Dado un número s (1 <= s <= 1000000000). Si s es la suma de los cubos de los primeros n números naturales, imprima n, de lo contrario imprima -1.
Los primeros números triangulares cuadrados son 1, 9, 36, 100, 225, 441, 784, 1296, 2025, 3025, …
Ejemplos:
Input : 9 Output : 2 Explanation : The given number is sum of cubes of first 2 natural numbers. 1*1*1 + 2*2*2 = 9 Input : 13 Output : -1
Una solución sencilla es sumar cubos de números naturales uno a uno. Si la suma actual es igual al número dado, devolvemos el recuento de los números naturales agregados hasta el momento. De lo contrario, devolvemos -1.
C++
// C++ program to check if a
// given number is sum of
// cubes of natural numbers.
#include <iostream>
using namespace std;
// Function to find if
// the given number is
// sum of the cubes of
// first n natural numbers
int findS(int s)
{
int sum = 0;
// Start adding cubes of
// the numbers from 1
for (int n = 1; sum < s; n++)
{
sum += n * n * n;
// If sum becomes equal to s
// return n
if (sum == s)
return n;
}
return -1;
}
// Driver code
int main()
{
int s = 9;
int n = findS(s);
n == -1 ? cout << "-1" : cout << n;
return 0;
}
C
// C program to check if a
// given number is sum of
// cubes of natural numbers.
#include <stdio.h>
// Function to find if
// the given number is
// sum of the cubes of
// first n natural numbers
int findS(int s)
{
int sum = 0;
// Start adding cubes of
// the numbers from 1
for (int n = 1; sum < s; n++)
{
sum += n * n * n;
// If sum becomes equal to s
// return n
if (sum == s)
return n;
}
return -1;
}
// Driver code
int main()
{
int s = 9;
int n = findS(s);
n == -1 ? printf("-1") : printf("%d",n);
return 0;
}
// This code is contributed by kothavvsaakash.
Java
// Java program to check if
// a given number is sum of
// cubes of natural numbers.
class GFG
{
// Function to find if
// the given number is
// sum of the cubes of
// first n natural numbers
static int findS(int s)
{
int sum = 0;
// Start adding cubes of
// the numbers from 1
for (int n = 1; sum < s; n++)
{
sum += n * n * n;
// If sum becomes equal to s
// return n
if (sum == s)
return n;
}
return -1;
}
// Drivers code
public static void main(String[] args)
{
int s = 9;
int n = findS(s);
if (n == -1)
System.out.println("-1");
else
System.out.println(n);
}
}
Python3
# Python3 program to find
# if the given number is
# sum of the cubes of first
# n natural numbers
# Function to find if the
# given number is sum of
# the cubes of first n
# natural numbers
def findS (s):
_sum = 0
n = 1
# Start adding cubes of
# the numbers from 1
while(_sum < s):
_sum += n * n * n
n += 1
n-= 1
# If sum becomes equal to s
# return n
if _sum == s:
return n
return -1
# Driver code
s = 9
n = findS (s)
if n == -1:
print("-1")
else:
print(n)
C#
// C# program to check if a
// given number is sum of
// cubes of natural numbers.
using System;
class GFG
{
// Function to find if the
// given number is sum of
// the cubes of first n
// natural numbers
public static int findS(int s)
{
int sum = 0;
// Start adding cubes of
// the numbers from 1
for (int n = 1; sum < s; n++)
{
sum += n * n * n;
// If sum becomes equal to s
// return n
if (sum == s)
return n;
}
return -1;
}
// Driver code
static public void Main (string []args)
{
int s = 9;
int n = findS(s);
if (n == -1)
Console.WriteLine("-1");
else
Console.WriteLine(n);
}
}
// This code is contributed by Ajit.
PHP
<?php
// PHP program to check if
// a given number is sum of
// cubes of natural numbers.
// Function to find if the
// given number is sum of
// the cubes of first n
// natural numbers
function findS($s)
{
$sum = 0;
// Start adding cubes of
// the numbers from 1
for ($n = 1; $sum < $s; $n++)
{
$sum += $n * $n * $n;
// If sum becomes equal to s
// return n
if ($sum == $s)
return $n;
}
return -1;
}
// Driver code
$s = 9;
$n = findS($s);
if($n == -1)
echo("-1");
else
echo($n);
// This code is contributed by Ajit.
