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67 step any further from this element.\medskip |
67 step any further from this element.\medskip |
68 |
68 |
69 \noindent |
69 \noindent |
70 The problem is to calculate a sequence of steps to reach the end of |
70 The problem is to calculate a sequence of steps to reach the end of |
71 the list by taking only steps indicated by the integers. For the list |
71 the list by taking only steps indicated by the integers. For the list |
72 above, possible sequence of steps are 3 - 2 - 1 - End, but also 3 - 4 |
72 above, possible sequences of steps are 3 - 2 - 1 - End, but also 3 - 4 |
73 - End. This is a recursive problem that can be thought of as a tree |
73 - End. This is a recursive problem that can be thought of as a tree |
74 where the root is a list and the children are all the lists that are |
74 where the root is a list and the children are all the lists that are |
75 reachable by a single step. For example for the list above this gives a |
75 reachable by a single step. For example for the list above this gives a |
76 tree like |
76 tree like |
77 |
77 |
78 \begin{center} |
78 \begin{center} |
79 \begin{tikzpicture}[grow=right,level distance=30mm,child anchor=north] |
79 \begin{tikzpicture} |
|
80 [grow=right,level distance=30mm,child anchor=north,line width=0.5mm] |
80 \node {[3,4,2,0,1]} |
81 \node {[3,4,2,0,1]} |
81 child {node {[0,1]}} |
82 child {node {[0,1]}} |
82 child {node {[2,0,1]} |
83 child {node {[2,0,1]} |
83 child {node {[1]} child [level distance=13mm] {node {End}}} |
84 child {node {[1]} child [level distance=13mm] {node {End}}} |
84 child {node {[0,1]}} |
85 child {node {[0,1]}} |