Function Run Fun
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 | Output |
|---|
1 1 1
2 2 2
10 4 6
50 50 50
-1 7 18
-1 -1 -1
| 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
|
代码?
#include<algorithm>
#include<iostream>
#include <stdio.h>
#include<cstring>
#include<cstdlib>
#include<cstdio>
#include<cmath>
#include<queue>
#include<vector>
using namespace std;
int m[25][25][25]={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)//先判断大于二十的情况就不用定义太大的数组
return w(20,20,20);
if(m[a][b][c])//避免重复计算已知的的数，减少时间损耗
return m[a][b][c];
if(a<b&&b<c)//其他情况得出结果后退出
m[a][b][c]=w(a,b,c-1)+w(a,b-1,c-1)-w(a,b-1,c);
else
m[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);
return m[a][b][c];
}
int main()
{
int a,b,c,d;
while(cin >>a>>b>>c)//while循环
{
if(a==-1&&b==-1&&c==-1)//满足条件退出
break;
d=w(a,b,c);
printf("w(%d, %d, %d) = %d\n",a,b,c,d);//一定注意输出格式！！！！！！
}
return 0;
}
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