ACM programming contest Introduction + Recursion

ACM International Collegiate Programming Contest (a.k.a. ACM ICPC, ACM competition, ICPC) is the largest university-level programming contest in the world. ACM - Association of Computing Machinery ◦ Largest association for computer science ◦ Organize research conference ◦ Publish journal, etc Background

Contest rule Each team: 3 students One computer per team 4- 6 hours problems (like the sudoku question) ◦ Input and output requirement ◦ Time limit Judge by some test cases (unknown to us) ◦ Pass all test cases = solve the question ◦ If you fail, you can resubmit Score ≈ "# of solved question" and "time used" Winner = most question solved, if draw, the one uses least time

Tentative schedule Topics Feb - April Basic topics: recursion, greedy, dynamic programming, graphs, breadth first search, depth first search MayTeam formation test for local contest June / JulyACM Hong Kong Local Contest July - August Intermediate topics: matching, coordinate geometry, math AugustTeam formation test for regional contest Sep - OctAdvanced topics: Contest like problems Oct / NovACM Asia Regional Contest MarchACM World Final Contest (by invitation)

Training tools Practice makes perfect - Online problem archive Ability ≈ number of problems you have solved Our first question: POJ 2719 Faulty Odometer Notice: input is between 1 to 999,999,999; 0 means the end Time limit: 1 second Every digit has only 9 possibilities; It is a base-9 number [0-3] -> [0-3] && [5-9] -> [4-8] See your ranking at

Recursion

Hanoi Tower Legend: Inside a Vietnamese temple there are three rods (labeled as r 1, r 2, and r 3 ), surrounded by n golden disks of different sizes. The monks of Hanoi wants to move these disks from r 1 to r 3 such that: at each step, take the upper disk of one rod and place it to the top of another rod no bigger disk can be placed on top of a smaller disk

Input and output format Input: A single integer n in [1, 20] Output: The steps to move the disks from r 1 to r 3 ; in the format of r i -> r j 3 r1 -> r3 r1 -> r2 r3 -> r1 r1 -> r3 r2 -> r1 r2 -> r3 r1 -> r3

Recursion Can we solve the problem by solving some smaller problems? To move n disks from r 1 to r 3 1.move n-1 disks from r 1 to r 2 2.move 1 disks from r 1 to r 3 3.move n-1 disks from r 2 to r 3 r1r1 r2r2 r3r3

Implementation Let hanoi( int n, int i, int j, int z ) be a function that will move n disks from rod i to rod j using rod k as the middle rod. void hanoi( int n, int i, int j, int k ){ if( n==1 ){ cout r" << j << endl; return; } hanoi( n-1, i, k, j ); hanoi( 1, i, j, k ); hanoi( n-1, k, j, i ); } int main(){ int n; cin >> n; hanoi( n ); return 0; }

How many moves are there? Let T(n) be the number of steps to move n disks T(1) = 1 T(n)= 2 T(n-1) + 1 = 4 T(n-2) =... = 2 n-1 T(1)+ 2 n = 2 n - 1 The running time is also Θ(2 n ) = exponential time Very slow But it is optimal already (prove by M.I. on n)

POJ 3601

Other recursion problems Look for easy problems first POJ 1920

POJ 2386 Lake counting

POJ 2227

Topological sort

POJ 1128

POJ 1094

Summary We have seen some examples on recursion. ◦ Hanoi tower ◦ Reverse of hanoi tower Flood fill is a recursive method to identify connected region. ◦ Running time = size of the region We can order a partial ordered set by topological sort ◦ Running time = number of edges Exercises: UVA 900, 254, 699, 10940, 527, 572, 657, 11110, 10305, 11686, 200