%%% ----------------------------------------------------------------------------
%%% pascaltriangle: Typeset Pascal triangle figure with LaTeX3
%%% Author    : Nan Geng <nangeng@nwafu.edu.cn>
%%% Repository: https://github.com/registor/pascaltriangle or https://gitee.com/nwafu_nan/pascaltriangle
%%% License   : The LaTeX Project Public License 1.3c
%%% ----------------------------------------------------------------------------

\NeedsTeXFormat{LaTeX2e}
\RequirePackage{expl3}
\ProvidesExplPackage{pascaltriangle}{2022-01-28}{v1.0.1}
  {Typeset Pascal triangle figure with LaTeX3}

\RequirePackage{xparse}

%% \tl_if_eq:NnTF 与texlive 2020的兼容性设置
\cs_if_exist:NF \tl_if_eq:NnTF
  {
    \tl_new:N \l__tblr_backport_b_tl
    \prg_new_protected_conditional:Npnn \tl_if_eq:Nn #1 #2 { T, F, TF }
      {
        \group_begin:
          \tl_set:Nn \l__tblr_backport_b_tl {#2}
          \exp_after:wN
        \group_end:
        \if_meaning:w #1 \l__tblr_backport_b_tl
          \prg_return_true:
        \else:
          \prg_return_false:
        \fi:
      }
    \prg_generate_conditional_variant:Nnn \tl_if_eq:Nn { c } { TF, T, F }
  }

\cs_if_exist:NF \seq_map_indexed_function:NN
  {
    \cs_set_eq:NN \seq_map_indexed_function:NN \seq_indexed_map_function:NN
  }

%% 解决TikZ库无法在Expl3中载入问题
\RequirePackage {amsmath, tikz, etoolbox}
\ExplSyntaxOff
\patchcmd
{\tcb@input@library@in}
  {%
   \input\tcbpkgprefix#1\relax%
  }
  {%
    \@pushfilename
    \input\tcbpkgprefix#1\relax%
    \@popfilename
  }
  {}{}

\patchcmd
{\pgfutil@InputIfFileExists}
  {\input #1}
  {%
    \@pushfilename
    \xdef\@currname{#1}%
    \input #1 %
    \@popfilename
  }
  {}{}
\ExplSyntaxOn
\usetikzlibrary{shapes.geometric}

%% 定义变量
\bool_new:N  \l__pascal_num_cell_bool   % 是否绘制行列号
\bool_new:N  \l__pascal_binom_cell_bool % 是否仅绘制二项式表达式

\tl_new:N    \l__pascal_cell_color_tl   % 单元格填充颜色
\tl_new:N    \l__pascal_shift_col_pt_tl % 列变换坐标
\tl_new:N    \l__pascal_shift_row_pt_tl % 行变换坐标
\tl_new:N    \l__pascal_font_size_tl    % 文件大小

\int_new:N    \l__pascal_shape_type_int % 形状(1---等腰，2---直角)
\int_new:N    \l__pascal_row_idx_int    % 行索引(从0计数)
\int_new:N    \l__pascal_col_idx_int    % 列索引(从0计数)
\int_new:N    \l__pascal_row_top_int    % 各列最大行数
\int_new:N    \l__pascal_total_idx_int  % 索引总数
\int_new:N    \l__pascal_fill_row_int   % 填充行号(最大值与当前列数有关，从顶向下从0计数)
\int_new:N    \l__pascal_fill_col_int   % 填充列号(从0计数)

\dim_new:N    \l__pascal_cell_radius_dim % 单元格大小(中心到顶点的半径)

%% 选项设计
\keys_define:nn { pascal }
  {
    % 是否需要行列编号
    withnum .bool_set:N = \l__pascal_num_cell_bool,
    withnum .default:n = true,
    withnum .initial:n = false,

    % 是否仅绘制二项式表达式
    binom .bool_set:N = \l__pascal_binom_cell_bool,
    binom .default:n = true,
    binom .initial:n = false,

