joj1024

 1024: Function Run Fun

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Result	TIME Limit	MEMORY Limit	Run Times	AC Times	JUDGE
	3s	8192K	2894	1177	Standard

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. For example:

1 1 1

2 2 2

10 4 6

50 50 50

-1 7 18

-1 -1 -1

Output

Print the value for w(a,b,c) for each triple, like this:

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

 

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This problem is used for contest: 60  183 

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用动态规划做，不知道尾递归优化能不能过。

 1 #include <iostream>
 2 
 3 using namespace std;
 4 
 5 int main(void)
 6 {
 7 
 8     int a[21][21][21];
 9     int i, j, k;
10 
11     for (i=0; i<21; i++)
12     {
13         for (j=0; j<21; j++)
14         {
15             a[0][i][j] = 1;
16             a[i][0][j] = 1;
17             a[i][j][0] = 1;
18         }
19     }
20 
21     for (i=1; i<21; i++)
22     {
23         for (j=1; j<21; j++)
24         {
25             for (k=1; k<21; k++)
26             {
27                 if (i<j && j<k)
28                 {
29                     a[i][j][k] = a[i][j][k-1]+a[i][j-1][k-1]-a[i][j-1][k];
30                 }
31                 else
32                 {
33                     a[i][j][k] = a[i-1][j][k]+a[i-1][j-1][k]+a[i-1][j][k-1]-a[i-1][j-1][k-1];
34                 }
35             }
36         }
37     }
38 
39 
40     while (cin>>i>>j>>k, i!=-1 || j!=-1 || k!=-1)
41     {
42         cout << "w(" << i << ", " << j << ", " << k <<") = " ;
43         if (i<=0 || j<=0 || k<=0)
44         {
45             cout << 1 <<endl;
46             continue;
47         }
48         if (i<=20 && j<=20 && k<=20)
49         {
50             cout << a[i][j][k] << endl;
51         }
52         else
53         {
54             cout << a[20][20][20] << endl;
55         }
56     }
57 
58     return 0;
59 }