Function Run Fun poj1579

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 12 2 210 4 650 50 50-1 7 18-1 -1 -1

Sample Output

w(1, 1, 1) = 2w(2, 2, 2) = 4w(10, 4, 6) = 523w(50, 50, 50) = 1048576w(-1, 7, 18) = 1

题意：设一个三维数组，预处理他们的值，自底向上，防止多次计算，不然可能会超时代码：

#include<iostream>using namespace std;long long a[25][25][25];int main(){    for(int i = 0;i<=20;i++)        for(int j = 0;j<=20;j++)        for(int k = 0;k<=20;k++)    {        if(i==0||j==0||k==0)            a[i][j][k] = 1;        else if(i<j&&j<k)            a[i][j][k] = a[i][j][k-1]+a[i][j-1][k-1]-a[i][j-1][k];        else            a[i][j][k] = a[i-1][j][k]+a[i-1][j-1][k]+a[i-1][j][k-1]-a[i-1][j-1][k-1];    }    int b,c,d;    while(cin>>b>>c>>d)    {        if(b==-1&&c==-1&&d==-1)            break;        if(b<=0||c<=0||d<=0)            cout<<"w("<<b<<", "<<c<<", "<<d<<") = 1"<<endl;        else if(b>20||c>20||d>20)            cout<<"w("<<b<<", "<<c<<", "<<d<<") = "<<a[20][20][20]<<endl;        else            cout<<"w("<<b<<", "<<c<<", "<<d<<") = "<<a[b][c][d]<<endl;    }}