LeetCode Unique Binary Search Trees
2014-03-24 23:53
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class Solution { public: int numTrees(int n) { return dfs(1, n); } int dfs(int start, int end) { if (start >= end) return 1; int count = 0; // choose different number from [start, end] as the root for (int i = start; i <= end; i++) { // number of left tree cases * number of right tree cases count += dfs(start, i - 1) * dfs(i + 1, end); } return count; } };
想到了就简单,再水一发
第二轮:
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
就是卡特兰数其实,f(n) = f(0) * f(n-1) + f(1) * f(n-2)... + f(n-1) * f(0),题目中递增序列具体区间没有关系,只要关心其内数字个数即可:
class Solution { public: int numTrees(int n) { if (n <= 1) { return 1; } vector<int> dp(n+1, 0); dp[0] = 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 ; } };
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