poj_1579 && hdoj_1331

Function Run Fun

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 13554		Accepted: 7056

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

之前用记忆化搜索写过。

三个for循环，从w[0][0][0]递推到w[20[20][20]

注意题目的优先计算顺序。先是考虑是否会小于0，然后才考虑是否会大于20，要不然就会WA。

//#include<iostream>
//#include<cstdio>
//#include<cstring>
//using namespace std;
//int w[100][100][100];
//
//int DFS(int a,int b,int c)
//{
// if(a<=0 || b<=0 || c<=0)
// {
// return 1;
// }
// if(a>20 || b>20 || c>20)
// {
// return DFS(20,20,20);
// }
// if(w[a][b][c]!=-1)
// {
// return w[a][b][c];
// }
// if(a<b && b<c)
// {
// w[a][b][c] = DFS(a, b, c-1) + DFS(a, b-1, c-1) - DFS(a, b-1, c);
// }
// else
// {
// w[a][b][c] = DFS(a-1, b, c) + DFS(a-1, b-1, c) + DFS(a-1, b, c-1) - DFS(a-1, b-1, c-1);
// }
// return w[a][b][c];
//}
//int main()
//{
// freopen("in.txt","r",stdin);
// int i,j,k;
// memset(w,-1,sizeof(w));
// while(cin>>i>>j>>k)
// {
// if(i==-1&&j==-1&&k==-1)
// break;
// printf("w(%d, %d, %d) = %d\n",i,j,k,DFS(i,j,k));
// }
//}

#include<iostream>
#include<cstdio>
#include<cstring>
using namespace std;
int w[25][25][25];

int main()
{
freopen("in.txt","r",stdin);
int i, j, k, a, b, c;
memset(w, 0, sizeof(w));

for(i=0; i<=20; i++)
{
for(j=0; j<=20; j++)
{
for(k=0; k<=20; k++)
{
if(i == 0 || j == 0 || k == 0)
{
w[i][j][k] = 1;
}
else if(i < j && j < k)
{
w[i][j][k] = w[i][j][k-1] + w[i][j-1][k-1] - w[i][j-1][k];
}
else
{
w[i][j][k] = w[i-1][j][k] + w[i-1][j-1][k] + w[i-1][j][k-1] - w[i-1][j-1][k-1];
}
}
}
}

while(cin >> a >> b >> c)
{
if(a == -1 && b == -1 && c == -1)
break;
if(a <= 0 || b <= 0 || c <= 0)
printf("w(%d, %d, %d) = %d\n",a,b,c,1);
else if(a > 20 || b > 20 || c > 20)
printf("w(%d, %d, %d) = %d\n",a,b,c,w[20][20][20]);
else
printf("w(%d, %d, %d) = %d\n",a,b,c,w[a][b][c]);

}
return 0;
}