POJ1579:Function Run Fun

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 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

Source

Pacific Northwest 1999

 

方法一：

直接递归会超时，预处理即可。实现把所有结果存到三维数组中。

 #include <iostream>
 #include <cstdio>

 using namespace std;

 int main()
 {
     int w[][][], ans, a, b, c;
     //预处理
     for(int i = ; i < ; i++)
         for(int j = ; j < ; j++)
             for(int k = ; k < ; k++)
             {
                 if(!i || !j || !k) w[i][j][k] = ;
                 else if(i < j && j < k)
                     w[i][j][k] = w[i][j][k-] + w[i][j-][k-] - w[i][j-][k];
                     //w(a, b, c-1) + w(a, b-1, c-1) - w(a, b-1, c)
                 else
                     w[i][j][k] = w[i-][j][k] + w[i-][j-][k] + w[i-][j][k-] - w[i-][j-][k-];
                     //w(a-1, b, c) + w(a-1, b-1, c) + w(a-1, b, c-1) - w(a-1, b-1, c-1)
             }
     while(scanf("%d %d %d", &a, &b, &c))
     {
         if(a == - && b == - && c == -) break;
         if(a <=  || b <=  || c <= ) ans = ;
         else if(a >  || b >  || c > ) ans = w[][][];
         else ans = w[a][b][c];
         printf("w(%d, %d, %d) = %d\n", a, b, c, ans);
     }
     return ;
 }

方法二：

总之要先把之前运算出来的结果存到三维数组中，避免重复运算。

 #include <stdio.h>
 #include <string.h>
 #include <algorithm>
 using namespace std;

 int dp[][][];

 int dfs(int a,int b,int c)
 {
     if(a<= || b<= || c<=)
         return ;
     if(a> || b> || c>)
         return dfs(,,);
     if(dp[a][b][c])
         return dp[a][b][c];
     if(a<b && b<c)
         dp[a][b][c] = dfs(a,b,c-)+dfs(a,b-,c-)-dfs(a,b-,c);
     else
         dp[a][b][c] = dfs(a-,b,c)+dfs(a-,b-,c)+dfs(a-,b,c-)-dfs(a-,b-,c-);
     return dp[a][b][c];
 }

 int main()
 {
     int a,b,c;
     memset(dp,,sizeof(dp));
     while(~scanf("%d%d%d",&a,&b,&c))
     {
         if(a == - && b == - && c == -)
             break;
         printf("w(%d, %d, %d) = %d\n",a,b,c,dfs(a,b,c));
     }

     return ;
 }