HDU1331 Function Run Fun

Function Run Fun

Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 3754    Accepted Submission(s): 1836

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
  
  
  
  


  
  
  
  


  
  
  
  

   
   
#include<iostream>
#include<stdio.h>
#include<cmath>
#include<string>
#include<string.h>
#include<queue>
#include<algorithm>
using namespace std;

int re[25][25][25];     //a,b,c∈（0,20）
int i,j,k;
int a,b,c;

int f(int a,int b,int c)
{
    if(a<=0||b<=0||c<=0) return 1;
    if(a>20||b>20||c>20) return f(20,20,20);
    if(re[a][b][c])return re[a][b][c];        //此if一定要在第三个位置，因为数组开的范围<25
    if(a<b&&b<c) re[a][b][c]=f(a, b, c-1) + f(a, b-1, c-1) - f(a, b-1, c);
    else re[a][b][c]=f(a-1, b, c) + f(a-1, b-1, c) + f(a-1, b, c-1) - f(a-1, b-1, c-1);
    return re[a][b][c];

}

int main()
{
    memset(re,0,sizeof(re));
    while(cin>>a>>b>>c)
    {
        if(a==-1&&b==-1&&c==-1)break;
       printf("w(%d, %d, %d) = %d\n",a,b,c,f(a,b,c));
    }
    return 0;
}