记忆化搜索

Function Run Fun

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 4302    Accepted Submission(s): 2090

Problem 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

 

 

 

code：

#include <iostream>
#include <cstring>
using namespace std;
int dp[25][25][25];
int w(int a,int b,int c)
{
if(a<=0||b<=0||c<=0)
return 1;
if(a>20||b>20||c>20)
return w(20,20,20);
if(dp[a][b][c])
return dp[a][b][c];
if(a<b&&b<c)
return (dp[a][b][c]=w(a,b,c-1)+w(a,b-1,c-1)-w(a,b-1,c));
return (dp[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));

}
int main()
{
int a,b,c;
while(cin>>a>>b>>c)
{
if(a==-1&&b==-1&&c==-1)
break;
memset(dp,0,sizeof(dp));
cout << "w(" << a << ", " << b << ", " << c << ") = " << w(a,b,c) << endl;
}
return 0;
}