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POJ1579：Function Run Fun(记忆化)

2024-07-14 14:54:53   215人阅读

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
状态方程都给出来了，直接无脑敲代码就行了
#include <stdio.h>
#include <string.h>
#include <algorithm>
using namespace std;

int dp[25][25][25];

int dfs(int a,int b,int c)
{
    if(a<=0 || b<=0 || c<=0)
        return 1;
    if(a>20 || b>20 || c>20)
        return dfs(20,20,20);
    if(dp[a][b][c])
        return dp[a][b][c];
    if(a<b && b<c)
        dp[a][b][c] = dfs(a,b,c-1)+dfs(a,b-1,c-1)-dfs(a,b-1,c);
    else
        dp[a][b][c] = dfs(a-1,b,c)+dfs(a-1,b-1,c)+dfs(a-1,b,c-1)-dfs(a-1,b-1,c-1);
    return dp[a][b][c];
}

int main()
{
    int a,b,c;
    memset(dp,0,sizeof(dp));
    while(~scanf("%d%d%d",&a,&b,&c))
    {
        if(a == -1 && b == -1 && c == -1)
            break;
        printf("w(%d, %d, %d) = %d\n",a,b,c,dfs(a,b,c));
    }

    return 0;
}

































        

            
                
                  
                
                

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