joj1024

 1024: Function Run Fun


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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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 }



 

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