From 1fb6398fb71d987a82c18867140f9a56c392bd7a Mon Sep 17 00:00:00 2001
From: Krzysztof Wojtas <kwojtas@gmail.com>
Date: Sun, 22 Sep 2024 03:17:27 +0200
Subject: [PATCH] #225 migrate 6.2-1

---
 chapter6/sections/2/1.tex   | 14 +++++++++++++-
 chapter6/sections/2/1.tikz  |  5 +++++
 chapter6/sections/2/1a.tikz | 24 ++++++++++++++++++++++++
 chapter6/sections/2/1b.tikz | 24 ++++++++++++++++++++++++
 chapter6/sections/2/1c.tikz | 24 ++++++++++++++++++++++++
 5 files changed, 90 insertions(+), 1 deletion(-)
 create mode 100644 chapter6/sections/2/1.tikz
 create mode 100644 chapter6/sections/2/1a.tikz
 create mode 100644 chapter6/sections/2/1b.tikz
 create mode 100644 chapter6/sections/2/1c.tikz

diff --git a/chapter6/sections/2/1.tex b/chapter6/sections/2/1.tex
index a0deb8f..a65abf3 100644
--- a/chapter6/sections/2/1.tex
+++ b/chapter6/sections/2/1.tex
@@ -1 +1,13 @@
-\workinprogress % TODO
+See \refFigure{6.1-2}.
+\begin{figure}[htb]
+    \captionsetup[subfigure]{}
+    \subcaptionbox{\label{fig:6.1-2a}}[0.5\textwidth]{\input{1a.tikz}}
+    \subcaptionbox{\label{fig:6.1-2b}}[0.5\textwidth]{\input{1b.tikz}}
+    \par\vspace{5mm}
+    \subcaptionbox{\label{fig:6.1-2c}}[0.5\textwidth]{\input{1c.tikz}}
+    \caption{The operation of $\proc{Max-Heapify}(A,3)$ on the array $A=\langle$27, 17, 3, 16, 13, 10, 1, 5, 7, 12, 4, 8, 9, 0$\rangle$, where $\attrib{A}{heap-size}=14$.\,
+    \textbf{(a)}\, The element $A[3]$ at node $i=3$ violates the max-heap property, since it is not larger than its left child $A[6]$.
+    \textbf{(b)}\, After exchanging $A[3]$ with $A[6]$ the max-heap property is restored for node 3, but is destroyed for node 6, because now $A[6]$ is not larger than both children.
+    In the recursive call $\proc{Max-Heapify}(A,6)$ the elements $A[6]$ and $A[13]$ are swapped, as shown in \textbf{(c)}.
+    The next recursive call $\proc{Max-Heapify}(A,13)$ just returns without making any further changes to the heap.} \label{fig:6.1-2}
+\end{figure}
diff --git a/chapter6/sections/2/1.tikz b/chapter6/sections/2/1.tikz
new file mode 100644
index 0000000..1ac0d33
--- /dev/null
+++ b/chapter6/sections/2/1.tikz
@@ -0,0 +1,5 @@
+\tikzset{
+    every node/.style = {tan vertex},
+    active/.style = {light blue vertex},
+    every label/.style = {index},
+}
diff --git a/chapter6/sections/2/1a.tikz b/chapter6/sections/2/1a.tikz
new file mode 100644
index 0000000..d5e4a87
--- /dev/null
+++ b/chapter6/sections/2/1a.tikz
@@ -0,0 +1,24 @@
+\input{1.tikz}
+\begin{tikzpicture}
+    \node[label=1] {27}
+        child {node[label=2] {17}
+            child {node[label=4] {16}
+                child {node[label=8] {5}}
+                child {node[label=9] {7}}
+            }
+            child {node[label=5] {13}
+                child {node[label=10] {12}}
+                child {node[label=11] {4}}
+            }
+        }
+        child {node[active, label=3, label=right:{$i$}] {3}
+            child {node[label=6] {10}
+                child {node[label=12] {8}}
+                child {node[label=13] {9}}
+            }
+            child {node[label=7] {1}
+                child {node[label=14] {0}}
+                child {node[draw=none, fill=none] {} edge from parent[draw=none]}
+            }
+        };
+\end{tikzpicture}
diff --git a/chapter6/sections/2/1b.tikz b/chapter6/sections/2/1b.tikz
new file mode 100644
index 0000000..84977d1
--- /dev/null
+++ b/chapter6/sections/2/1b.tikz
@@ -0,0 +1,24 @@
+\input{1.tikz}
+\begin{tikzpicture}
+    \node[label=1] {27}
+        child {node[label=2] {17}
+            child {node[label=4] {16}
+                child {node[label=8] {5}}
+                child {node[label=9] {7}}
+            }
+            child {node[label=5] {13}
+                child {node[label=10] {12}}
+                child {node[label=11] {4}}
+            }
+        }
+        child {node[label=3] {10}
+            child {node[active, label=6, label=right:{$i$}] {3}
+                child {node[label=12] {8}}
+                child {node[label=13] {9}}
+            }
+            child {node[label=7] {1}
+                child {node[label=14] {0}}
+                child {node[draw=none, fill=none] {} edge from parent[draw=none]}
+            }
+        };
+\end{tikzpicture}
diff --git a/chapter6/sections/2/1c.tikz b/chapter6/sections/2/1c.tikz
new file mode 100644
index 0000000..7974aeb
--- /dev/null
+++ b/chapter6/sections/2/1c.tikz
@@ -0,0 +1,24 @@
+\input{1.tikz}
+\begin{tikzpicture}
+    \node[label=1] {27}
+        child {node[label=2] {17}
+            child {node[label=4] {16}
+                child {node[label=8] {5}}
+                child {node[label=9] {7}}
+            }
+            child {node[label=5] {13}
+                child {node[label=10] {12}}
+                child {node[label=11] {4}}
+            }
+        }
+        child {node[label=3] {10}
+            child {node[label=6] {9}
+                child {node[label=12] {8}}
+                child {node[active, label=13, label=20:{$i$}] {3}}
+            }
+            child {node[label=7] {1}
+                child {node[label=14] {0}}
+                child {node[draw=none, fill=none] {} edge from parent[draw=none]}
+            }
+        };
+\end{tikzpicture}