    % 形状选择(iso---等腰三角形, rt---直角三角形)
    shape .choice:,
    shape .value_required:n = true,
    shape .choices:nn =
      { iso, rt }
      { \int_set_eq:NN \l__pascal_shape_type_int \l_keys_choice_int },
    shape .initial:n = iso,

    % 单元格半径(中心到顶点)
    radius .dim_set:N  = \l__pascal_cell_radius_dim,
    radius .initial:n = 0.5cm,

    % 文字大小
    fontsize .tl_set:N  = \l__pascal_font_size_tl,
    fontsize .initial:n = \small,

    % 要填充单元格行数(按列从顶向下，从0开始计数)
    fillr .int_set:N = \l__pascal_fill_row_int,
    fillr .initial:n = 1 ,
    % 要填充单元格列数(从左向右，从0开始计数)
    fillc .int_set:N = \l__pascal_fill_col_int,
    fillc .initial:n = 1 ,
    fillrc  .meta:n = { fillr = #1 , fillc = #1 },

    unknown .code:n = { \__pascal_error:n { unknown-option } }
  }

\msg_new:nnn { pascal } { unknown-option }
  { package~ option~ "\l_keys_key_tl"~ is~ unknown. }

%% 参数设置用户接口
\NewDocumentCommand \pascalset { m }
  { \keys_set:nn { pascal } {#1} }

%% 利用LaTeX3的fact阶乘计算函数计算组合数
\cs_set:Npn \__pascal_binomcoeff:nn #1#2
  {
    \fp_eval:n { fact(#1) / (fact(#2) * fact(#1 - #2)) }
  }

%% 组合数计算用户接口
\NewDocumentCommand{\binomc}{m m}
  {
    \__pascal_binomcoeff:nn{#1}{#2}
  }

%% 绘制Pascal三角形
%% 注意":"无法使用造成极坐标不能用的问题，以下网站给出了解决方案
%% https://tex.stackexchange.com/questions/501333/how-to-use-colon-as-part-of-tikz-syntax-while-in-explsyntaxon-environment
%% 将":"用\c_colon_str代替

%% 根据形状类型计算列变换坐标(极坐标)
\cs_set:Npn \__pascal_shift_col_pt:n #1
  {
    \int_case:nn { \l__pascal_shape_type_int }
      {
        {1}{
          \tl_set:Nn \l__pascal_shift_col_pt_tl { -60 \c_colon_str
              \fp_eval:n {sqrt(3) * \l__pascal_cell_radius_dim * #1}pt
            }
        }
        {2}{
          \tl_set:Nn \l__pascal_shift_col_pt_tl { -45 \c_colon_str
              \fp_eval:n {2 * \l__pascal_cell_radius_dim * #1}pt
            }
        }
      }
  }

%% 根据形状类型计算行变换坐标(极坐标)
\cs_set:Npn \__pascal_shift_row_pt:n #1
  {
    \int_case:nn { \l__pascal_shape_type_int }
      {
        {1}{
          \tl_set:Nn \l__pascal_shift_row_pt_tl { -120 \c_colon_str
              \fp_eval:n {sqrt(3) * \l__pascal_cell_radius_dim * #1}pt
            }
        }
        {2}{
          \tl_set:Nn \l__pascal_shift_row_pt_tl { -90 \c_colon_str
              \fp_eval:n {sqrt(2) * \l__pascal_cell_radius_dim * #1}pt
            }
        }
      }
  }

%% 正六边形闭合路径代码
\cs_set:Npn \__pascal_hex_cell:
  {
    (30  \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) --
    (90  \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) --
    (150 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) --
    (210 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) --
    (270 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) --
    (330 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) --
    cycle (90 \c_colon_str 0)
  }

%% 正方形闭合路径代码
\cs_set:Npn \__pascal_square_cell:
  {
    (45  \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) --
    (134 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) --
    (225 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) --
    (-45 \c_colon_str \fp_eval:n{\l__pascal_cell_radius_dim}pt) --
    cycle (90 \c_colon_str 0)
  }

