POJ-1579-201308122106.txt

Function Run Fun
Time Limit: 1000MS  Memory Limit: 10000K
Total Submissions: 14939  Accepted: 7735

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 "stdio.h"

int d[22][22][22];

int w(int a,int b,int c)
{
  if(a<=0||b<=0||c<=0)
{
  return 1;
}
  if(a>20||b>20||c>20)
 {
  d[20][20][20]=w(20,20,20);
  return d[20][20][20];
 }
  if(d[a][b][c])
 return  d[a][b][c];
 if(a<b&&b<c)
{    d[a][b][c]=w(a,b,c-1)+w(a,b-1,c-1)-w(a,b-1,c);
 return d[a][b][c];
 }
else
{d[a][b][c]=w(a-1,b,c)+w(a-1,b-1,c)+w(a-1,b,c-1)-w(a-1,b-1,c-1);
return d[a][b][c]; 
}
//if(d[a][b][c])
// return  d[a][b][c];
}
 
 
 
 
int main()
{int a,b,c;
 while(scanf("%d %d %d",&a,&b,&c),!(a==-1&&b==-1&&c==-1))
{
 //memset(w,0,sizeof(w));
 printf("w(%d, %d, %d) = %d\n",a,b,c,w(a,b,c));
 }
 return 0;
 }