?>
Javascript
<script>
// Javascript program to check if a
// given number is sum of
// cubes of natural numbers.
// Function to find if
// the given number is
// sum of the cubes of
// first n natural numbers
function findS(s)
{
let sum = 0;
// Start adding cubes of
// the numbers from 1
for (let n = 1; sum < s; n++)
{
sum += n * n * n;
// If sum becomes equal to s
// return n
if (sum == s)
return n;
}
return -1;
}
// Driver code
let s = 9;
let n = findS(s);
n == -1 ? document.write("-1") :document.write(n);
// This code is contributed by aashish1995
</script>
Producción:
2
Una solución eficiente se basa en la fórmula [n(n+1)/2] 2 para la suma de los primeros n cubos. Podemos ver que todos los números son cuadrados.
1) Comprueba si el número dado es un cuadrado perfecto.
2) Compruebe si la raíz cuadrada es triangular (consulte el método 2 de números triangulares para esto)
C++
// C++ program to check if a
// given number is sum of
// cubes of natural numbers.
#include <bits/stdc++.h>
using namespace std;
// Returns root of n(n+1)/2 = num
// if num is triangular (or integer
// root exists). Else returns -1.
int isTriangular(int num)
{
if (num < 0)
return false;
// Considering the equation
// n*(n+1)/2 = num. The equation
// is : a(n^2) + bn + c = 0";
int c = (-2 * num);
int b = 1, a = 1;
int d = (b * b) - (4 * a * c);
if (d < 0)
return -1;
// Find roots of equation
float root1 = ( -b + sqrt(d)) / (2 * a);
float root2 = ( -b - sqrt(d)) / (2 * a);
// checking if root1 is natural
if (root1 > 0 && floor(root1) == root1)
return root1;
// checking if root2 is natural
if (root2 > 0 && floor(root2) == root2)
return root2;
return -1;
}
// Returns square root of x if it is
// perfect square. Else returns -1.
int isPerfectSquare(long double x)
{
// Find floating point value of
// square root of x.
long double sr = sqrt(x);
// If square root is an integer
if ((sr - floor(sr)) == 0)
return floor(sr);
else
return -1;
}
// Function to find if the given number
// is sum of the cubes of first n
// natural numbers
int findS(int s)
{
int sr = isPerfectSquare(s);
if (sr == -1)
return -1;
return isTriangular(sr);
}
// Driver code
int main()
{
int s = 9;
int n = findS(s);
n == -1 ? cout << "-1" : cout << n;
return 0;
}
C
// C program to check if a
// given number is sum of
// cubes of natural numbers.
#include <stdio.h>
#include <stdbool.h>
#include <math.h>
// Returns root of n(n+1)/2 = num
// if num is triangular (or integer
// root exists). Else returns -1.
int isTriangular(int num)
{
if (num < 0)
return false;
// Considering the equation
// n*(n+1)/2 = num. The equation
// is : a(n^2) + bn + c = 0";
int c = (-2 * num);
int b = 1, a = 1;
int d = (b * b) - (4 * a * c);
if (d < 0)
return -1;
// Find roots of equation
float root1 = ( -b + sqrt(d)) / (2 * a);
float root2 = ( -b - sqrt(d)) / (2 * a);
// checking if root1 is natural
if (root1 > 0 && floor(root1) == root1)
return root1;
// checking if root2 is natural
if (root2 > 0 && floor(root2) == root2)
return root2;
return -1;
}
// Returns square root of x if it is
// perfect square. Else returns -1.
int isPerfectSquare(long double x)
{
// Find floating point value of
// square root of x.
long double sr = sqrt(x);
// If square root is an integer
if ((sr - floor(sr)) == 0)
return floor(sr);
else
return -1;
}
// Function to find if the given number
// is sum of the cubes of first n
// natural numbers
int findS(int s)
{
int sr = isPerfectSquare(s);
if (sr == -1)
return -1;
return isTriangular(sr);
}
// Driver code
int main()
{
int s = 9;
int n = findS(s);
n == -1 ? printf("-1") : printf("%d",n);
return 0;
}
// This code is contributed by kothavvsaakash.
