2017年10月29日

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<=0||b<=0||c<=0)  return 1;

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 main(int argc, char const *argv[])

{   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;

    else if(a>=20||b>=20||c>=20)//要用else if

cout<<"w"<<"("<<a<<","<<" "<<b<<","<<" "<<c<<")"<<" "<<"="<<" "<<w[20][20][20]<<endl;

    else

cout<<"w"<<"("<<a<<","<<" "<<b<<","<<" "<<c<<")"<<" "<<"="<<" "<<w[a][b][c]<<endl;

}

  return 0;

}