lintcode: Unique Binary Search Trees

Given n, how many structurally unique BSTs (binary search trees) that store values 1...n?

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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

Tags

class Solution {public:    /**     * @paramn n: An integer     * @return: An integer     */         int numTrees(int n) {        // write your code here        /*        if (n==1 || n==0)            return 1;                static vector<int> dp(n+1); //因为loop从1到n, 所以设置 dp为 n+1                if (dp[n] != 0)            return dp[n];                int retVal = 0;        for (int i=1; i<=n; i++)        {            if (i==1 || i==n)                retVal += numTrees(n-1);            else                retVal += (numTrees(i-1)*numTrees(n-i));        }        dp[n] = retVal;                return retVal;                */                if (n == 1 || n == 0)            return 1;                    vector<int> nums(n+1);                nums[0] = 1;                for (int i=1; i<=n; i++)        {            for (int j=1; j<=i; j++)            {                nums[i] += nums[j-1]*nums[i-j];            }        }                return nums[n];    }};