poj1579

 

Function Run Fun

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 14814		Accepted: 7658

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>
void main()
{
 int a,b,c;long w[21][21][21],d;
    for(a=0;a<=20;a++)
    for(b=0;b<=20;b++)
    for(c=0;c<=20;c++)
    if(a==0||b==0||c==0)w[a][b][c]=1;
    else
    if(a<b&&b<c)w[a][b][c]=w[a][b][c-1]+w[a][b-1][c-1]-w[a][b-1][c];
    else w[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];
 while(scanf("%d%d%d",&a,&b,&c),a!=-1||b!=-1||c!=-1)
 {
  if(a<=0||b<=0||c<=0)d=1;
  else
        if(a>20||b>20||c>20)d=w[20][20][20];
        else d=w[a][b][c];
        printf("w(%d, %d, %d) = %I64d",a,b,c,d);
        printf("\n");
 } 
}