Operators DECREASE in strength toward the Bottom

Transcription

1 Complex Java Expression Page 1 Java Operator Precedence 2:42 PM STRONGEST operators at top of table Family Name Operators Unary! ~ Multiply * / % Add + Compare < > <= >= Equality ==!= Logic And && Logic Or VERY strong operators Really WEAK operator Operators DECREASE in strength toward the Bottom

2 Complex Java Expression Page 2 Complex Java Expression1 ( a * b c / 6 ) * ( b / c * 12 e f ) Here is a complex Java expression with parentheses and both unary and binary "" operators. As before, draw all the operands along the bottom of your workpage.

3 Complex Java Expression Page 3 Complex Java Expression2 Subtract has Number 12 just To left. ( a * b c / 6 ) * ( b / c * 12 e f ) Subtract has Variable b just to left. You need to be able To tell apart a unary negative operator from A binary subtract operator. The subtracts have either a number, or variable, or a close parenthesis ) just to their LEFT. ALL the rest are unary negative operators. They have VERY STRONG order of operation.

4 Complex Java Expression Page 4 Complex Java Expression3 ( a * b c / 6 ) * ( b / c * 12 e f ) Begin Work as far INSIDE Parentheses as you can get. For this example begin looking ONLY at the blue part.

5 Complex Java Expression Page 5 Complex Java Expression4 Multiply is fairly strong, But WEAKER than unary Binary subtract is very weak. ( a * b c / 6 ) * ( b / c * 12 e f ) Look ONLY at the operators Within the previously selected Region of the formula. That region is in blue. The operators are in red. You must find the STRONGEST operators in that region. The unary are the strongest operators in the selected region.

6 Complex Java Expression Page 6 Complex Java Expression5 ( a * b c / 6 ) * ( b / c * 12 e f ) One of the strongest operators In the blue selected region Is the circled unary negative.

7 Complex Java Expression Page 7 Complex Java Expression6 ( a * b c / 6 ) * ( b / c * 12 e f ) Enclose these parts in a rectangle: 1. The unary operator 2. Its RIGHT operand a. NOTE: because the operator Is unary it ONLY has a RIGHT operand and NO left operand.

8 Complex Java Expression Page 8 Complex Java Expression7 ( a * b c / 6 ) * ( b / c * 12 e f ) Draw the branch of the tree corresponding to the enclosed part of the formula. Note that the unary oval has ONLY ONE leg beneath it. This contrasts with a binary subtract oval (done later) which will have two legs below it.

9 Complex Java Expression Page 9 Complex Java Expression8 ( a * b c / 6 ) * ( b / c * 12 e f ) Within the original selected region, there is another unary operator and so it is (as usual) one of the strongest. This slide shows its enclosing rectangle AND the tree branch for it.

10 Complex Java Expression Page 10 Complex Java Expression9 ( a * b c / 6 ) * ( b / c * 12 e f ) Within the original selected region, there is yet another unary operator and so it is (as usual) one of the strongest. Notice the with c is a subtract. This slide shows its enclosing rectangle AND the tree branch for it.

11 Complex Java Expression Page 11 Complex Java Expression10 ( a * b c / 6 ) * ( b / c * 12 e f ) Now there were only three operators left unboxed in the selected blue region. The subtract is pretty weak. The safest choice among the strongest operators * and / is the LEFTMOST one. Hence the * is chosen for the next tree branch. When enclosing it in a box, be careful to draw around the two smaller boxes NEXT to the operator. *

12 Complex Java Expression Page 12 Complex Java Expression11 ( a * b c / 6 ) * ( b / c * 12 e f ) Now there were only two operators left unboxed in the selected blue region. The strongest operator is the divide /. So it is enclosed and drawn next. * /

13 Complex Java Expression Page 13 Complex Java Expression12 ( a * b c / 6 ) * ( b / c * 12 e f ) Only the subtract operator was left unboxed in the selected blue region. When only ONE operator is left within The parenthesized area, the parenthesies are used as PART OF the box. Note that the oval has TWO legs Because the subtract is BINARY. * /

14 Complex Java Expression Page 14 Complex Java Expression13 ( a * b c / 6 ) * ( b / c * 12 e f ) The remaining slides will proceed more quickly. If this confuses you, go back to the preceding slides and pay better attention. Note 1) Work INSIDE parentheses FIRST. Note 2) Of equally strong operators choose the leftmost first. * / /

15 Complex Java Expression Page 15 Complex Java Expression14 ( a * b c / 6 ) * ( b / c * 12 e f ) * / * /

16 Complex Java Expression Page 16 Complex Java Expression15 ( a * b c / 6 ) * ( b / c * 12 e f ) Note that the left subtract is done before the equally strong right subtract Because the leftmost is done first. * / * /

17 Complex Java Expression Page 17 Complex Java Expression16 ( a * b c / 6 ) * ( b / c * 12 e f ) * / * /

18 Complex Java Expression Page 18 Complex Java Expression17 ( a * b c / 6 ) * ( b / c * 12 e f ) Root gets stub * * / * /

19 Complex Java Expression Page 19 Complex Java Expression18 ( a * b c / 6 ) * ( b / c * 12 e f ) #1 * Note when numbering operators, to always increase down any leg. #2 #3 #6 * / #4 #5 #7 #11 / #10 * #9 #8

20 Complex Java Expression Page 20 Complex Java Expression19 Entablement of Tree ( a * b c / 6 ) * ( b / c * 12 e f ) #1 * #8 #2 #9 #3 #6 #10 * / * #4 #5 #7 #11 / 1 * #2 #8 2 #3 #6 3 * #4 #5 4 a 5 b 6 / c # #9 f 9 #10 e 10 * # / b c Note unary operators have only one leg.