1. Recursive program Zhen Jiang West Chester University zjiang@wcupa.edu

2. Outline Review of function/method Introduction Design idea Keys Static Analysis Examples

3. Review of Function/Method Why function/method To avoid copying the same code in many places Format Call Declaration Working procedure Details of the use of function/method Functions without arguments ([2], p120) Functions with arguments ([2], p130) Value and reference parameters ([2], p296) Using object with function, & ([2], p321) Return Using pointer with function (will be reviewed later)

4. Introduction Divide-and-conquer multi-layer job division (job becomes smaller) Results collection Result reporting (to caller)

5. Introduction (cont.) f ( Job ) f ( Job.sub-job1 )f ( Job.sub-job2 ) f ( Job.sub-job1. sub-sub-job1 ) f ( Job.sub-job1. sub-sub-job2 )

6. Keys Division (The assignment and reporting of the requested job is divided into smaller pieces: job division, results collection, and result reporting, in divide-conquer tree by many non-leaf node.) Recursive procedure (ensure each node in the divide-conquer tree has similar procedure that can be written in a general/common format, but more abstract) Terminated condition (decide who will really do the job) Samples to see these keys (in static analysis) Introduction (cont.)

7. Static Analysis Check the whole execution. Think about: You are a computer and run the program statement by statement. Need to check the result after each statement. Show the procedure called at different time.

8. Examples f(int i) { if (i ==0) return 1; else return i*f(i-1); } 4*f(3)3*f(2)2*f(1)1*f(0) 1 1 2 624 f(4)? job divisionResults collection Result reporting Terminated condition General format, all same f(4)f(3)f(2)f(1)f(0)

9. Examples (cont.) f(int i) { if (i <=1) return 1; else return f(i-1)+f(i-2); } f(3)? f(2)+f(1)f(1)+f(0) 1 1 23 f(3)f(2)f(1)f(0)

10. Examples (cont.) f(int i) { int y=i; Static int z=0; z++; if (i <=1) { System.out.println(y+” ”+z); return 1; } else return f(i-1)+f(i-2); } f(3)? f(4)? f(2)+f(1) f(1)+f(0) 11 23 f(3)f(2)f(1)f(0) y=3 z=0 z=1 y=2 z=2 y=1 z=3 1 3 y=0 z=4 0 4 ? 1 f(1) y=1 z=5 1 5

11. Examples (cont.) f(int i) { if (i <=1) return 1; else if (i==3) return f(i-1)-f(i-2); else return f(i-1)+f(i-2); } f(3)? f(2)-f(1)f(1)+f(0) 11 21 f(3)f(2)f(1)f(0)