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:
if a > 20 or b > 20 or c > 20, then w(a, b, c)
returns:
if a < b and b < c, then w(a, b, c) returns:
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
题目不算太难。就是共享结果。
#include "iostream"
#include
#include
using namespace std;
int w[22][22][22];
int rec(int a,int b,int c)
{
if(w[a][b][c]!=-1)
return w[a][b][c];
if(a==20||b==20||c==20)
return 1048576;
if(a
return (rec(a,b,c-1)+rec(a,b-1,c-1)-rec(a,b-1,c));
else
return
rec(a-1,b,c)+rec(a-1,b-1,c)+rec(a-1,b,c-1)-rec(a-1,b-1,c-1);
}
{ int a,b,c;
memset(w,-1,sizeof(w));
w[0][0][0]=1;
for(int i=0;i<=21;i++)
for (int j = 0; j <=21; ++j)
for(int k=0;k<=21;++k)
w[i][j][k]=rec(i,j,k);
while(cin>>a>>b>>c)
{
if(a==-1&&b==-1&&c==-1)
break;
if(a<=0||b<=0||c<=0)
cout<<"w"<<"("<<a<<","<<"
"<<b<<","<<" "<<c<<")"<<"
"<<"="<<" "<<w[0][0][0]<<endl;
cout<<"w"<<"("<<a<<","<<"
"<<b<<","<<" "<<c<<")"<<"
"<<"="<<" "<<w[20][20][20]<<endl;
cout<<"w"<<"("<<a<<","<<"
"<<b<<","<<" "<<c<<")"<<"
"<<"="<<" "<<w[a][b][c]<<endl;
}
}