用 2 的 N+1 次方表示 2^N

给定一个正整数N ，任务是将2^N表示为2的幂和正好是N+1项。打印那些N+1项。

例子：

Input: N = 4
Output: 1 1 2 4 8
Explanation: 2^4 = 2^0 + 2^0 + 2^1 + 2^2 + 2^3 = 1 + 1 + 2 + 4 + 8

Input: N = 5
Output: 1 1 2 4 8 16

编程需要懂一点英语

方法：我们知道：

2^0 + 2^1 +…. 2^(N-1) = 2^N -1

编程需要懂一点英语

因此，在2的一系列幂的开头添加1将导致2^N正好N+1项。

1 + 2^0 + 2^1 +…. 2^(N-1) = 2^N

编程需要懂一点英语

下面是上述方法的实现

C++

// C++ program for the above approach
 
#include 
using namespace std;
 
// Function to find exactly N + 1 terms
// of powers of 2 series,  whose sum is 2^N
void powerOf2(long long N)
{
    cout << 1 << ' ';
    for (int i = 0; i < N; ++i) {
        cout << (long long)pow(2, i) << ' ';
    }
}
 
// Driver Code
int main()
{
    long long N = 5;
 
    powerOf2(N);
}

Java

// Java program for the above approach
import java.util.*;
public class GFG
{
// Function to find exactly N + 1 terms
// of powers of 2 series,  whose sum is 2^N
static void powerOf2(long N)
{
    System.out.print(1);
    for (int i = 0; i < N; ++i) {
        System.out.print(" " + (long)Math.pow(2, i));
    }
}
 
// Driver Code
public static void main(String args[])
{
    long N = 5;
    powerOf2(N);
}
}
// This code is contributed by Samim Hossain Mondal

C#

// C# program for the above approach
using System;
class GFG
{
// Function to find exactly N + 1 terms
// of powers of 2 series,  whose sum is 2^N
static void powerOf2(long N)
{
    Console.Write(1);
    for (int i = 0; i < N; ++i) {
        Console.Write(" " + (long)Math.Pow(2, i));
    }
}
 
// Driver Code
public static void Main()
{
    long N = 5;
    powerOf2(N);
}
}
// This code is contributed by Samim Hossain Mondal

Python3

# Python3 program for the above approach
import math
 
# Function to find exactly N + 1 terms
# of powers of 2 series,  whose sum is 2^N
def powerOf2(N) :
 
    print(1,end= ' ');
    for i in range(N) :
        print(int(math.pow(2, i)),end = ' ');
 
# Driver Code
if __name__ == "__main__" :
 
    N = 5;
 
    powerOf2(N);
     
    # This code is contributed by AnkThon

Javascript

输出

1 1 2 4 8 16

时间复杂度： O(N)
辅助空间： O(1)