Kraken - 1 year ago 79
C Question

# Catalan Number in using Dynamic Prog

I was calculating the number of Binary Search Trees with n nodes, and I found out that it is Catalan Number.

Now, using DP, here's my attempt.

``````create arr[n+1];
arr[0]=1;
arr[1]=1;
for(i=2;i<n+1;i++)
arr[i]=0;
for(j=1;j<i;j++)
arr[i]+=arr[i-j]*arr[j];

``````

Is this the right way?

Can it be any better?

I don't think that your code works. Do you mean the number of unique Binary Search Trees with numbers from `1` to `n`?

For `n = 3`, the number should be `5`. But your code gave me the result `2`.

``````1         3     3      2      1
\       /     /      / \      \
3     2     1      1   3      2
/     /       \                 \
2     1         2                 3
``````

Here is my solution:

``````int numTrees(int n) {
int dp[n+1];
memset(dp, 0, sizeof(dp));
dp[0] = 1;
dp[1] = 1;
for (int i = 2; i <= n; ++i)
for (int j = 1; j <= i; j++)
dp[i] += dp[j-1] * dp[i-j];
return dp[n];
}
``````

For Catalan Number, `P(3) = P(1)P(2) + P(2)P(1)`.

But in this problem, `P(3) = P(0)P(2) + P(1)P(1) + P(2)P(0)`.

So, I guess it's not Catalan Numbers. Hope this could help you.

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