -
lower_bound( $RHS , $index , $val ));
}
return $result ;
}
$arr = array (2, 3);
$n = count ( $arr );
print (findSextuplets( $arr , $n ));
?>
|
Javascript
<script>
function upper_bound(array , length , value)
{
var low = 0;
var high = length;
while (low < high) {
var mid = parseInt((low + high) / 2);
if (value >= array[mid]) {
low = mid + 1;
} else {
high = mid;
}
}
return low;
}
function lower_bound(array , length , value)
{
var low = 0;
var high = length;
while (low < high) {
var mid = parseInt((low + high) / 2);
if (value <= array[mid]) {
high = mid;
} else {
low = mid + 1;
}
}
return low;
}
function findSextuplets(arr , n)
{
var index = 0;
var RHS = Array.from({length: n * n * n + 1},
(_, i) => 0);
for (i = 0; i < n; i++)
{
if (arr[i] != 0)
{
for (j = 0; j < n; j++)
{
for (k = 0; k < n; k++)
{
RHS[index++] = arr[i] *
(arr[j] + arr[k]);
}
}
}
}
RHS.sort((a,b)=>a-b);
var result = 0;
for (i = 0; i < n; i++)
{
for (j = 0; j < n; j++)
{
for (k = 0; k < n; k++)
{
var val = arr[i] * arr[j] + arr[k];
result += (upper_bound(RHS, index, val)-
lower_bound(RHS, index, val));
}
}
}
return result;
}
var arr = [2, 3];
var n = arr.length;
document.write(findSextuplets(arr, n));
</script>
|
Time Complexity : O(N3 log N)
Auxiliary Space: O(N3) as it is using extra space for array RHS
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