给定一个整数N ,任务是检查这个数字是否可以表示为两个连续的完美立方体的总和。
例子:
Input: N = 35
Output: Yes
Explanation:
Since, 35 = 23 + 33, therefore the required answer is Yes.
Input: N = 14
Output: No
朴素方法:解决问题的最简单方法是从 1 迭代到N 的立方根,并检查任意两个连续数的完全立方之和是否等于N。如果发现是真的,打印“是”。否则,打印“否”。
下面是上述方法的实现:
C++
// C++ Program of the
// above approach
#include
using namespace std;
// Function to check if a number
// can be expressed as the sum of
// cubes of two consecutive numbers
bool isCubeSum(int n)
{
for (int i = 1; i * i * i <= n; i++) {
if (i * i * i
+ (i + 1) * (i + 1) * (i + 1)
== n)
return true;
}
return false;
}
// Driver Code
int main()
{
int n = 35;
if (isCubeSum(n))
cout << "Yes";
else
cout << "No";
}
Java
// Java program of the
// above approach
import java.util.*;
class GFG{
// Function to check if a number
// can be expressed as the sum of
// cubes of two consecutive numbers
static boolean isCubeSum(int n)
{
for(int i = 1; i * i * i <= n; i++)
{
if (i * i * i + (i + 1) *
(i + 1) * (i + 1) == n)
return true;
}
return false;
}
// Driver Code
public static void main(String[] args)
{
int n = 35;
if (isCubeSum(n))
System.out.print("Yes");
else
System.out.print("No");
}
}
// This code is contributed by Amit Katiyar
Python3
# Python3 program of the
# above approach
# Function to check if a number
# can be expressed as the sum of
# cubes of two consecutive numbers
def isCubeSum(n):
for i in range(1, int(pow(n, 1 / 3)) + 1):
if (i * i * i + (i + 1) *
(i + 1) * (i + 1) == n):
return True;
return False;
# Driver Code
if __name__ == '__main__':
n = 35;
if (isCubeSum(n)):
print("Yes");
else:
print("No");
# This code is contributed by Amit Katiyar
C#
// C# program of the
// above approach
using System;
class GFG{
// Function to check if a number
// can be expressed as the sum of
// cubes of two consecutive numbers
static bool isCubeSum(int n)
{
for(int i = 1; i * i * i <= n; i++)
{
if (i * i * i + (i + 1) *
(i + 1) * (i + 1) == n)
return true;
}
return false;
}
// Driver Code
public static void Main(String[] args)
{
int n = 35;
if (isCubeSum(n))
Console.Write("Yes");
else
Console.Write("No");
}
}
// This code is contributed by Amit Katiyar
Javascript
C++
// C++ Program to
// implement above approach
#include
using namespace std;
// Function to check that a number
// is the sum of cubes of 2
// consecutive numbers or not
bool isSumCube(int N)
{
int a = cbrt(N);
int b = a - 1;
// Condition to check if a
// number is the sum of cubes of 2
// consecutive numbers or not
return ((a * a * a + b * b * b) == N);
}
// Driver Code
int main()
{
int i = 35;
// Function call
if (isSumCube(i)) {
cout << "Yes";
}
else {
cout << "No";
}
return 0;
}
Java
// Java program to implement
// above approach
class GFG{
// Function to check that a number
// is the sum of cubes of 2
// consecutive numbers or not
static boolean isSumCube(int N)
{
int a = (int)Math.cbrt(N);
int b = a - 1;
// Condition to check if a
// number is the sum of cubes of 2
// consecutive numbers or not
return ((a * a * a + b * b * b) == N);
}
// Driver Code
public static void main(String[] args)
{
int i = 35;
// Function call
if (isSumCube(i))
{
System.out.print("Yes");
}
else
{
System.out.print("No");
}
}
}
// This code is contributed by Amit Katiyar
Python3