Java
// Java program to check
// if a given number is
// sum of cubes of natural
// numbers.
// import java.Math.*;
class GFG
{
// Returns root of n(n+1)/2 = num
// if num is triangular (or
// integer root exists). Else
// returns -1.
public static int isTriangular(int num)
{
if (num < 0)
return 0;
// Considering the equation
// n*(n+1)/2 = num. The equation
// is : a(n^2) + bn + c = 0";
int c = (-2 * num);
int b = 1, a = 1;
int d = (b * b) -
(4 * a * c);
if (d < 0)
return -1;
// Find roots of equation
double root1 = (-b +
Math.sqrt(d)) / (2 * a);
double root2 = (-b -
Math.sqrt(d)) / (2 * a);
// checking if root1 is natural
if ((int)(root1) > 0 &&
(int)(Math.floor(root1)) ==
(int)(root1))
return (int)(root1);
// checking if
// root2 is natural
if ((int)(root2) > 0 &&
(int)(Math.floor(root2)) ==
(int)(root2))
return (int)(root2);
return -1;
}
// Returns square root
// of x if it is perfect
// square. Else returns -1.
static int isPerfectSquare(double x)
{
// Find floating point
// value of square root of x.
double sr = Math.sqrt(x);
// If square root
// is an integer
if ((sr - Math.floor(sr)) == 0)
return (int)(Math.floor(sr));
else
return -1;
}
// Function to find if the
// given number is sum of
// the cubes of first n
// natural numbers
static int findS(int s)
{
int sr = isPerfectSquare(s);
if (sr == -1)
return -1;
return isTriangular(sr);
}
// Driver code
public static void main(String[] args)
{
int s = 9;
int n = findS(s);
if(n == -1)
System.out.println("-1");
else
System.out.println(n);
}
}
// This code is contributed
// by mits.
Python3
# Python3 program to check
# if a given number is sum of
# cubes of natural numbers.
import math
# Returns root of n(n+1)/2 = num
# if num is triangular (or integer
# root exists). Else returns -1.
def isTriangular(num):
if (num < 0):
return False;
# Considering the equation
# n*(n+1)/2 = num. The equation
# is : a(n^2) + bn + c = 0";
c = (-2 * num);
b = 1;
a = 1;
d = (b * b) - (4 * a * c);
if (d < 0):
return -1;
# Find roots of equation
root1 = (-b + math.sqrt(d)) // (2 * a);
root2 = (-b - math.sqrt(d)) // (2 * a);
# checking if root1 is natural
if (root1 > 0 and
math.floor(root1) == root1):
return root1;
# checking if root2 is natural
if (root2 > 0 and
math.floor(root2) == root2):
return root2;
return -1;
# Returns square root of
# x if it is perfect square.
# Else returns -1.
def isPerfectSquare(x):
# Find floating point value
# of square root of x.
sr = math.sqrt(x);
# If square root is an integer
if ((sr - math.floor(sr)) == 0):
return math.floor(sr);
else:
return -1;
# Function to find if the given
# number is sum of the cubes of
# first n natural numbers
def findS(s):
sr = isPerfectSquare(s);
if (sr == -1):
return -1;
return int(isTriangular(sr));
# Driver code
s = 9;
n = findS(s);
if(n == -1):
print("-1");
else:
print(n);
# This code is contributed by mits.
C#
// C# program to check if a
// given number is sum of
// cubes of natural numbers.
using System;
class GFG
{
// Returns root of n(n+1)/2 = num
// if num is triangular (or integer
// root exists). Else returns -1.
static int isTriangular(int num)
{
if (num < 0)
return 0;
// Considering the equation
// n*(n+1)/2 = num. The equation
// is : a(n^2) + bn + c = 0";
int c = (-2 * num);
int b = 1, a = 1;
int d = (b * b) -
(4 * a * c);
if (d < 0)
return -1;
// Find roots of equation
double root1 = (-b + Math.Sqrt(d)) / (2 * a);
double root2 = (-b - Math.Sqrt(d)) / (2 * a);
// checking if root1 is natural
if ((int)(root1) > 0 &&
(int)(Math.Floor(root1)) == (int)(root1))
return (int)(root1);
// checking if root2 is natural
if ((int)(root2) > 0 &&
(int)(Math.Floor(root2)) == (int)(root2))
return (int)(root2);
return -1;
}
// Returns square root of x
// if it is perfect square.
