杨辉三角型打印

注：

利用杨辉三角形可以快速的列出牛顿二项式分解。
如：杨辉三角第6行值是 1 6 15 20 15 6 1
对应的二项式分解就是
$m+n)^6=m^6+6m^5n+15m^4n^2+20m^3n^3+15m^2n^4+6mn^5+n^6$

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;namespace 杨辉三角
{public class Program{private const string spaceChar = "      ";/// <summary>/// 主函数/// </summary>/// <param name="args"></param>public static void Main( string[] args ){PrintYangHui( 13 );//PrintYangHui( 8, 8 );YangHui( 13 );Console.ReadLine();}/// <summary>/// 递归调用-打印三角形/// </summary>/// <param name="n"></param>/// <returns></returns>public static int[] PrintYangHui( int n ){if ( n == 1 ) return Print( new int[] { 1 } );if ( n == 2 ){PrintYangHui( n - 1 );return Print( new int[] { 1, 1 } );}int[] pR = PrintYangHui( n - 1 );int[] R = new int[n];R[0] = 1;for ( int i = 1; i < R.Length - 1; i++ ) R[i] = pR[i] + pR[i - 1];R[R.Length - 1] = 1;return Print( R );}/// <summary>/// 格式化输出到控制台的样式/// </summary>/// <param name="result"></param>public static int[] Print( int[] result ){StringBuilder Space = new StringBuilder();string spaceChar = "      ";for ( int i = 0; i < result.Length; i++ ) Console.Write( result[i].ToString() + spaceChar );Console.WriteLine();return result;}/// <summary>/// 打印居中的杨辉三角形/// </summary>/// <param name="totalLevel">总的层次数，用来控制第一行的前面需要多少个分隔符</param>/// <param name="level ">打印第几层</param>/// <returns></returns>public static int[] PrintYangHui( int totalLevel, int level ){if ( Level == 1 ) return Print( totalLevel, new int[] { 1 } );if ( Level == 2 ){PrintYangHui( totalLevel, Level - 1 );return Print( totalLevel, new int[] { 1, 1 } );}int[] pR = PrintYangHui( totalLevel, Level - 1 );int[] R = new int[Level];R[0] = 1;for ( int i = 1; i < R.Length - 1; i++ ) R[i] = pR[i] + pR[i - 1];R[R.Length - 1] = 1;return Print( totalLevel, R );}/// <summary>/// 打印居中的杨辉三角形/// </summary>/// <param name="result"></param>public static int[] Print( int totalLevel, int[] result ){StringBuilder Space = new StringBuilder();for ( int i = totalLevel; i > result.Length; i-- ) Space.Append( spaceChar );Console.Write( Space );for ( int i = 0; i < result.Length; i++ ) Console.Write( FormatString( 5, result[i] ) + spaceChar );Console.WriteLine();return result;}/// <summary>/// 格式化数字串/// </summary>/// <param name="Len"></param>/// <param name="num"></param>/// <returns></returns>public static string FormatString( int Len, int num ){char[] outString;string strNum = num.ToString();int startIndex = 0;if ( strNum.Length < Len ){outString = new char[Len];startIndex = ( Len - strNum.Length ) / 2;}elseoutString = new char[strNum.Length];for ( int i = 0; i < outString.Length; i++ ){if ( i >= startIndex && i < startIndex + strNum.Length )outString[i] = strNum[i - startIndex];elseoutString[i] = ' ';}return new String( outString );}/// <summary>/// 打印杨辉三角型的某一层，通过位置，计算出每层每个位置的数值，节省运行空间/// </summary>/// <param name="N">本次打印二项式N次方的系数</param>public static void Print( int N ){for ( int k = 0; k <= N; k++ ){int V = 1; // 用来保存N阶乘除以i阶乘的值int S = 1; // 用来保存N-i的阶乘int I = 0;for ( int i = k + 1; i <= N; i++ )	// N阶除以(N-i)阶后再除以i阶{V *= i;I = ( N - i + 1 );S *= I;if ( V % I == 0 )// 如果此时V可以被I整除，就先整除，以免最终V的阶乘太大导致数据溢出{V /= I;S /= I;}else if ( V % S == 0 )// 如果此时V可以被S整除，就先整除，以免最终V的阶乘数太大导致数据溢出{V /= S;S = 1;}}V /= S;Console.Write( V.ToString() + spaceChar );}Console.WriteLine();}/// <summary>/// 打印居中的杨辉三角形/// </summary>/// <param name="n"></param>/// <returns></returns>public static void YangHui( int totalLevel){for ( int i = 0; i < totalLevel; i++ ){//StringBuilder Space = new StringBuilder();//for ( int j = TotalLevel; j > i; j-- ) Space.Append( spaceChar );//Console.Write( Space );Print( i );}}}
}