# Python3 program to
# implement above approach
# Function to check that a number
# is the sum of cubes of 2
# consecutive numbers or not
def isSumCube(N):
a = int(pow(N, 1 / 3))
b = a - 1
# Condition to check if a
# number is the sum of cubes of 2
# consecutive numbers or not
ans = ((a * a * a + b * b * b) == N)
return ans
# Driver Code
i = 35
# Function call
if(isSumCube(i)):
print("Yes")
else:
print("No")
# This code is contributed by Shivam Singh
C#
// C# program to implement
// above approach
using System;
class GFG{
// Function to check that a number
// is the sum of cubes of 2
// consecutive numbers or not
static bool isSumCube(int N)
{
int a = (int)Math.Pow(N, (double) 1 / 3);
int b = a - 1;
// Condition to check if a
// number is the sum of cubes of 2
// consecutive numbers or not
return ((a * a * a + b * b * b) == N);
}
// Driver Code
public static void Main(String[] args)
{
int i = 35;
// Function call
if (isSumCube(i))
{
Console.Write("Yes");
}
else
{
Console.Write("No");
}
}
}
// This code is contributed by 29AjayKumar
Javascript
输出:
Yes
高效的方法:上述方法可以基于以下观察进行优化:
- 如果两个连续数的立方根之和等于N ,则一个数可以表示为两个连续数的完全立方之和。
- 这可以通过公式来检查:
- 例如,如果N = 35 ,则检查 os 下面的等式是否等于N :
下面是上述方法的实现:
C++
// C++ Program to
// implement above approach
#include
using namespace std;
// Function to check that a number
// is the sum of cubes of 2
// consecutive numbers or not
bool isSumCube(int N)
{
int a = cbrt(N);
int b = a - 1;
// Condition to check if a
// number is the sum of cubes of 2
// consecutive numbers or not
return ((a * a * a + b * b * b) == N);
}
// Driver Code
int main()
{
int i = 35;
// Function call
if (isSumCube(i)) {
cout << "Yes";
}
else {
cout << "No";
}
return 0;
}
Java
// Java program to implement
// above approach
class GFG{
// Function to check that a number
// is the sum of cubes of 2
// consecutive numbers or not
static boolean isSumCube(int N)
{
int a = (int)Math.cbrt(N);
int b = a - 1;
// Condition to check if a
// number is the sum of cubes of 2
// consecutive numbers or not
return ((a * a * a + b * b * b) == N);
}
// Driver Code
public static void main(String[] args)
{
int i = 35;
// Function call
if (isSumCube(i))
{
System.out.print("Yes");
}
else
{
System.out.print("No");
}
}
}
// This code is contributed by Amit Katiyar
蟒蛇3
# Python3 program to
# implement above approach
# Function to check that a number
# is the sum of cubes of 2
# consecutive numbers or not
def isSumCube(N):
a = int(pow(N, 1 / 3))
b = a - 1
# Condition to check if a
# number is the sum of cubes of 2
# consecutive numbers or not
ans = ((a * a * a + b * b * b) == N)
return ans
# Driver Code
i = 35
# Function call
if(isSumCube(i)):
print("Yes")
else:
print("No")
# This code is contributed by Shivam Singh
C#
// C# program to implement
// above approach
using System;
class GFG{
// Function to check that a number
// is the sum of cubes of 2
// consecutive numbers or not
static bool isSumCube(int N)
{
int a = (int)Math.Pow(N, (double) 1 / 3);
int b = a - 1;
// Condition to check if a
// number is the sum of cubes of 2
// consecutive numbers or not
return ((a * a * a + b * b * b) == N);
}
// Driver Code
public static void Main(String[] args)
{
int i = 35;
// Function call
if (isSumCube(i))
{
Console.Write("Yes");
}
else
{
Console.Write("No");
}
}
}
// This code is contributed by 29AjayKumar
Javascript
输出:
Yes
时间复杂度: O(1)
辅助空间: O(1)