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

#include<stdio.h>
#include<iostream>
#include<string.h>
#define inf 0x3f3f3f3f
typedef long long ll;
using namespace std;

int book[25][25][25];
int w(int a,int b,int 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(book[a][b][c]!=-1)
        return book[a][b][c];
    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);
  //  return book[a][b][c];
}
int main()
{
    int a,b,c;
    while(~scanf("%d %d %d",&a,&b,&c))
    {
        if(a==-1&&b==-1&&c==-1)
            break;
        memset(book,-1,sizeof(book));
        printf("w(%d, %d, %d) = %d\n",a,b,c,w(a,b,c));
    }
    return 0;
}

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);
}