Function Run Fun

http://acm.zju.edu.cn/show_problem.php?pid=1168

Time limit: 1 Seconds

Memory limit: 32768K

We all love recursion! Don't we?

Consider a three-parameter recursive function w(a, b, c):

if a <= 0 or b <= 0 or c <= 0, then w(a, b, c) returns: 1

if a > 20 or b > 20 or c > 20, then w(a, b, c) returns: w(20, 20, 20)

if a < b and b < c, then w(a, b, c) returns: w(a, b, c-1) + w(a, b-1, c-1) - w(a, b-1, c)

otherwise it returns: w(a-1, b, c) + w(a-1, b-1, c) + w(a-1, b, c-1) - w(a-1, b-1, c-1)

This is an easy function to implement. The problem is, if implemented directly, for moderate values of a, b and c (for example, a = 15, b = 15, c = 15), the program takes hours to run because of the massive recursion.

1. Input

The input for your program will be a series of integer triples, one per line, until the end-of-file flag of -1 -1 -1. Using the above technique, you are to calculate w(a, b, c) efficiently and print the result. For example:

2. Output

Print the value for w(a,b,c) for each triple, like this:

w(1, 1, 1) = 2
w(2, 2, 2) = 4
w(10, 4, 6) = 523
w(50, 50, 50) = 1048576
w(-1, 7, 18) = 1

Problem Source: Pacific Northwest 1999

   1 /* 1168 ymC */
   2 #include <stdio.h>
   3 const int N3=9261;
   4 const int N2=441;
   5 const int N1=21;
   6 int w[9261];
   7 void init()
   8 {
   9      int a,b,c;
  10      int t;
  11      int i;
  12      for(a=0;a<N1;a++)
  13      {
  14         for(b=0;b<N1;b++)
  15           w[a*N2+b*N1]=1;
  16         for(c=0;c<N1;c++)
  17           w[a*N2+c]=1;
  18      }
  19      for(b=0;b<N1;b++)
  20         for(c=0;c<N1;c++)
  21           w[b*N1+c]=1; 
  22           
  23      for(i=0;i<N3;i++)
  24      {
  25           if(w[i]!=1)
  26           {
  27               a=i/N2;
  28               c=i%N1;
  29               b=i/N1-a*N1;
  30               if(a<b&&b<c)              
  31                   w[i]=w[i-1]+w[i-N1-1]-w[i-N1];
  32               else
  33                   w[i]=w[i-N2]+w[i-N2-N1]+w[i-N2-1]-w[i-N2-N1-1];
  34           }
  35      }     
  36 }
  37 int main()
  38 {
  39     int a,b,c;
  40     init();
  41     scanf("%d %d %d",&a,&b,&c);
  42     while(a!=-1||b!=-1||c!=-1)
  43     {
  44           printf("w(%d, %d, %d) = ",a,b,c);
  45           if(a<=0||b<=0||c<=0)
  46                printf("1\n");
  47           else if(a>20||b>20||c>20)
  48               printf("%d\n",w[N3-1]);
  49           else
  50           {
  51                printf("%d\n",w[a*N2+b*N1+c]);
  52           }
  53           scanf("%d %d %d",&a,&b,&c);
  54     }
  55     
  56 }