The nth Taxicab number Taxicab(n), also called the n-th Hardy-Ramanujan number, is defined as the smallest number that can be expressed as a sum of two positive cube numbers in n distinct ways.
The most famous taxicab number is 1729 = Taxicab(2) = (1 ^ 3) + (12 ^ 3) = (9 ^ 3) + (10 ^ 3).
Given a number N, print first N Taxicab(2) numbers.
Examples:
Input: N = 1 Output: 1729 Explanation: 1729 = (1 ^ 3) + (12 ^ 3) = (9 ^ 3) + (10 ^ 3) Input: N = 2 Output: 1729 4104 Explanation: 1729 = (1 ^ 3) + (12 ^ 3) = (9 ^ 3) + (10 ^ 3) 4104 = (16 ^ 3) + (2 ^ 3) = (15 ^ 3) + (9 ^ 3)
We try all numbers one by one and check if it is a taxicab number. To check if a number is Taxicab, we use two nested loops:
In outer loop, we calculate cube root of a number.
In inner loop, we check if there is a cube-root that yield the result.
// C++ implementation to print first N Taxicab(2) // numbers : #include<bits/stdc++.h> using namespace std;
void printTaxicab2( int N)
{ // Starting from 1, check every number if
// it is Taxicab until count reaches N.
int i = 1, count = 0;
while (count < N)
{
int int_count = 0;
// Try all possible pairs (j, k) whose cube
// sums can be i.
for ( int j = 1; j <= pow (i, 1.0/3); j++)
for ( int k = j + 1; k <= pow (i, 1.0/3); k++)
if (j*j*j + k*k*k == i)
int_count++;
// Taxicab(2) found
if (int_count == 2)
{
count++;
cout << count << " " << i << endl;
}
i++;
}
} // Driver code int main()
{ int N = 5;
printTaxicab2(N);
return 0;
} |
// JAVA Code for Taxicab Numbers import java.util.*;
class GFG {
public static void printTaxicab2( int N)
{
// Starting from 1, check every number if
// it is Taxicab until count reaches N.
int i = 1 , count = 0 ;
while (count < N)
{
int int_count = 0 ;
// Try all possible pairs (j, k) whose
// cube sums can be i.
for ( int j = 1 ; j <= Math.pow(i, 1.0 / 3 ); j++)
for ( int k = j + 1 ; k <= Math.pow(i, 1.0 / 3 );
k++)
if (j * j * j + k * k * k == i)
int_count++;
// Taxicab(2) found
if (int_count == 2 )
{
count++;
System.out.println(count + " " + i);
}
i++;
}
}
/* Driver program to test above function */
public static void main(String[] args)
{
int N = 5 ;
printTaxicab2(N);
}
} // This code is contributed by Arnav Kr. Mandal. |
# Python3 implementation to print # first N Taxicab(2) numbers import math
def printTaxicab2(N):
# Starting from 1, check every number if
# it is Taxicab until count reaches N.
i, count = 1 , 0
while (count < N):
int_count = 0
# Try all possible pairs (j, k)
# whose cube sums can be i.
for j in range ( 1 , math.ceil(\
pow (i, 1.0 / 3 )) + 1 ):
for k in range (j + 1 ,\
math.ceil( pow (i, 1.0 / 3 )) + 1 ):
if (j * j * j + k * k * k = = i):
int_count + = 1
# Taxicab(2) found
if (int_count = = 2 ):
count + = 1
print (count, " " , i)
i + = 1
# Driver code N = 5
printTaxicab2(N) # This code is contributed by Anant Agarwal. |
// C# Code for Taxicab Numbers using System;
class GFG {
public static void printTaxicab2( int N)
{
// Starting from 1, check every number if
// it is Taxicab until count reaches N.
int i = 1, count = 0;
while (count < N)
{
int int_count = 0;
// Try all possible pairs (j, k) whose
// cube sums can be i.
for ( int j = 1; j <= Math.Pow(i, 1.0/3); j++)
for ( int k = j + 1; k <= Math.Pow(i, 1.0/3);
k++)
if (j * j * j + k * k * k == i)
int_count++;
// Taxicab(2) found
if (int_count == 2)
{
count++;
Console.WriteLine(count + " " + i);
}
i++;
}
}
// Driver program
public static void Main()
{
int N = 5;
printTaxicab2(N);
}
} // This code is contributed by vt_m. |
<?php // PHP implementation to print first // N Taxicab(2) numbers : function printTaxicab2( $N )
{ // Starting from 1, check every
// number if it is Taxicab until
// count reaches N.
$i = 1; $count = 0;
while ( $count < $N )
{
$int_count = 0;
// Try all possible pairs (j, k)
// whose cube sums can be i.
for ( $j = 1; $j <= pow( $i , 1.0/3); $j ++)
for ( $k = $j + 1; $k <= pow( $i , 1.0/3); $k ++)
if ( $j * $j * $j + $k * $k * $k == $i )
$int_count ++;
// Taxicab(2) found
if ( $int_count == 2)
{
$count ++;
echo $count , " " , $i , "\n" ;
}
$i ++;
}
} // Driver code $N = 5;
printTaxicab2( $N );
// This code is contributed by ajit. ?> |
<script> // Javascript implementation to print first // N Taxicab(2) numbers : function printTaxicab2(N)
{ // Starting from 1, check every
// number if it is Taxicab until
// count reaches N.
let i = 1; count = 0;
while (count < N)
{
let int_count = 0;
// Try all possible pairs (j, k)
// whose cube sums can be i.
for (let j = 1; j <= Math.pow(i, 1.0/3); j++)
for (let k = j + 1; k <= Math.pow(i, 1.0/3); k++)
if (j * j * j + k * k * k == i)
int_count++;
// Taxicab(2) found
if (int_count == 2)
{
count++;
document.write(count + " " + i + "<br>" );
}
i++;
}
} // Driver code let N = 5;
printTaxicab2(N);
// This code is contributed by _saurabh_jaiswal. </script> |
1 1729 2 4104 3 13832 4 20683 5 32832
Time Complexity: O(i^(5/3)) were i is the last number checked for being a Taxicab number. Basically time complexity in this is output sensitive.
Auxiliary Space: O(1)