joj1175

 1175: The Binomial Function

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Result	TIME Limit	MEMORY Limit	Run Times	AC Times	JUDGE
	3s	8192K	2837	844	Standard

1st Jilin University ACM International Collegiate Programming Contest

In this problem, you are to write a program to make the value of the binomial function:

where n and m are integers.

Input Specification

The input consists of several pairs of n and m(0<=n, m<=30). The end of input is marked by n=m=0, which should not be processed.

Output Specification

For each pair of n and m, you should print a line like this: "Binom(n, m) = v", where n, m and v have to be replaced by the values of n, m and v.

Sample Input

5 5

7 0

5 9

0 0

Sample Output

Binom(5, 5) = 1

Binom(7, 0) = 1

Binom(5, 9) = 32

 

 

主要是递归效率的问题，直接写递归会超时。用备忘优化一下AC。改成递推写，AC。

 

 1 #include <stdio.h>
 2 
 3 int array[31][31];
 4 
 5 int binomA(int a, int b); //纯递归，会超时
 6 int binomB(int a, int b); //带有备忘录
 7 int binomC(int a, int b); //递推写法
 8 
 9 int main(void)
10 {
11     freopen("in.txt", "r", stdin);
12 
13     int a, b;
14 
15     while ((scanf("%d%d", &a, &b))==2)
16     {
17         if (0==a && 0==b)
18         {
19             break;
20         }
21         printf("Binom(%d, %d) = %d\n", a, b, binomB(a, b));
22     }
23 
24 
25     return 0;
26 }
27 
28 int binomA(int a, int b)
29 {
30     if (0==a || 0==b || a==b)
31     {
32         return 1;
33     }
34     else
35     {
36         return binomA(a-1, b)+binomA(a-1, b-1);
37     }
38 }
39 
40 int binomB(int a, int b)
41 {
42     if (0==a || 0==b || a==b)
43     {
44         return 1;
45     }
46     else if (array[a][b])
47     {
48         return array[a][b];
49     }
50     else
51     {
52         return array[a][b] = binomB(a-1,b)+binomB(a-1,b-1);
53     }
54 }
55 
56 
57 int binomC(int a, int b)
58 {
59     int i, j;
60     for (i=0; i<31; i++)
61     {
62         array[0][i] = 1;
63         array[i][0] = 1;
64         array[i][i] = 1;
65     }
66     for (i=1; i<31; i++)
67     {
68         for (int j=1; j<31; j++)
69         {
70             if (i != j)
71             {
72                 array[i][j] = array[i-1][j]+array[i-1][j-1];
73             }
74         }
75     }
76     return array[a][b];
77 }