Function Run Fun
| Time Limit: 1000MS | Memory Limit: 10000K | |
| Total Submissions:13896 | Accepted: 7233 |
Description
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.
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
1 #include <cstdio> 2 #include <cstring> 3 using namespace std; 4 int ww[22][22][22]; 5 int w(int a, int b, int c){ 6 if (a <= 0 || b <= 0 || c <= 0) return 1; 7 if (a > 20 || b > 20 || c > 20) return w(20, 20, 20); 8 if (ww[a][b][c] > 0) return ww[a][b][c]; 9 if (a < b && b < c) return ww[a][b][c] = w(a, b, c-1) + w(a, b-1, c-1) - w(a, b-1, c); 10 else return ww[a][b][c] = w(a-1, b, c) + w(a-1, b-1, c) + w(a-1, b, c-1) - w(a-1, b-1, c-1); 11 } 12 int main(void){ 13 int a, b, c; 14 #ifndef ONLINE_JUDGE 15 freopen("poj1759.in", "r", stdin); 16 #endif 17 while (~scanf("%d%d%d", &a, &b, &c)){ 18 if (a == b && b == c && c == -1) break; 19 memset(ww, -1, sizeof(ww)); 20 printf("w(%d, %d, %d) = %d\n", a, b, c, w(a, b, c)); 21 } 22 return 0; 23 }
基本思想就是标记的思想，避免重复计算，水题，看了讨论板学会的，突然发现好久不做水题了……
有一个事情，就是敲代码的时候，要认真，千万要避免打字错误……次奥，超级让人崩溃的