给定一个整数N ,任务是计算直到N次方的偶数和奇数二项式系数的数量。
例子:
Input: N = 4
Output:
Odd: 2
Even: 3
Explanation:
The binomial coefficients are as follows:
4C0 = 1, 4C1 = 4 , 4C2 = 6 , 4C3 = 4 , 4C4 = 1.
Therefore, it can be observed that there exists exactly 2 odd and 3 even Binomial Coefficients.
Input: N = 5
Output:
Odd: 4
Even: 2
Explanation:
The binomial coefficients are as follows:
5C0 = 1, 5C1 = 5, 5C2 = 10, 5C3 = 10, 5C4 = 5, 5C5 = 1.
Therefore, there are 4 odd and 2 even coefficients.
解决方法:解决此问题的想法是使用位操作。在给定的整数N中找到设置的位。奇二项式系数的计数等于N中置位的2 ^计数。同样,偶数二项式系数的计数等于(N + 1-2 ^ N中的置位计数) 。
下面是上述方法的实现:
C++
// C++ program for the above approach
#include
#include
using namespace std;
// Function to count set bits in
// binary representation of number N
int countSetBits(int N)
{
int count = 0;
// Count set bits in N
while (N) {
N = N & (N - 1);
count++;
}
// Return the final count
return count;
}
// Driver Code
int main()
{
int N = 4;
int bits = countSetBits(N);
// Print odd Binomial coefficents
cout << "Odd "
<< ": " << pow(2, bits) << "\n";
// Print even Binomial coefficents
cout << "Even "
<< ": " << N + 1 - pow(2, bits)
<< "\n";
return 0;
}
Java
// Java program for the above approach
import java.util.*;
class GFG{
// Function to count set bits in
// binary representation of number N
static int countSetBits(int N)
{
int count = 0;
// Count set bits in N
while (N != 0)
{
N = N & (N - 1);
count++;
}
// Return the final count
return count;
}
// Driver code
public static void main(String[] args)
{
int N = 4;
int bits = countSetBits(N);
// Print odd Binomial coefficents
System.out.println("Odd " + ": " +
(int)(Math.pow(2, bits)));
// Print even Binomial coefficents
System.out.println("Even " + ": " +
(N + 1 - (int)(Math.pow(2, bits))));
}
}
// This code is contributed by susmitakundugoaldanga
Python3
# Python3 program for the above approach
# Function to count set bits in
# binary representation of number N
def countSetBits(N: int) -> int:
count = 0
# Count set bits in N
while (N):
N = N & (N - 1)
count += 1
# Return the final count
return count
# Driver Code
if __name__ == "__main__":
N = 4
bits = countSetBits(N)
# Print odd Binomial coefficents
print("Odd : {}".format(pow(2, bits)))
# Print even Binomial coefficents
print("Even : {}".format(N + 1 - pow(2, bits)))
# This code is contributed by sanjeev2552
C#
// C# program for the above approach
using System;
class GFG{
// Function to count set bits in
// binary representation of number N
static int countSetBits(int N)
{
int count = 0;
// Count set bits in N
while (N != 0)
{
N = N & (N - 1);
count++;
}
// Return the final count
return count;
}
// Driver Code
public static void Main()
{
int N = 4;
int bits = countSetBits(N);
// Print odd Binomial coefficents
Console.WriteLine("Odd " + ": " +
(int)(Math.Pow(2, bits)));
// Print even Binomial coefficents
Console.WriteLine("Even " + ": " +
(N + 1 - (int)(Math.Pow(2, bits))));
}
}
// This code is contributed by sanjoy_62
Javascript
输出:
Odd : 2
Even : 3
时间复杂度: O(1)
辅助空间: O(1)