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Recursion: Function and Programming Software Engineering at Azusa Pacific University  Evolutionary Approach  Examples and Algorithms  Programming in.

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Presentation on theme: "Recursion: Function and Programming Software Engineering at Azusa Pacific University  Evolutionary Approach  Examples and Algorithms  Programming in."— Presentation transcript:

1 Recursion: Function and Programming Software Engineering at Azusa Pacific University  Evolutionary Approach  Examples and Algorithms  Programming in C++  Recursion and Iteration  Summary This is an example in regard to programming and algorithm. Here I took part of material from my previous teaching. August 10, 2015 1 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

2  Evolutionary Approach (Present = Past + Span) Let’s learn from math (break-down / gather-up) Span Solvable Unsolved ==+ Present Past ==+ ==+ Break-down Gather-up Recursion: Function and Programming Software Engineering at Azusa Pacific University August 10, 2015 2 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

3  With recursively thinking and programming, we do break-down-into-past first, then gather-up-to-present funcT RunBack (T timeTag) { if (bEarlyEnough(timeTag))// termination return Answer; else // recursive approach return RunBack (DeTimeTag) + Span (timeTag); } A function calls to itself (directly or indirectly) Recursion: Function and Programming Software Engineering at Azusa Pacific University  Examples and Algorithms (typical pattern) August 10, 2015 3 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

4  Examples and Algorithms (Factorial) /*Fact = 1 * 2 * (i-1) * i * … 8 * *Fact (i) = Fact(i-1) * i * * Past Span Assume we need to do factorial. We use the number as time tag, so that i refers to the present while i-1 to the previous (or past). The recursive function calling itself fulfils recursion Recursion: Function and Programming Software Engineering at Azusa Pacific University *==== How the recursion works is described as follows ===== * Fact = Fact(7) * 8 * └  fact(6) * 7 * └  Fact(5) * 6 *… …. * └  fact(0) *1  8! = (7!)*8 = 40320  7! = (6!)*7 = 5040  6! = (5!)*4 =720  1 */ Gather-up Break-down August 10, 2015 4 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

5  Evolutionary Approach  Examples and Algorithms  Programming in C++  Recursion and Iteration  Summary Recursion: Function and Programming Software Engineering at Azusa Pacific University August 10, 2015 5 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

6  Programming in C++ (Factorial) /* ==== recursive function ======= * !! What a intuitive mapping !! *F n = F n-1 * n * * (1) (2) (3) */ long Fact (int n) // n is time tag { if (n == 1)// Termination return n; else// recurring back return Fact (n-1) * n; } Recall that the Fibonacci numbers are defined recursively: However, the algorithm used in left program is non-recursive --it is iterative, while in right program we use the definition of Fibonacci numbers to implement directly a recursive algorithm. /*===== iterative implementation === * ?? Where is intuitive definition?? */ int IterativeFact (int n) { int previous = -1, result = 0; for (int i=0; I <= n; i++) { int const sum = result + previous; previous = result; result = sum; } return result; } Recursion: Function and Programming Software Engineering at Azusa Pacific University August 10, 2015 6 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

7  Evolutionary Approach  Examples and Algorithms  Programming in C++  Recursion and Iteration  Summary Recursion: Function and Programming Software Engineering at Azusa Pacific University August 10, 2015 7 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

8  Life cycle issues (logic equivalence)  Tree elements for both iteration and recursion Initialization / Termination / Decrease /* ======Recursive Process=====*/ int main () { int ret = Fact(8); // Initialization } long Factint n) // n is time tag { if (i == 1) // Termination return 1; else return Fact(n-1) * n; // Decrease } /* ===== Iterative Process======*/ int main () { long ret= 1; // Initialization while (n>0)// Termination { ret *= n; n--;// Decrease }  Recursion and Iteration Recursion: Function and Programming Software Engineering at Azusa Pacific University August 10, 2015 8 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

9  Life cycle issues (logic equivalence)  Logic equivalent solution (I/T/D)  Recursion and Iteration Recursion: Function and Programming Software Engineering at Azusa Pacific University /* General recursive function * F n = F n-1 + S n * *========= * Fact = Fact(7) * 8 * └  fact(6) * 7 * └  Fact(5) * 6 * └  Fact(4) * 5 * └  Fact(3) * 4 * └  Fact(2) * 3 * └  Fact(1) * 2 * └  1 *1 8 7 6 5 4 3 2 = 40320 = 5040 = 720 = 120 = 24 = 6 = 2 = 1 2 3 4 5 6 7 8 Break down to pastGather up to present August 10, 2015 9 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

10  Life cycle issues (logic equivalence)  Logic equivalent solution (I/T/D)  Recursion and Iteration Recursion: Function and Programming Software Engineering at Azusa Pacific University /* General recursive function * F n = F n-1 + S n * ========= Long ret = 1 for (i=8; I > 0; i--) { // descending to past push (I, stack) } For (i=8; i > 0; i --) { // ascending to present ret *= pop (stack) } 8 7 6 5 4 3 2 = 40320 = 5040 = 720 = 120 = 24 = 6 = 2 = 1 2 3 4 5 6 7 8 August 10, 2015 10 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

11  Life cycle issues (logic equivalence)  Logic equivalent solution (I/T/D)  Recursion and Iteration Recursion: Function and Programming Software Engineering at Azusa Pacific University By means of stack, we can always find a iterative equivalence to any recursive algorithm. However some iterative solution will be very difficult to understand, because it loses straightforwardness August 10, 2015 11 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

12  Recursion and Iteration  Simplified thought (KISS)  Inefficient running (procedural call)  Straightforward (intuitive in math)  Life cycle issues ( Initialization / Termination / Decrease )  Tricky exercise between recursion and iteration  Iteration provides plane algorithm  Complicated thinking thread  Efficient running (just iteratively going through)  Non-straightforward in description (twisty)  Recursion provides solid algorithm Recursion: Function and Programming Software Engineering at Azusa Pacific University August 10, 2015 12 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

13  Life cycle issues ( Initialization / Termination / Decrease )  Tricky exercise between recursion and iteration  Mechanical conversion from recursion to iteration  Converted by compilers and algorithm designer  Keep it simplified (for man to write)  Auto complicated (for machine to convert)  Efficiency improved (for application)  Go do right thing with recursive design because keeping it simple is really wise, while taking advantage of computer for conversion if necessary  Recursion and Iteration Recursion: Function and Programming Software Engineering at Azusa Pacific University August 10, 2015 13 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

14  Evolutionary Approach  Examples and Algorithms  Programming in C++  Recursion and Iteration  Summary Recursion: Function and Programming Software Engineering at Azusa Pacific University August 10, 2015 14 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

15  Summary of Recursion  Recursive thinking:  Mathematic intuition (straightforwardness)  Be wise: looking back prior to looking ahead  Recursive programming  Function calls itself, directly or indirectly  Remember this: the past is the key to the present  Recurring back:  If complicated, break down to past  Conquer the parts, then gather up to present Recursion: Function and Programming Software Engineering at Azusa Pacific University August 10, 2015 15 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

16 Software Engineering at Azusa Pacific University August 10, 2015 16 Azusa Pacific University, Azusa, CA 91702, Tel: (800) 825-5278 Department of Computer Science, http://www.apu.edu/clas/computerscience/http://www.apu.edu/clas/computerscience/

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