%% 绘制行列编号标记单元格
\cs_set:Npn \__pascal_num_draw:nnn #1#2#3
  {
    \int_case:nn { \l__pascal_shape_type_int }
      {
        {1}{% 正六边形
          \int_compare:nNnT { #1 } = {0}% 最左列
            {
              \int_compare:nNnT { #2 } = { #3 - 1 }% 最底行
                {
                  \begin{scope}[shift={(-150\c_colon_str {\fp_eval:n{3*\l__pascal_cell_radius_dim}pt})}]
                    \draw[dashed, top~color=gray!10,bottom~color=gray!20]
                      \__pascal_hex_cell:
                      node[rotate=-45] {$m,n$};
                  \end{scope}
                }
            }
          \int_compare:nNnT { #1 } = { 0 }% 最左列
            {
              \begin{scope}[shift={(-180\c_colon_str {\fp_eval:n{sqrt(3)*\l__pascal_cell_radius_dim}pt})}]
                \draw[dashed, top~color=gray!10,bottom~color=gray!20]
                  \__pascal_hex_cell:
                  node{$(\int_eval:n {#2})$};
              \end{scope}
            }
          \int_compare:nNnT { #2 } = { #3 - 1 }% 最底行
            {
              \begin{scope}[shift={(-120\c_colon_str {\fp_eval:n{sqrt(3)*\l__pascal_cell_radius_dim}pt})}]
                \draw[dashed, top~color=gray!10,bottom~color=gray!20]
                  \__pascal_hex_cell:
                  node {$(\int_eval:n {#1})$};
              \end{scope}
            }
        }
        {2}{% 正方形
          \int_compare:nNnT { #1 } = {0}% 最左列
            {
              \int_compare:nNnT { #2 } = { #3 - 1 }% 最底行
                {
                  \begin{scope}[shift={(-135\c_colon_str {\fp_eval:n{2*\l__pascal_cell_radius_dim}pt})}]
                    \draw[dashed, top~color=gray!10,bottom~color=gray!20]
                      \__pascal_square_cell:
                      node[scale=0.8,rotate=-45] {$m,n$};
                  \end{scope}
                }
            }
          \int_compare:nNnT { #1 } = { 0 }% 最左列
            {
              \begin{scope}[shift={(-180\c_colon_str {\fp_eval:n{sqrt(2)*\l__pascal_cell_radius_dim}pt})}]
                \draw[dashed, top~color=gray!10,bottom~color=gray!20]
                  \__pascal_square_cell:
                  node{$(\int_eval:n {#2})$};
              \end{scope}
            }
          \int_compare:nNnT { #2 } = { #3 - 1 }% 最底行
            {
              \begin{scope}[shift={(-90\c_colon_str {\fp_eval:n{sqrt(2)*\l__pascal_cell_radius_dim}pt})}]
                \draw[dashed, top~color=gray!10,bottom~color=gray!20]
                  \__pascal_square_cell:
                  node {$(\int_eval:n {#1})$};
              \end{scope}
            }
        }
      }
  }

%% 绘制三角形单元格
\cs_set:Npn \__pascal_cell_draw:nn #1#2
  {
    \int_case:nn { \l__pascal_shape_type_int }
      {
        {1}{% 正六边形
          \draw[top~color=\l__pascal_cell_color_tl!20,bottom~color=\l__pascal_cell_color_tl!60]
            \__pascal_hex_cell:
            \bool_if:NTF \l__pascal_binom_cell_bool
              {
                node {$\binom{\int_eval:n {#1}}{\int_eval:n {#2}}$};
              }
              {
                node {$\__pascal_binomcoeff:nn {#1}{#2}$};
              }
        }
        {2}{% 正方形
          \draw[top~color=\l__pascal_cell_color_tl!20,bottom~color=\l__pascal_cell_color_tl!60]
            \__pascal_square_cell:
            \bool_if:NTF \l__pascal_binom_cell_bool
              {
                node {$\binom{\int_eval:n {#1}}{\int_eval:n {#2}}$};
              }
              {
                node {$\__pascal_binomcoeff:nn {#1}{#2}$};
              }
        }
      }
  }

