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>  
        /// 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>  
        /// 打印出杨辉三角形  
        /// </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="n"></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;  
            }  
            else  
                outString = new char[strNum.Length];  
  
            for ( int i = 0; i < outString.Length; i++ )  
            {  
                if ( i >= startIndex && i < startIndex + strNum.Length )  
                    outString[i] = strNum[i - startIndex];  
                else  
                    outString[i] = ' ';  
            }  
  
            return new String( outString );  
        }  
        /// <summary>  
        /// 打印杨辉三角型的某一层  
        /// </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 );  
            }  
        }  
    }  
}