二项式系数表程序

给定最大整数，打印二项式系数表将打印所有二项式系数B(m，x)，其中m和x从0到最大值变化
例子 ：

Input : max = 3
Output :  
 0   1
 1   1   1
 2   1   2   1
 3   1   3   3   1

解释什么是二项式系数最简单的方法是说，它们计算对项目进行分组的某些方式。具体而言，二项式系数B(m，x)计算形成从n个不同项目的集合中选择的k个项目的无序集合的方式的数量。
二项式系数用于研究二项式分布和多分量冗余系统。它是由$B(m, x)= m! / x!(m - x)!, m> = x$
例子 ：

Compute B(7, 3)  where m = 7 and x = 1 
          (7!/3!(7-3)!)7
        = 7!/3!*4!
        = (7*6*5*4*3*2*1)/(3*2*1)*(4*3*2*1)
        = 35

需要一个二项式系数表来确定任何值m和x的二项式系数。
问题分析：
二项式系数可以递归计算如下：
$B(m, x) = B(m, x - 1) [m - x + 1 / x], x = 1, 2, 3 .... m$更多， $b(0, 0) = 1$
也就是说，当x为零或m为零时，二项式系数为1。该程序将打印二项式系数表$m = 10$ 。

C++

// C++ program for binomial coefficients
#include 
 
// Function to print binomial table
int printbinomial(int max)
{
    for (int m = 0; m <= max; m++) {
        printf("%2d", m);
        int binom = 1;
        for (int x = 0; x <= m; x++) {
 
            // B(m, x) is 1 if either m or x is
            // is 0.
            if (m != 0 && x != 0)
 
                // Otherwise using recursive formula
                // B(m, x) = B(m, x - 1) * (m - x + 1) / x
                binom = binom * (m - x + 1) / x;
 
            printf("%4d", binom);
        }
        printf("\n");
    }
}
 
// Driver Function
int main()
{
    int max = 10;
    printbinomial(max);
    return 0;
}

Java

// Java program for
// binomial coefficients
import java.io.*;
 
class GFG
{
     
// Function to print
// binomial table
static void printbinomial(int max)
{
    for (int m = 0; m <= max; m++)
    {
        System.out.print(m + " ");
        int binom = 1;
        for (int x = 0; x <= m; x++)
        {
 
            // B(m, x) is 1 if either
            // m or x is is 0.
            if (m != 0 && x != 0)
 
                // Otherwise using
                // recursive formula
                // B(m, x) = B(m, x - 1) *
                //            (m - x + 1) / x
                binom = binom * (m - x + 1) / x;
 
            System.out.print(binom + " ");
        }
        System.out.println();
    }
}
 
// Driver Code
public static void main (String[] args)
{
    int max = 10;
    printbinomial(max);
}
}
 
// This code is contributed
// by akt_mit

Python3

# Python3 program for binomial
# coefficients
 
# Function to print binomial table
def printbinomial (max):
     
    for m in range(max + 1):
        print( '% 2d'% m, end = ' ')
        binom = 1
        for x in range(m + 1):
             
            # B(m, x) is 1 if either m
            # or x is is 0.
            if m != 0 and x != 0:
                 
                # Otherwise using recursive
                # formula
                # B(m, x) = B(m, x - 1) *
                #           (m - x + 1) / x
                binom = binom * (m - x + 1) / x
            print( '% 4d'% binom, end = ' ')
        print("\n", end = '')
         
# Driver Function
max = 10
printbinomial(max)
 
# This code is contributed by "Sharad_bhardwaj".

C#

// C# program for binomial coefficients
using System;
 
public class GFG {
 
    // Function to print binomial table
    static void printbinomial(int max)
    {
        for (int m = 0; m <= max; m++) {
            Console.Write(m + " ");
            int binom = 1;
            for (int x = 0; x <= m; x++) {
 
                // B(m, x) is 1 if either m
                // or x is is 0.
                if (m != 0 && x != 0)
 
                    // Otherwise using recursive formula
                    // B(m, x) = B(m, x - 1) * (m - x + 1) / x
                    binom = binom * (m - x + 1) / x;
 
                Console.Write(binom + " ");
            }
            Console.WriteLine();
        }
    }
 
    // Driver Function
    static public void Main()
    {
        int max = 10;
        printbinomial(max);
    }
}
 
// This code is contributed by vt_m.

Javascript

// Javascript program for
// binomial coefficients
 
// Function to print
// binomial table
function printbinomial(max)
{
    for (let m = 0; m <= max; m++)
    {
        document.write(m);
        let binom = 1;
        for (let x = 0; x <= m; x++)
        {
 
            // B(m, x) is 1 if either
            // m or x is 0.
            if (m != 0 && x != 0)
             
                // Otherwise using
                // recursive formula
                // B(m, x) = B(m, x - 1) *
                //            (m - x + 1) / x
                binom = binom * (m - x + 1) / x;
             
            document.write(" " + binom + " ");
        }
    document.write("<br>");
    }
}
 
// Driver Code
let max = 10;
printbinomial(max);
 
// This code is contributed by _saurabh_jaiswal

输出 ：

0   1
 1   1   1
 2   1   2   1
 3   1   3   3   1
 4   1   4   6   4   1
 5   1   5  10  10   5   1
 6   1   6  15  20  15   6   1
 7   1   7  21  35  35  21   7   1
 8   1   8  28  56  70  56  28   8   1
 9   1   9  36  84 126 126  84  36   9   1
10   1  10  45 120 210 252 210 120  45  10   1