HDU

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

一个超级水的记忆化搜索，然而，然而。。。。。。。。

我WA了几次，一脸懵逼，请注意第一个条件和第二个条件的先后顺序，原本以为一样手贱先写了大于20的判断，后来发现不一样，比如说w（-1,50,50），而题目的 意思是想让你先按照小于0，天天debug

#include <iostream>#include <cstdio>#include <cstring>using namespace std;int d[21][21][21];int w(int a,int b,int c){if(a<=0||b<=0||c<=0){return 1;}if(a>20||b>20||c>20){if(d[20][20][20]!=-1){return d[20][20][20];}else{d[20][20][20] = w(20,20,20);return d[20][20][20];}}if(a<b&&b<c){if(d[a][b][c-1]==-1){d[a][b][c-1] = w(a,b,c-1);}if(d[a][b-1][c-1]==-1){d[a][b-1][c-1] = w(a,b-1,c-1);}if(d[a][b-1][c]==-1){d[a][b-1][c] = w(a,b-1,c);}return d[a][b][c-1]+d[a][b-1][c-1]-d[a][b-1][c];}else{if(d[a-1][b][c]==-1){d[a-1][b][c] = w(a-1, b, c);}if(d[a-1][b-1][c]==-1){d[a-1][b-1][c] = w(a-1, b-1, c);}if(d[a-1][b][c-1]==-1){d[a-1][b][c-1] = w(a-1, b, c-1);}if(d[a-1][b-1][c-1]==-1){d[a-1][b-1][c-1] = w(a-1, b-1, c-1);}return d[a-1][b][c] + d[a-1][b-1][c] + d[a-1][b][c-1] - d[a-1][b-1][c-1]; }}int main(){int a,b,c;memset(d,-1,sizeof(d)); while(scanf("%d%d%d",&a,&b,&c)&&(a!=-1||b!=-1||c!=-1)){printf("w(%d, %d, %d) = %d\n",a,b,c,w(a,b,c));}}