leetcode 96. Unique Binary Search Trees 唯一二叉搜索树

下一题 95. Unique Binary Search Trees II

题意

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

相比下一题这一题简单多了

解1

// 无脑递归，速度比较慢 // Runtime: 988 ms, faster than 9.55% of Java online submissions for Unique Binary Search Trees. //Memory Usage: 35.9 MB, less than 17.36% of Java online submissions for Unique Binary Search Trees. public int numTrees(int n) { if (n == 0) return 1; if (n == 1) return 1; if (n == 2) return 2; int sum = 0; for (int i = 1; i <= n; i++) { sum += numTrees(i - 1) * numTrees(n - i); } return sum; }

解2

优化解1

// 用了数组存结果 // Runtime: 0 ms, faster than 100.00% of Java online submissions for Unique Binary Search Trees. //Memory Usage: 35.4 MB, less than 17.36% of Java online submissions for Unique Binary Search Trees. public int numTrees2(int n) { int[] counts = new int[20]; counts[0] = 1; counts[1] = 1; counts[2] = 2; for (int i = 3; i <= n; i++) { int sum = 0; for (int j = 1; j <= i; j++) { sum += counts[j - 1] * counts[i - j]; } counts[i] = sum; } return counts[n]; }