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#
Authors:
Michael T. Goodrich, Roberto Tamassia, Michael H. Goldwasser
Chapter:
Trees
Exercise:
Exercises
Question:11 | ISBN:9781118771334 | Edition: 6

Question

Draw an arithmetic expression tree that has four external nodes, storing the numbers 1, 5, 6, and 7 (with each number stored in a distinct external node, but not necessarily in this order), and has three internal nodes, each storing an operator from the set {+,−,∗,/}, so that the value of the root is 21. The operators may return and act on fractions, and an operator may be used more than once

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Answer

The following arithmetic expression tree that has four external nodes, storing the numbers 1, 5, 6, and 7 (with each number stored in a distinct external node, but not necessarily in this order), and has three internal nodes, each storing an operator from the set {+,−,∗,/}, so that the value of the root is 21:

        *
       / \
      +   7
     / \
    /   \
   1     -
        / \
       /   \
      5     6

In this expression tree:

  • The external nodes (leaves) store the numbers 1, 5, 6, and 7.
  • The internal nodes store the operators +, -, and *.
  • The value of the root is 21.
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