HDU 1331 Function Run Fun

Function Run Fun

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 2799    Accepted Submission(s): 1349

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 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

AC代码：

#include <iostream>#include <cstdio>#include <cstring>using namespace std;const int N = 21 ;int dp[N][N][N] ;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;        else        {            memset( dp , 0 , sizeof(dp)) ;            printf("w(%d, %d, %d) = %d\n" , a,b,c, w(a,b,c) );        }    }    return 0;}