动态规划【 Function Run Fun】

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 <iostream>
using namespace std;
long long  a,b,c,d;

int dp[21][21][21];
int w(int i,int j,int k)
{
    if(i <= 0 || j <= 0 || k <= 0)
        return 1;
    return dp[i][j][k];
}
void W()
{
    int i,j,k;
    for(i = 1; i < 21; i++)
        for(j = 1; j < 21; j++)
            for(k = 1; k < 21; k++)
            {
                if(i < j && j < k)
                    dp[i][j][k] = w(i,j,k-1) + w(i,j-1,k-1) - w(i,j-1,k);
                else
                    dp[i][j][k] = w(i-1,j,k) + w(i-1,j-1,k) + w(i-1,j,k-1) - w(i-1,j-1,k-1);
            }
}
int Ww(int i,int j,int k)
{
    if(i <= 0 || j <= 0 || k <= 0)
        return 1;
    if(i > 20 || j > 20 || k > 20)
        return dp[20][20][20];
    else
        return dp[i][j][k];
}
int main()
{
    W();
    while(cin>>a>>b>>c)
    {
        if(a==-1&&b==-1&&c==-1)
            break;
        else d=Ww(a,b,c);

        cout<<"w("<<a<<", "<<b<<", "<<c<<") "<<"= "<<d<<endl;
    }

return 0;
}