Binary Expression Trees

  1. Given the BXT at right, state the following:
    • infix form
    • postfix form
    • prefix form
    • evaluate

  2. Evaluate the prefix expression / - + A B C D, where A = 6, B = 5, C = 2, D = 3
    Give its postfix form.
    Draw the BXT.

  3. Express the algebraic expression below in postfix form.

    Evaluate the following postfix expressions.
  1. 3 4 2 * +
  2. 3 4 + 5 *
  3. 2 4 + 5 3 - *
  4. 3 2 ^ 2 3 * 5 * + 5 2 ^ +
  5. 4 5 7 6 9 + * + *
  6. 2 3 4 + * 7 3 2 * + /
  7. 2 3 4 * + 2 8 1 4 3 * + + * /
  8. 1 2 3 4 5 * + - +

    Evaluate the following postfix expressions.

  9. + * 2 3 4
  10. * + 2 3 4
  11. + - 2 3 / 6 3
  12. / - 9 3 * 3 2
  13. * + 2 3 + * 4 5 6

    Translate the infix expressions into postfix.

  14. 2 * (3 + 4 * 5) * 6
  15. (1 + 2) * (A - 3) ^ 2 * F
  16. (A + B) * (C * (D - E) + F) - G
  17. A + B + C
  18. A * B + C * (D + E) / F + G
  19. A + (B * C) + D / E * (F + G)
  20. A / B + C * (D + E) * (F / G)
  21. A / (B * (C - (D * (E + (F * G)))))

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