Leetcode#96Unique Binary Search Trees

Unique Binary Search Trees

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Question Solution

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

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分析，该问题不考虑节点的不同，只考虑树形状的不同，遍历所有可能难于实现并且时间开销大

这种问题可以考虑动态规划，因为一棵大树可以分解成两颗小的子树组合的形式，因此获得子树的各种树形即刻求出大树的不同树形

public class Solution {

public int numTrees(int n) {

if (n == 1)

return 1;

if (n == 2)

return 2;

int[] record = new int[n + 1];

record[0] = 1;

record[1] = 1;

record[2] = 2;

for (int i = 3; i <= n; i++) {

int tmp = 0;

for (int k = 0; k < i; k++) {

tmp += (record[k] * record[i - k - 1]);

}

record[i] = tmp;

}

return record[n];

}

}