function for fun递归好题记忆化动归

Function Run Fun

Time Limit : 2000/1000ms (Java/Other)   Memory Limit : 20000/10000K (Java/Other)
Total Submission(s) : 28   Accepted Submission(s) : 15
[align=left]Problem Description[/align]
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.

 

[align=left]Input[/align]
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.
 

[align=left]Output[/align]
Print the value for w(a,b,c) for each triple.
 

[align=left]Sample Input[/align]

1 1 1
2 2 2
10 4 6
50 50 50
-1 7 18
-1 -1 -1

 

[align=left]Sample Output[/align]

w(1, 1, 1) = 2
w(2, 2, 2) = 4
w(10, 4, 6) = 523
w(50, 50, 50) = 1048576ACcode:#include <iostream>
#include<cstdio>
using namespace std;
int dp[51][51][51];//定义一个数组后，默认全部为0
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  w(20,20,20);
    if(w(a,b,c))
        return w(a,b,c);//有了就AC，没有这句就Time Limit，这是为了避免重复运算，记忆化搜索
    if(a<b&&b<c)
        return w(a, b, c-1) + w(a, b-1, c-1) - w(a, b-1, c) ;
    else
        return  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;
    while(scanf("%d%d%d",&a,&b,&c))
    {
        if(a==-1&&b==-1&&c==-1)
            break;
        cout<<"w("<<a<<", "<<b<<", "<<c<<") = ";
        printf("%d\n",w(a,b,c));
    }
    return 0;
}

w(-1, 7, 18) = 1