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OWASP Speed Talks – Math Kata Demo

OWASP Speed Talks – Math Kata Demo. Yang Li OWASP Assistant Organizer NJ Chapter yang.li@owasp.org (917) 667-1972. Jan 11, 2012. Math Kata Demo.

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OWASP Speed Talks – Math Kata Demo

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  1. OWASP Speed Talks – Math Kata Demo Yang Li OWASP Assistant Organizer NJ Chapter yang.li@owasp.org (917) 667-1972 Jan 11, 2012

  2. Math Kata Demo • Math Kata - A term extended from “Code Kata”, which in turn borrowed from Japanese martial art kata concept. A math kata is an exercise which help security professional horn his/her math and code skill through practices.

  3. Math Kata Demo • Why? Keep up your mind power in excellent shape before the battlefield. • How? Internet, bookstore and OWASP are your best friends. • What? I’ll give you a demo in this talk.

  4. Math Kata Demo • Example: Starting in the top left corner of a 2x2 grid, there are 6 routes (without backtracking) to the bottom right corner. How many routes are there through a 20x20 grid?

  5. Math Kata Demo • My Initial Comprehension: Use a matrix with array (x,y) to represent the route position in the 2-dimentional grid. For example, the starting point is (0,0), the end point is (2,2) in 2x2 grid: Route 1: [(0,0), (1,0), (2,0), (2,1), (2,2)] Route 2: [(0,0), (1,0), (1,1), (2,1), (2,2)] Route 3: [(0,0), (1,0), (1,1), (2,1), (2,2)] Route 4: [(0,0), (0,1), (1,1), (2,1), (2,2)] Route 5: [(0,0), (0,1), (1,1), (1,2), (2,2)] Route 6: [(0,0), (0,1), (0,2), (1,2), (2,2)]

  6. Math Kata Demo • Patterns anyone? 1. Number of steps from start (0,0) -> end (2,2) are always the same (4 moves). 2. The number of steps need from (0,0) -> (2,2) is calculated as Count(2,2) - Count(0,0) = (2-0) + (2-0) =4. 3. For a larger grid 20x20, it would take Count(20,20) - Count(0,0) = (20-0) + (20-0) = 40 steps from start to end.

  7. Math Kata Demo • Patterns anyone? 4. Except for the intersection on the edges (x=0, or y=0) of the grid, there are always two ways to move to next intersection in the route (no backtracking rule). 5. For the intersection on the edges (x=0, or y=0) of the grid, there are only one way to move to the next intersection in the route (no backtracking rule).

  8. Math Kata Demo • More sketching?

  9. Math Kata Demo • Code It Out (Ruby): def pascals_triangle(x,y) return 1 if (x==0 or y==0) result = pascals_triangle(x-1,y) + pascals_triangle(x,y-1) return result end puts pascals_triangle(20,20)

  10. Math Kata Demo • Code It Out (Ruby): def pascals_triangle(x,y) return 1 if (x==0 or y==0) result = pascals_triangle(x-1,y) + pascals_triangle(x,y-1) return result end puts pascals_triangle(20,20) Recursive Function: I use a generic recursive function "pascals_triangle" to solve the puzzle. A recursion function is a function that call itself up until certain border condition is met. It's a simple and elegant solution with less than 10 line of code.

  11. Math Kata Demo

  12. Math Kata Demo • Code It Again (in “C”) – “Ruby” is too slow? #include <stdio.h> long long pascals_triangle (int x, int y); int main (void) { long long result = pascals_triangle(20,20); printf ("My calculation result is: %lld \n", result); } long long pascals_triangle (int x, int y) { if (x<=0 || y<=0) { return 1; } else { long long result = pascals_triangle(x-1,y) + pascals_triangle(x,y-1); return result; } }

  13. Math Kata Demo • It’s Faster in “C” – 46 minutes later: $ gcc euler_15.c -o pas $ time ./pas My calculation result is: 137846528820 real 46m34.642s user 46m31.517s sys 0m1.203s $

  14. Math Kata Demo • Algorithm Optimization: Space-Time Trade-off: If we could store the answer of previous calculation into cache, then we could retrieve it without re-calculation again.

  15. Math Kata Demo • Cache Mechanism Implementation (Ruby): require "memoize.rb" include Memoize def pascals_triangle(x,y) return 1 if (x==0 or y==0) return ( pascals_triangle(x-1,y) + pascals_triangle(x,y-1) ) end memoize :pascals_triangle puts pascals_triangle(20,20)

  16. Math Kata Demo • Now this is really FAST: $ time ruby euler_15.rb 137846528820 real 0m0.020s user 0m0.015s sys 0m0.006s $ Conclusion: Language does not matter speed wide, as long as your algorithm is sound.

  17. Math Kata Demo • Can you show me your code?

  18. Math Kata Demo • Credits: • Project Euler Question 15: http://projecteuler.net/ • Ruby Memoize Module: http://rubyforge.org/projects/memoize/

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