I am not sure of this is what you need; I borrowed some code from this answer from Jake to pgfplots: mark max/min value of a function to automatically find the maximum and minimum values, and then, I used after end axis/.append code to \draw the line:
\documentclass{report}
\usepackage[left=2.5cm,right=2cm,top=2cm,bottom=2cm]{geometry}
\usepackage[T1]{fontenc}
\usepackage{pgfplots}
\colorlet{maxcolor}{blue}
\usetikzlibrary{calc,trees,positioning,arrows,chains,shapes.geometric,%
decorations.pathreplacing,decorations.pathmorphing,shapes,%
matrix,shapes.symbols,automata}
\makeatletter
\pgfplotsset{
/tikz/max node/.style={color=blue,
anchor=south,
},
/tikz/min node/.style={
anchor=north,
name=minimum
},
mark min/.style={
point meta rel=per plot,
visualization depends on={x \as \xvalue},
scatter/@pre marker code/.code={%
\ifx\pgfplotspointmeta\pgfplots@metamin
\def\markopts{}%
\coordinate (minimum);
\node [min node] {
(\pgfmathprintnumber[fixed]{\xvalue},%
\pgfmathprintnumber[fixed]{\pgfplotspointmeta})
};
\else
\def\markopts{mark=none}
\fi
\expandafter\scope\expandafter[\markopts,every node near coord/.style=green]
},%
scatter/@post marker code/.code={%
\endscope
},
scatter,
},
mark max/.style={
point meta rel=per plot,
visualization depends on={x \as \xvalue},
scatter/@pre marker code/.code={%
\ifx\pgfplotspointmeta\pgfplots@metamax
\def\markopts{}%
\coordinate (maximum);
\node [max node] {
(\pgfmathprintnumber[fixed]{\xvalue},%
\pgfmathprintnumber[fixed]{\pgfplotspointmeta})
};
\else
\def\markopts{mark=none}
\fi
\expandafter\scope\expandafter[\markopts]
},%
scatter/@post marker code/.code={%
\endscope
},
scatter
}
}
\makeatother
\begin{document}
\begin{figure}[H]
\begin{tikzpicture}
\begin{axis}[%
width=1*\textwidth,
height=8cm,
xlabel={Query},
ylabel={Elapsed Time (in seconds)},
grid = both,
minor x tick num=3,
minor y tick num=3,
enlarge x limits=0,
after end axis/.append code={
\draw [thick,maxcolor] (maximum) --({rel axis cs:0,0}-|maximum);
},
mark options={fill=maxcolor,draw=maxcolor}
]
\addplot [mark max,
color=red,
solid,
line width=1.0pt
]
coordinates{
(0,6.66003) (1,9.10814) (2,182.761) (3,109.154) (4,246.253) (5,206.129) (6,212.653) (7,240.088) (8,4.49266) (9,263.248) (10,257.65) (11,147.81) (12,87.5402) (13,127.389) (14,167.028) (15,2.35324) (16,120.594) (17,2.4295) (18,13.0306) (19,126.756) (20,64.0324) (21,100.611) (22,14.7892) (23,2.41528) (24,132.193) (25,9.94301) (26,156.253) (27,123.016) (28,186.208) (29,102.549) (30,194.67) (31,184.039)
};
\end{axis}
\end{tikzpicture}
\caption{Blah}
\end{figure}
\end{document}
For a horizontal line you could use
\documentclass{report}
\usepackage[left=2.5cm,right=2cm,top=2cm,bottom=2cm]{geometry}
\usepackage[T1]{fontenc}
\usepackage{pgfplots}
\colorlet{maxcolor}{blue}
\usetikzlibrary{calc,trees,positioning,arrows,chains,shapes.geometric,%
decorations.pathreplacing,decorations.pathmorphing,shapes,%
matrix,shapes.symbols,automata}
\makeatletter
\pgfplotsset{
/tikz/max node/.style={color=blue,
anchor=south,
},
/tikz/min node/.style={
anchor=north,
name=minimum
},
mark min/.style={
point meta rel=per plot,
visualization depends on={x \as \xvalue},
scatter/@pre marker code/.code={%
\ifx\pgfplotspointmeta\pgfplots@metamin
\def\markopts{}%
\coordinate (minimum);
\node [min node] {
(\pgfmathprintnumber[fixed]{\xvalue},%
\pgfmathprintnumber[fixed]{\pgfplotspointmeta})
};
\else
\def\markopts{mark=none}
\fi
\expandafter\scope\expandafter[\markopts,every node near coord/.style=green]
},%
scatter/@post marker code/.code={%
\endscope
},
scatter,
},
mark max/.style={
point meta rel=per plot,
visualization depends on={x \as \xvalue},
scatter/@pre marker code/.code={%
\ifx\pgfplotspointmeta\pgfplots@metamax
\def\markopts{}%
\coordinate (maximum);
\node [max node] {
(\pgfmathprintnumber[fixed]{\xvalue},%
\pgfmathprintnumber[fixed]{\pgfplotspointmeta})
};
\else
\def\markopts{mark=none}
\fi
\expandafter\scope\expandafter[\markopts]
},%
scatter/@post marker code/.code={%
\endscope
},
scatter
}
}
\makeatother
\begin{document}
\begin{figure}[H]
\begin{tikzpicture}
\begin{axis}[%
width=1*\textwidth,
height=8cm,
xlabel={Query},
ylabel={Elapsed Time (in seconds)},
grid = both,
minor x tick num=3,
minor y tick num=3,
enlarge x limits=0,
after end axis/.append code={
\draw [thick,maxcolor] ({rel axis cs:0,1}|-maximum) -- ({rel axis cs:1,1}|-maximum);
},
mark options={fill=maxcolor,draw=maxcolor}
]
\addplot [mark max,
color=red,
solid,
line width=1.0pt
]
coordinates{
(0,6.66003) (1,9.10814) (2,182.761) (3,109.154) (4,246.253) (5,206.129) (6,212.653) (7,240.088) (8,4.49266) (9,263.248) (10,257.65) (11,147.81) (12,87.5402) (13,127.389) (14,167.028) (15,2.35324) (16,120.594) (17,2.4295) (18,13.0306) (19,126.756) (20,64.0324) (21,100.611) (22,14.7892) (23,2.41528) (24,132.193) (25,9.94301) (26,156.253) (27,123.016) (28,186.208) (29,102.549) (30,194.67) (31,184.039)
};
\end{axis}
\end{tikzpicture}
\caption{Blah}
\end{figure}
\end{document}
