forked from spaghetti-source/algorithm
-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathcatalanumber.cpp
More file actions
40 lines (33 loc) · 881 Bytes
/
catalanumber.cpp
File metadata and controls
40 lines (33 loc) · 881 Bytes
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
#include<iostream>
using namespace std;
// Returns value of Binomial Coefficient C(n, k)
unsigned long int binomialCoeff(unsigned int n, unsigned int k)
{
unsigned long int res = 1;
// Since C(n, k) = C(n, n-k)
if (k > n - k)
k = n - k;
// Calculate value of [n*(n-1)*---*(n-k+1)] / [k*(k-1)*---*1]
for (int i = 0; i < k; ++i)
{
res *= (n - i);
res /= (i + 1);
}
return res;
}
// A Binomial coefficient based function to find nth catalan
// number in O(n) time
unsigned long int catalan(unsigned int n)
{
// Calculate value of 2nCn
unsigned long int c = binomialCoeff(2*n, n);
// return 2nCn/(n+1)
return c/(n+1);
}
// Driver program to test above functions
int main()
{
for (int i = 0; i < 10; i++)
cout << catalan(i) << " ";
return 0;
}