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POJ1579:Function Run Fun

时间:2015-09-27 17:31:56      阅读:180      评论:0      收藏:0      [点我收藏+]

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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: 


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

 
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。
技术分享
 1 #include <iostream>
 2 #include <cstdio>
 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                 else
19                     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 }
View Code

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。

技术分享
 1 #include <stdio.h>
 2 #include <string.h>
 3 #include <algorithm>
 4 using namespace std;
 5 
 6 int dp[25][25][25];
 7 
 8 int dfs(int a,int b,int c)
 9 {
10     if(a<=0 || b<=0 || c<=0)
11         return 1;
12     if(a>20 || b>20 || c>20)
13         return dfs(20,20,20);
14     if(dp[a][b][c])
15         return dp[a][b][c];
16     if(a<b && b<c)
17         dp[a][b][c] = dfs(a,b,c-1)+dfs(a,b-1,c-1)-dfs(a,b-1,c);
18     else
19         dp[a][b][c] = dfs(a-1,b,c)+dfs(a-1,b-1,c)+dfs(a-1,b,c-1)-dfs(a-1,b-1,c-1);
20     return dp[a][b][c];
21 }
22 
23 int main()
24 {
25     int a,b,c;
26     memset(dp,0,sizeof(dp));
27     while(~scanf("%d%d%d",&a,&b,&c))
28     {
29         if(a == -1 && b == -1 && c == -1)
30             break;
31         printf("w(%d, %d, %d) = %d\n",a,b,c,dfs(a,b,c));
32     }
33 
34     return 0;
35 }
View Code

 

 

POJ1579:Function Run Fun

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原文地址:http://www.cnblogs.com/to-creat/p/4842392.html

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