POJ1579Function Run Fun

Function Run Fun

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 13471		Accepted: 7014

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>
#include<cstdio>
#include<cstring>
using namespace std;
int w[25][25][25];

int DFS(int a,int b,int c)
{
	if(a<=0 || b<=0 || c<=0)
	{
		return 1;
	}
	if(a>20 || b>20 || c>20)
	{
		return DFS(20,20,20);
	}
	if(w[a][b][c]!=-1)
	{
		return w[a][b][c];
	}
	if(a<b && b<c)
	{
		w[a][b][c] = DFS(a, b, c-1) + DFS(a, b-1, c-1) - DFS(a, b-1, c);
	}
	else
	{
		w[a][b][c] = DFS(a-1, b, c) + DFS(a-1, b-1, c) + DFS(a-1, b, c-1) - DFS(a-1, b-1, c-1);
	}
	return w[a][b][c];
}
int main()
{
	freopen("in.txt","r",stdin);
	int i,j,k;
	memset(w,-1,sizeof(w));
	while(cin>>i>>j>>k)
	{
		if(i==-1&&j==-1&&k==-1)
			break;
		printf("w(%d, %d, %d) = %d\n",i,j,k,DFS(i,j,k));
	}
}