Function Run Fun-递归+细节处理

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

 1 #include<stdio.h>
 2 #include<iostream>
 3 #include<string.h>
 4 #define inf 0x3f3f3f3f
 5 typedef long long ll;
 6 using namespace std;
 7 
 8 int book[25][25][25];
 9 int w(int a,int b,int c)
10 {
11     if(a<=0||b<=0||c<=0)
12        return 1;
13     else if(a>20||b>20||c>20)
14         return w(20,20,20);
15     else if(book[a][b][c]!=-1)
16         return book[a][b][c];
17     else if(a<b&&b<c)
18         return book[a][b][c]=w(a,b,c-1)+w(a,b-1,c-1)-w(a,b-1,c);
19     else
20         return book[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);
21   //  return book[a][b][c];
22 }
23 int main()
24 {
25     int a,b,c;
26     while(~scanf("%d %d %d",&a,&b,&c))
27     {
28         if(a==-1&&b==-1&&c==-1)
29             break;
30         memset(book,-1,sizeof(book));
31         printf("w(%d, %d, %d) = %d\n",a,b,c,w(a,b,c));
32     }
33     return 0;
34 }

int w(int a,int b,int c)
{
    if(a>=0&&a<=20&&b>=0&&b<=20&&c>=0&&c<=20&&book[a][b][c]!=-1)//防止越界
        return book[a][b][c];
    if(a<=0||b<=0||c<=0)
        return 1;
    else if(a>20||b>20||c>20)
        return w(20,20,20);
    else if(a<b&&b<c)
        return book[a][b][c]=w(a,b,c-1)+w(a,b-1,c-1)-w(a,b-1,c);
    else
        return book[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);
}