task_1.tex

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{positioning, arrows.meta}

\begin{document}

\begin{figure}
\centering
\begin{tikzpicture}[auto, node distance=1.5cm,>=Stealth]

    % Define node styles
    \tikzstyle{node} = [circle, draw, minimum size=8mm]
    \tikzstyle{source} = [circle, draw, minimum size=8mm, fill=black!20]
    \tikzstyle{sink} = [circle, draw, minimum size=8mm, fill=black!20]
    \tikzstyle{edge} = [->, thick]
    
    % Nodes
    \node[source] (source) at (-3, -3.75) {source};
    \node[node, right=3cm of source, yshift=9.00cm] (A1) {A1};
    \node[node, below of=A1] (A2) {A2};
    \node[node, below of=A2] (A3) {A3};
    \node[node, below of=A3] (A4) {A4};
    \node[node, below of=A4] (A5) {A5};
    \node[node, below of=A5] (A6) {A6};
    \node[node, below of=A6] (B1) {B1};
    \node[node, below of=B1] (B2) {B2};
    \node[node, below of=B2] (B3) {B3};
    \node[node, below of=B3] (B4) {B4};
    \node[node, below of=B4] (C1) {C1};
    \node[node, below of=C1] (C2) {C2};
    \node[node, below of=C2] (C3) {C3};
    
    \node[node, right=4cm of A1, yshift=-5.5cm] (F1) {F1};
    \node[node, below of=F1] (F2) {F2};
    \node[node, below of=F2] (F3) {F3};
    \node[node, below of=F3] (F4) {F4};
    \node[node, below of=F4] (F5) {F5};
    \node[node, below of=F5] (F6) {F6};
    \node[sink, right=3cm of F3, yshift=-0.25cm] (sink) {sink};
    
    % Source edges
    \foreach \i in {A1, A2, A3, A4, A5, A6, B1, B2, B3, B4, C1, C2, C3}
        \draw[edge] (source) -- (\i);

    % Edges between left and right nodes with weights
    \draw[edge, blue] (A1) -- node[above] {7} (F1);
    \draw[edge, blue] (A2) -- node[above] {7} (F2);
    \draw[edge, blue] (A3) -- node[above] {7} (F3);
    \draw[edge, blue] (A4) -- node[above] {7} (F4);
    \draw[edge, blue] (A5) -- node[above] {7} (F5);
    \draw[edge, blue] (A6) -- node[above] {7} (F6);

    \draw[edge, red] (B1) -- node[above right] {8} (F1);
    \draw[edge, red] (B2) -- node[above right] {8} (F2);
    \draw[edge, red] (B3) -- node[above] {8} (F4);
    \draw[edge, red] (B4) -- node[above] {8} (F6);

    \draw[edge, green] (C1) -- node[above right] {5} (F1);
    \draw[edge, green] (C1) -- node[above right] {5} (F2);
    \draw[edge, green] (C2) -- node[above] {10} (F3);
    \draw[edge, green] (C3) -- node[above] {10} (F5);
    
    % Right-side edges to sink
    \foreach \i/\w in {F1/20, F2/20, F3/17, F4/15, F5/17, F6/15}
        \draw[edge] (\i) -- node[above] {\w} (sink);

\end{tikzpicture}
\caption{Network flow graph}
\end{figure}

\begin{figure}
    \begin{tikzpicture}
    % Define spacing and length variables
    \def\lineLength{12} % Length of each line
    \def\tickSpacing{0.1} % Spacing between ticks

    % Adjust y-coordinates for larger spacing
    \def\lineAShift{5} % y-coordinate of line A
    \def\lineBShift{2.5} % y-coordinate of line B
    \def\lineCShift{0} % y-coordinate of line C

    % Draw line A
    \node[left] at (0, \lineAShift) {};
    \draw[->] (0, \lineAShift) -- ++(\lineLength, 0);
    \foreach \x in {0,...,11} % Add tick marks along the line
        \draw (\x, \lineAShift - 0.2) -- ++(0, 0.4);

    % Frame 1
    \draw[fill=blue!20, draw=blue] (0, \lineAShift) rectangle (0.7, \lineAShift + 0.5);
    \node at (0.35, \lineAShift + 0.2) {$A_1$};
    \node at (0.35, \lineAShift + 1) {7};
    
