poj1579

Function Run Fun

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 15623		Accepted: 8080

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 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


思路：若直接用递归，肯定会超时，需要用三维数组进行记忆化，减少时间。

#include<iostream>
#include<stdio.h>
#include<string.h>
using namespace std;
int dp[22][22][22];
int DFS(int a,int b,int c)
{
    if(dp[a][b][c]!=-1)
        return dp[a][b][c];
    if(a<=0||b<=0||c<=0)
        return 1;
    else if(a>20||b>20||c>20)
        return DFS(20,20,20);
    else if(a<b&&b<c)
        return DFS(a, b, c-1) + DFS(a, b-1, c-1) - DFS(a, b-1, c);
    else
        return DFS(a-1, b, c) + DFS(a-1, b-1, c) + DFS(a-1, b, c-1) - DFS(a-1, b-1, c-1);
}
int main()
{
    int a,b,c,i,j,k;
    memset(dp,-1,sizeof(dp));
    for(i=0; i<=20; i++)
        for(j=0; j<=20; j++)
            for(k=0; k<=20; k++)
                dp[i][j][k]=DFS(i,j,k);
    while(cin>>a>>b>>c)
    {
        if(a==-1&&b==-1&&c==-1)
            break;
        if(a<=0||b<=0||c<=0)
            printf("w(%d, %d, %d) = 1
",a,b,c);
        else if(a>20||b>20||c>20)
            printf("w(%d, %d, %d) = %d
",a,b,c,dp[20][20][20]);
        else
            printf("w(%d, %d, %d) = %d
",a,b,c,dp[a][b][c]);
    }
    return 0;
}