Function Run Fun
| Time Limit: 1000MS | Memory Limit: 10000K | |
| Total Submissions: 13734 | Accepted: 7154 |
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.
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 12 2 210 4 650 50 50-1 7 18-1 -1 -1
Sample Output
w(1, 1, 1) = 2w(2, 2, 2) = 4w(10, 4, 6) = 523w(50, 50, 50) = 1048576w(-1, 7, 18) = 1
Source
直接递归会超时，预处理即可。
1 #include2 #include 3 4 using namespace std; 5 6 int main() 7 { 8 int w[21][21][21], ans, a, b, c; 9 //预处理 10 for(int i = 0; i < 21; i++)11 for(int j = 0; j < 21; j++)12 for(int k = 0; k < 21; k++)13 {14 if(!i || !j || !k) w[i][j][k] = 1;15 else if(i < j && j < k) 16 w[i][j][k] = w[i][j][k-1] + w[i][j-1][k-1] - w[i][j-1][k];17 //w(a, b, c-1) + w(a, b-1, c-1) - w(a, b-1, c)18 else19 w[i][j][k] = w[i-1][j][k] + w[i-1][j-1][k] + w[i-1][j][k-1] - w[i-1][j-1][k-1];20 //w(a-1, b, c) + w(a-1, b-1, c) + w(a-1, b, c-1) - w(a-1, b-1, c-1) 21 }22 while(scanf("%d %d %d", &a, &b, &c))23 {24 if(a == -1 && b == -1 && c == -1) break;25 if(a <= 0 || b <= 0 || c <= 0) ans = 1;26 else if(a > 20 || b > 20 || c > 20) ans = w[20][20][20];27 else ans = w[a][b][c]; 28 printf("w(%d, %d, %d) = %d\n", a, b, c, ans);29 }30 return 0;31 }