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Recursive program

Recursive program. Zhen Jiang West Chester University zjiang@wcupa.edu. Outline. Review of function/method Introduction Design idea Keys Static Analysis Examples. Review of Function/Method. Why function/method To avoid copying the same code in many places Format Call Declaration

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Recursive program

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  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. Introduction (cont.) • 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)

  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(4) f(3) f(2) f(1) f(0) 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 24 6 1 2 f(4)? General format, all same Terminated condition job division Results collection Result reporting

  9. Examples (cont.) f(3) f(2) f(1) f(0) 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 3 2

  10. Examples (cont.) f(3) f(2) f(1) f(0) 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)? ? y=3 z=0 z=1 y=1 z=3 y=0 z=4 y=2 z=2 f(1)+f(0) 1 3 0 4 f(2)+f(1) 1 1 3 2 f(1) y=1 z=5 1 5 1

  11. Examples (cont.) f(3) f(2) f(1) f(0) 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) 1 1 1 2

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