Function Run Fun
http://acm.zju.edu.cn/show_problem.php?pid=1168
Time limit: 1 Seconds
Memory limit: 32768K
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.
1. 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
2. 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
Problem Source: Pacific Northwest 1999
1 /* 1168 ymC */
2 #include <stdio.h>
3 const int N3=9261;
4 const int N2=441;
5 const int N1=21;
6 int w[9261];
7 void init()
8 {
9 int a,b,c;
10 int t;
11 int i;
12 for(a=0;a<N1;a++)
13 {
14 for(b=0;b<N1;b++)
15 w[a*N2+b*N1]=1;
16 for(c=0;c<N1;c++)
17 w[a*N2+c]=1;
18 }
19 for(b=0;b<N1;b++)
20 for(c=0;c<N1;c++)
21 w[b*N1+c]=1;
22
23 for(i=0;i<N3;i++)
24 {
25 if(w[i]!=1)
26 {
27 a=i/N2;
28 c=i%N1;
29 b=i/N1-a*N1;
30 if(a<b&&b<c)
31 w[i]=w[i-1]+w[i-N1-1]-w[i-N1];
32 else
33 w[i]=w[i-N2]+w[i-N2-N1]+w[i-N2-1]-w[i-N2-N1-1];
34 }
35 }
36 }
37 int main()
38 {
39 int a,b,c;
40 init();
41 scanf("%d %d %d",&a,&b,&c);
42 while(a!=-1||b!=-1||c!=-1)
43 {
44 printf("w(%d, %d, %d) = ",a,b,c);
45 if(a<=0||b<=0||c<=0)
46 printf("1\n");
47 else if(a>20||b>20||c>20)
48 printf("%d\n",w[N3-1]);
49 else
50 {
51 printf("%d\n",w[a*N2+b*N1+c]);
52 }
53 scanf("%d %d %d",&a,&b,&c);
54 }
55
56 }