Function Run Fun
Time Limit: 1000MS  Memory Limit: 10000K
Total Submissions: 6420  Accepted: 3526

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>
long data[21][21][21] = {0};
int fun(int a,int b,int c)//根據題意來寫函數
{
if(a<=0||b<=0||c<=0)
return 1;
else if(a>20||b>20||c>20)
return fun(20,20,20);
if(data[a][b][c])//要是 data已經存在的話就直接返回值
return data[a][b][c];
else if(a<b&&b<c)
return fun(a, b, c-1) + fun(a, b-1, c-1) - fun(a, b-1, c);
else
return fun(a-1, b, c) + fun(a-1, b-1, c) + fun(a-1, b, c-1) - fun(a-1, b-1, c-1);
}
int main()
{
int a, b ,c;//三維
data[0][0][0] = 1;
for(a = 0;a<=20;a++)
for(b = 0;b<=20; b++)
for(c = 0;c <=20; c ++)
{
data[a][b][c] = fun(a,b,c);
}
while(scanf("%d%d%d",&a,&b,&c)!=EOF)
{
if(a==-1&&b==-1&&c==-1)
return 1;
printf("w(%d, %d, %d) = %d\n",a,b,c,fun(a,b,c));
}
return 0;
}