From : https://leetcode.com/problems/unique-binary-search-trees/
Given n, how many structurally unique BST's (binary search trees) that store values 1...n?
For example,
Given n = 3, there are a total of 5 unique BST's.
1 3 3 2 1
\ / / / \ \
3 2 1 1 3 2
/ / \ \
2 1 2 3
任选一个结点作为根结点,那么这棵树的组合为其左边树的组合数目乘以右边的组合数目,即
num[i] = Σ num[k-1]*num[i-k] (1<=k<=i)
那么从小到大求可以依次求出num[i[, 最后返回num[n]即可。
class Solution {
public:
int numTrees(int n) {
if(n < 1) return 0;
if(n < 3) return n;
vector<int> num(n+1);
num[0] = 1;
num[1] = 1;
num[2] = 2;
for(int i=3; i<=n; i++){
for(int j=1; j<=i; j++)
num[i] += num[j-1]*num[i-j];
}
return num[n];
}
};
public class Solution {
public int numTrees(int n) {
if (n < 1) {
return 0;
}
if (n < 3) {
return n;
}
int[] num = new int[n + 1];
num[0] = 1;
num[1] = 1;
num[2] = 2;
for (int i = 3; i <= n; i++) {
// length = i
for (int j = 1; j <= i; j++) {
// root is j
num[i] += num[j - 1] * num[i - j];
}
}
return num[n];
}
}