POJ1579:Function Run Fun

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Function Run Fun

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 14772 Accepted: 7639

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

Pacific Northwest 1999

=======================================代码=======================================

水题直接贴代码。

#include<stdio.h>int a,b,c,DP[25][25][25];int w(int a,int b,int c){if(a<=0||b<=0||c<=0) return 1;if(a>20||b>20||c>20) return w(20,20,20);if(DP[a][b][c]) return DP[a][b][c];if(a<b&&b<c) return DP[a][b][c]=w(a,b,c-1)+w(a,b-1,c-1)-w(a,b-1,c);return DP[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);}int main(){while(scanf("%d%d%d",&a,&b,&c)==3&&!(a==-1&&b==-1&&c==-1)){printf("w(%d, %d, %d) = %d\n",a,b,c,w(a,b,c));}return 0;}