poj 1579 Function Run Fun

Function Run Fun

Time Limit: 1000MS
Memory Limit: 10000K

Total Submissions: 11932
Accepted: 6255

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

  1: #include<iostream>

  2: using namespace std;

  3: int main()

  4: {

  5: 	const int maxlen=20;

  6: 	int a,b,c;

  7: 	int i,j,k;

  8: 	int matrix[22][22][22];

  9: 	for(i=0;i<=maxlen;i++)

 10: 		for(j=0;j<=maxlen;j++)

 11: 			for(k=0;k<=maxlen;k++)

 12: 				matrix[i][j][k]=1;

 13: 	for(i=1;i<=maxlen;i++)

 14: 		for(j=1;j<=maxlen;j++)

 15: 			for(k=1;k<=maxlen;k++)

 16: 			{

 17: 				if(i<j&&j<k)

 18: 					matrix[i][j][k]=matrix[i][j][k-1]+matrix[i][j-1][k-1]-matrix[i][j-1][k];

 19: 				else

 20: 					matrix[i][j][k]=matrix[i-1][j][k]+matrix[i-1][j-1][k]+matrix[i-1][j][k-1]-matrix[i-1][j-1][k-1];

 21: 			}

 22: 	while(1)

 23: 	{

 24: 		cin>>a>>b>>c;

 25: 		if(a==-1&&b==-1&&c==-1)

 26: 			break;

 27: 		if(a<=0||b<=0||c<=0)

 28: 			cout<<"w("<<a<<", "<<b<<", "<<c<<") = 1"<<endl;

 29: 		else if(a>20||b>20||c>20)

 30: 			cout<<"w("<<a<<", "<<b<<", "<<c<<") = "<<matrix[20][20][20]<<endl;

 31: 		else

 32: 			cout<<"w("<<a<<", "<<b<<", "<<c<<") = "<<matrix[a][b][c]<<endl;	

 33: 	}

 34: 	return 0;

 35: }

 36: