HDU 1579 Function Run Fun(记忆化搜索)

Function Run Fun

Time Limit: 1000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2519 Accepted Submission(s): 1324

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
   
   
   
   

Source

冬练三九之一  

/*
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)

数组开三维22就行 

*/
#include<iostream>
#include <string.h>
using namespace std;
int num[22][22][22]; 
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 num[20][20][20]=w(20,20,20);
	if(num[a][b][c]!=-1)
	   return num[a][b][c];
	if(a<b&&b<c)
	  return num[a][b][c]=w(a,b,c-1)+w(a,b-1,c-1)-w(a,b-1,c);
	return num[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; 
    memset(num,-1,sizeof(num));
    while(cin>>a>>b>>c){
    	if(a==-1&&b==-1&&c==-1)
    	 break;
    	cout<<"w("<<a<<", "<<b<<", "<<c<<") = "<<w(a,b,c)<<endl;
	}
	return 0;
}