HDU 1579 Function Run Fun(记忆化搜索)

Function Run Fun

Time Limit: 1000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 2519 Accepted Submission(s): 1324

Problem 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

冬练三九之一  

/*if a <= 0 or b <= 0 or c <= 0, then w(a, b, c) returns:  1if 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)数组开三维22就行 */#include<iostream>#include <string.h>using namespace std;int num[22][22][22]; 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 num[20][20][20]=w(20,20,20);if(num[a][b][c]!=-1)   return num[a][b][c];if(a<b&&b<c)  return num[a][b][c]=w(a,b,c-1)+w(a,b-1,c-1)-w(a,b-1,c);return num[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(){      int a,b,c;     memset(num,-1,sizeof(num));    while(cin>>a>>b>>c){    if(a==-1&&b==-1&&c==-1)     break;    cout<<"w("<<a<<", "<<b<<", "<<c<<") = "<<w(a,b,c)<<endl;}return 0;}