%% 绘制Pascal三角形
% 等腰三角形的绘制原理参考了 https://texample.net/tikz/examples/pascal-triangle/
% Author: M.H. Ahmadi
\cs_set:Npn \__pascal_triangle_draw:n #1
  {
    % 设置正常单元格为灰色
    \tl_set:Nn \l__pascal_cell_color_tl {gray}
    % 记录绘制列数
    \int_set:Nn \l_tmpa_int {#1}

    % 使用TikZ绘制
    \begin{tikzpicture}[font=\l__pascal_font_size_tl]
      % 列循环
      \int_step_inline:nn {\l_tmpa_int}
        {
          % 调整为从0计数，以便于后续计算
          \int_set:Nn \l__pascal_col_idx_int { ##1 - 1 }

          % 计算列变换坐标(极坐标)
          \__pascal_shift_col_pt:n {\l__pascal_col_idx_int}

          % 用scope环境变换各列到指定位置
          \begin{scope}[shift={(\l__pascal_shift_col_pt_tl)}]
            % 计算每列最多行数
            \int_set:Nn \l__pascal_row_top_int {\l_tmpa_int - ##1 + 1}

            % 行循环
            \int_step_inline:nn { \l__pascal_row_top_int }
            {
              % 调整为从0计数，以便于后续计算
              \int_set:Nn \l__pascal_row_idx_int { ####1 - 1 }

              % 计算组合数计算中的行数
              \int_zero:N \l__pascal_total_idx_int
              \int_add:Nn \l__pascal_total_idx_int { \l__pascal_row_idx_int }
              \int_add:Nn \l__pascal_total_idx_int { \l__pascal_col_idx_int }

              % 为指定行设置绘制颜色
              \int_case:nn { \l__pascal_col_idx_int }
                {
                  {0}{
                    \tl_set:Nn \l__pascal_cell_color_tl { pink }
                  }
                  {1}{
                    \tl_set:Nn \l__pascal_cell_color_tl { yellow }
                  }
                  {2}{
                    \tl_set:Nn \l__pascal_cell_color_tl { blue }
                  }
                  {3}{
                    \tl_set:Nn \l__pascal_cell_color_tl { green }
                  }
                  {\l__pascal_fill_col_int - 1}{
                    \int_compare:nNnTF{\l__pascal_row_idx_int} < { \l__pascal_fill_row_int + 1 }
                      {\tl_set:Nn \l__pascal_cell_color_tl { purple }}
                      {\tl_set:Nn \l__pascal_cell_color_tl { gray }}
                  }
                  {\l__pascal_fill_col_int}{
                    \int_compare:nNnTF{\l__pascal_row_idx_int} = { \l__pascal_fill_row_int }
                      {\tl_set:Nn \l__pascal_cell_color_tl { purple }}
                      {\tl_set:Nn \l__pascal_cell_color_tl { gray }}
                  }
                }

              % 计算行变换坐标(极坐标)
              \__pascal_shift_row_pt:n {\l__pascal_row_idx_int}
              % 用scope环境变换各行到指定位置
              \begin{scope}[shift={(\l__pascal_shift_row_pt_tl)}]
                % 是否绘制行列编号
                \bool_if:NT \l__pascal_num_cell_bool
                  {
                    \__pascal_num_draw:nnn { \l__pascal_col_idx_int }
                                           { \l__pascal_row_idx_int }
                                           { \l__pascal_row_top_int }
                  }
                % 绘制一个单元格
                \__pascal_cell_draw:nn{\l__pascal_total_idx_int}{\l__pascal_col_idx_int}
              \end{scope}
            }
          \end{scope}
        }
    \end{tikzpicture}
  }

%% 绘制Pascal三角形用户接口
\NewDocumentCommand{\pascal}{O{} m}
  {
    \group_begin:
      \keys_set:nn { pascal } {#1}
      \__pascal_triangle_draw:n{#2}
    \group_end:
  }

\endinput