// Else returns -1.
static int isPerfectSquare(double x)
{
// Find floating point
// value of square root of x.
double sr = Math.Sqrt(x);
// If square root
// is an integer
if ((sr - Math.Floor(sr)) == 0)
return (int)(Math.Floor(sr));
else
return -1;
}
// Function to find if the
// given number is sum of
// the cubes of first n
// natural numbers
static int findS(int s)
{
int sr = isPerfectSquare(s);
if (sr == -1)
return -1;
return isTriangular(sr);
}
// Driver code
public static void Main()
{
int s = 9;
int n = findS(s);
if(n == -1)
Console.Write("-1");
else
Console.Write(n);
}
}
// This code is contributed by mits.
PHP
<?php
// PHP program to check if a
// given number is sum of
// cubes of natural numbers.
// Returns root of n(n+1)/2 = num
// if num is triangular (or integer
// root exists). Else returns -1.
function isTriangular($num)
{
if ($num < 0)
return false;
// Considering the equation
// n*(n+1)/2 = num. The equation
// is : a(n^2) + bn + c = 0";
$c = (-2 * $num);
$b = 1;
$a = 1;
$d = ($b * $b) - (4 * $a * $c);
if ($d < 0)
return -1;
// Find roots of equation
$root1 = (-$b + sqrt($d)) /
(2 * $a);
$root2 = (-$b - sqrt($d)) /
(2 * $a);
// checking if root1 is natural
if ($root1 > 0 &&
floor($root1) == $root1)
return $root1;
// checking if root2 is natural
if ($root2 > 0 &&
floor($root2) == $root2)
return $root2;
return -1;
}
// Returns square root of
// x if it is perfect square.
// Else returns -1.
function isPerfectSquare($x)
{
// Find floating point value
// of square root of x.
$sr = sqrt($x);
// If square root is an integer
if (($sr - floor($sr)) == 0)
return floor($sr);
else
return -1;
}
// Function to find if the given
// number is sum of the cubes of
// first n natural numbers
function findS($s)
{
$sr = isPerfectSquare($s);
if ($sr == -1)
return -1;
return isTriangular($sr);
}
// Driver code
$s = 9;
$n = findS($s);
if($n == -1)
echo "-1";
else
echo $n;
// This code is contributed by mits.
?>
Javascript
<script>
// javascript program to check
// if a given number is
// sum of cubes of natural
// numbers.
// Returns root of n(n+1)/2 = num
// if num is triangular (or
// integer root exists). Else
// returns -1.
function isTriangular(num)
{
if (num < 0)
return 0;
// Considering the equation
// n*(n+1)/2 = num. The equation
// is : a(n^2) + bn + c = 0";
var c = (-2 * num);
var b = 1, a = 1;
var d = (b * b) - (4 * a * c);
if (d < 0)
return -1;
// Find roots of equation
var root1 = (-b + Math.sqrt(d)) / (2 * a);
var root2 = (-b - Math.sqrt(d)) / (2 * a);
// checking if root1 is natural
if (parseInt( (root1)) > 0 && parseInt( (Math.floor(root1))) == parseInt( (root1)))
return parseInt(root1);
// checking if
// root2 is natural
if (parseInt( (root2)) > 0 && parseInt( (Math.floor(root2))) == parseInt( (root2)))
return parseInt( (root2));
return -1;
}
// Returns square root
// of x if it is perfect
// square. Else returns -1.
function isPerfectSquare(x)
{
// Find floating point
// value of square root of x.
var sr = Math.sqrt(x);
// If square root
// is an integer
if ((sr - Math.floor(sr)) == 0)
return parseInt( (Math.floor(sr)));
else
return -1;
}
// Function to find if the
// given number is sum of
// the cubes of first n
// natural numbers
function findS(s) {
var sr = isPerfectSquare(s);
if (sr == -1)
return -1;
return isTriangular(sr);
}
// Driver code
var s = 9;
var n = findS(s);
if (n == -1)
document.write("-1");
else
document.write(n);
// This code is contributed by Rajput-Ji.
</script>
Producción :
2
Publicación traducida automáticamente
Artículo escrito por pawan_asipu y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA