[POJ] 1579 -> Function Run Fun

Function Run Fun

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 16896 Accepted: 8721

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

递归水题

Code：

#include <iostream>  using namespace std;#define MAX 21int main(){int arr[MAX][MAX][MAX];memset(arr, 0, sizeof(int)* MAX);for (int a = 0; a < MAX; ++a){for (int b = 0; b < MAX; ++b){for (int c = 0; c < MAX; ++c){if (a == 0 || b == 0 || c == 0) arr[a][b][c] = 1;else if (a < b && b < c) arr[a][b][c] = arr[a][b][c - 1] + arr[a][b - 1][c - 1] - arr[a][b - 1][c];else arr[a][b][c] = arr[a - 1][b][c] + arr[a - 1][b - 1][c] + arr[a - 1][b][c - 1] - arr[a - 1][b - 1][c - 1];}}}int a, b, c, x, y, z;while (cin >> a >> b >> c, a + 1 || b + 1 || c + 1){x = a, y = b, z = c;if (x < 0 || y < 0 || z < 0){x = 0; y = 0; z = 0;}if (x > 20 || y > 20 || z > 20){x = 20; y = 20; z = 20;}printf("w(%d, %d, %d) = %d\n", a, b, c, arr[x][y][z]);}return 0;}