Function Run Fun（记忆化搜索）

Function Run Fun

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

题意很明确，关系都给出来了，所以直接写出来肯定不对，会超时，就需要用记忆化搜索

（但下面好像是打表。。。）

#include<iostream>
#include<algorithm>
#include<string.h>

using namespace std;
int dp[21][21][21];

int a,b,c;
int ww[100][100][100];	

int main(){
	
	for(int i=0;i<21;i++){
		for(int j=0;j<21;j++){
			for(int t=0;t<21;t++){
				if(i<=0||j<=0||t<=0) ww[i][j][t]=1;
			
	
	else if(i<j&&j<t){
		ww[i][j][t]=ww[i][j][t-1]+ww[i][j-1][t-1]-ww[i][j-1][t];	}
	
	else ww[i][j][t]=ww[i-1][j][t]+ww[i-1][j-1][t]+ww[i-1][j][t-1]-ww[i-1][j-1][t-1];
			}
		}
	}
	
	while(cin>>a>>b>>c){
		if(a==-1&&b==-1&&c==-1) break;
		
		int i,j,t;
		i=a;j=b;t=c;
		if(a<=0||b<=0||c<=0){
			a=0;
			b=0;
			c=0;
		}
		if(a>20||b>20||c>20){
			a=20;
			b=20;
			c=20;
		}
		cout<<"w("<<i<<", "<<j<<", "<<t<<") = "<<ww[a][b][c]<<endl;
	}
	return 0;
}