    \draw[fill=red!20, draw=red] (0.7, \lineAShift) rectangle (1.5, \lineAShift + 0.5);
    \node at (1.1, \lineAShift + 0.2) {$B_1$};
    \node at (1.1, \lineAShift + 1) {8};
    
    \draw[fill=green!20, draw=green] (1.5, \lineAShift) rectangle (2, \lineAShift + 0.5);
    \node at (1.75, \lineAShift + 0.2) {$C_1$};
    \node at (1.75, \lineAShift + 1) {5};

    % Frame 2
    \draw[fill=blue!20, draw=blue] (2, \lineAShift) rectangle (2.7, \lineAShift + 0.5);
    \node at (2.35, \lineAShift + 0.2) {$A_2$};
    \node at (2.35, \lineAShift + 1) {7};

    \draw[fill=green!20, draw=green] (2.7, \lineAShift) rectangle (3.3, \lineAShift + 0.5);
    \node at (3.0, \lineAShift + 0.2) {$C_1$};
    \node at (3.0, \lineAShift + 1) {5};
    
    \draw[fill=red!20, draw=red] (3.3, \lineAShift) rectangle (4, \lineAShift + 0.5);
    \node at (3.65, \lineAShift + 0.2) {$B_2$};
    \node at (3.65, \lineAShift + 1) {8};

    % Frame 3
    \draw[fill=blue!20, draw=blue] (4, \lineAShift) rectangle (4.7, \lineAShift + 0.5);
    \node at (4.35, \lineAShift + 0.2) {$A_3$};
    \node at (4.35, \lineAShift + 1) {7};

    \draw[fill=green!20, draw=green] (4.7, \lineAShift) rectangle (5.7, \lineAShift + 0.5);
    \node at (5.2, \lineAShift + 0.2) {$C_2$};
    \node at (5.2, \lineAShift + 1) {10};

    % Frame 4
    \draw[fill=blue!20, draw=blue] (6, \lineAShift) rectangle (6.7, \lineAShift + 0.5);
    \node at (6.35, \lineAShift + 0.2) {$A_4$};
    \node at (6.35, \lineAShift + 1) {7};

    \draw[fill=red!20, draw=red] (6.7, \lineAShift) rectangle (7.5, \lineAShift + 0.5);
    \node at (7.1, \lineAShift + 0.2) {$B_3$};
    \node at (7.1, \lineAShift + 1) {8};

    % Frame 5
    \draw[fill=blue!20, draw=blue] (8, \lineAShift) rectangle (8.7, \lineAShift + 0.5);
    \node at (8.35, \lineAShift + 0.2) {$A_5$};
    \node at (8.35, \lineAShift + 1) {7};

    \draw[fill=green!20, draw=green] (8.7, \lineAShift) rectangle (9.7, \lineAShift + 0.5);
    \node at (9.2, \lineAShift + 0.2) {$C_3$};
    \node at (9.2, \lineAShift + 1) {10};

    % Frame 6
    \draw[fill=blue!20, draw=blue] (10, \lineAShift) rectangle (10.7, \lineAShift + 0.5);
    \node at (10.35, \lineAShift + 0.2) {$A_6$};
    \node at (10.35, \lineAShift + 1) {7};
    
    \draw[fill=red!20, draw=red] (10.7, \lineAShift) rectangle (11.5, \lineAShift + 0.5);
    \node at (11.1, \lineAShift + 0.2) {$B_4$};
    \node at (11.1, \lineAShift + 1) {8};
    
    % Arrows under timesteps on line A
    \node[below] at (0, \lineAShift - 0.2) {0};
    \node[below] at (2, \lineAShift - 0.2) {20};
    \node[below] at (4, \lineAShift - 0.2) {40};
    \node[below] at (6, \lineAShift - 0.2) {60};
    \node[below] at (8, \lineAShift - 0.2) {80};
    \node[below] at (10, \lineAShift - 0.2) {100};
    
    \end{tikzpicture}
    \caption{Frame-based Schedule}
\end{figure}
\end{document}