Fun C program 100.9 draw Yang Hui Triangle

Description: 1. The problem stems from "C language Classics, interesting, practical programming programming hundred examples of fine solutions", all the procedures for myself to write. Marked with a difference from the original program.

2. All programs in this series are compiled with Codeblocks and the operating system is Windows XP.

Problem: Display Yang Hui triangle on screen

1

1 1

1 2 1

1 3 3 1

1 4 6) 4 1

1 5 10 10 5 1

....................................

Analysis: I use the characteristics of graphics, design two arrays, the loop output, the code is as follows.

#include <stdio.h>#include<stdlib.h>intMainvoid){    intI=0, j=0; inta[ -]={0}, b[ -]={0}; a[0]=1; intRows=1; printf ("Please input rows:"); scanf ("%d", &rows);//control how many lines are output     for(i=1; i<=rows; i++)    {         for(j=0; j<rows-i; J + +)//control the space before each line of the output{printf ("  "); }         for(j=0; j<rows; J + +)//copy array A to array b{B[j]=A[j]; }         for(j=1; j<=i-1; J + +)//assign a value to the next line through array b{A[j]= b[j-1] +B[j]; }         for(j=0; j<rows; J + +)//output a new line of array a        {            if(a[j]!=0) printf ("%4d", A[j]); } printf ("\ n"); }    return 0;}

The output is as follows:

Figure 1

The original book analysis is as follows:

The number in the Yang Hui triangle is exactly the coefficient of the N-Power expansion of the (x+y). From the characteristics of Yang Hui triangle, we can summarize:

1) The nth line has a n+1 value (set the starting behavior 0 lines);

2) for the nth row of the J value: (n>=2);

When J=1 or j=n+1: the value is 1;

J! =1 and J! =n+1: The value is the J-1 value of the N-1 row and the value of the first J.

The above features are refined into mathematical formulas that can be expressed as:

1 X=1 or X=n+1

C (x, y) =c (x-1,y-1) +c (x-1,y)

#include <stdio.h>#include<stdlib.h>intYanghui (intXinty);intMainvoid){    intI, J, n= -; printf ("n=");  while(n> A) scanf ("%d", &n);//control Enter the correct values to ensure that the graphics on the screen are displayed correctly     for(i=0; i<=n; i++)//control output N rows    {         for(j=0; j< --2*i; J + +) printf (" ");//control output Space before line I         for(j=1; j<i+2; J + +) printf ("%4d", Yanghui (i, j));//outputs the J value of line Iprintf ("\ n"); }    return 0;}intYanghui (intXinty) {    intZ; if((y==1)|| (y==x+1))        return 1; Z=yanghui (x1, Y1) +yanghui (x1, y); returnZ;}

The output is as follows:

Figure 2

Fun C program 100.9 draw Yang Hui Triangle