LeetCode - Unique Binary Search Trees
Problem description
Given n, how many structurally unique BST’s (binary search trees) that store values 1 … n?
Example:
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Input: 3
Output: 5
Explanation:
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
Analysis
Basically, we can use dp to solve this question based on these observations.
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for n nodes, we need to separate n into three parts, 0 to i-1, i, i+1 to n, for i from 1 to n-1.
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for i from 1 to n-1 part, the relative order of these nodes are the same. So the number of unique BST trees are only determined by the nodes amount.
So we have
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for (int j = 1; j <= i; j++){
dp[i] += dp[j-1] * dp[i-j];
}
And the solution:
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class Solution {
public int numTrees(int n) {
int[] dp = new int[n+1];
dp[0] = 1;
dp[1] = 1;
for (int i = 2; i < n+1; i++){
for (int j = 1; j <= i; j++){
dp[i] += dp[j-1] * dp[i-j];
}
}
return dp[n];
}
}