Kraken - 6 months ago 47

C Question

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];

//arr[n] gives the answer?

Is this the right way?

Can it be any better?

Answer

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.