POJ 1579 Function Run Fun【递归转循环】

Function Run Fun

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 18342 Accepted: 9376

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

 

AC代码：

#include<cstdio>int w[22][22][22];int main(){int a,b,c;for(int i=0;i<21;++i) {for(int j=0;j<21;++j) {//w(a-1, b, c) + w(a-1, b-1, c) + w(a-1, b, c-1) - w(a-1, b-1, c-1) for(int k=0;k<21;++k) {if(!i||!j||!k) w[i][j][k]=1;else if(i<j&&j<k) w[i][j][k]=w[i][j][k-1]+w[i][j-1][k-1]-w[i][j-1][k];else 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];//printf("%d %d %d %d\n",i,j,k,w[i][j][k]);}}}while(scanf("%d%d%d",&a,&b,&c),~a||~b||~c){int ans=0;if(a<=0||b<=0||c<=0) ans=1;else if(a>20||b>20||c>20) ans=w[20][20][20];else ans=w[a][b][c];printf("w(%d, %d, %d) = %d\n",a,b,c,ans); }return 0;}