Function Run Fun

Problem Description

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.

 

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.

 

Output

Print the value for w(a,b,c) for each triple.

 

Sample Input

1 1 1 2 2 2 10 4 6 50 50 50 -1 7 18 -1 -1 -1

 

Sample Output

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

#include<iostream>
using namespace std;
int p[22][22][22];
int fun(int a,int b,int c)
{
 if(a<=0||b<=0||c<=0)  return p[a][b][c]=1;
 else return p[a][b][c];
}
void compute()
{
  int i,j,k;
  for(i=1;i<21;i++)
  {
   for(j=1;j<21;j++)
   {
    for(k=1;k<21;k++)
    {
     if(i<j&&j<k)  p[i][j][k]=fun(i,j,k-1)+fun(i,j-1,k-1)-fun(i,j-1,k);
     else p[i][j][k]=fun(i-1,j,k)+fun(i-1,j-1,k)+fun(i-1,j,k-1)-fun(i-1,j-1,k-1);
    }
   }
  }
}
int sr(int i,int j,int k)
{
    if(i<=0||j<=0||k<=0) return 1;
 if(i>20||j>20||k>20) return p[20][20][20];
 return p[i][j][k];
}
int main()
{
    int a,b,c;
 while(scanf("%d%d%d",&a,&b,&c)&&(a!=-1||b!=-1||c!=-1))
 {
  compute();
  printf("w(%d, %d, %d) = %d\n",a,b,c,sr(a,b,c));
 }
 return 0;
}