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[Leetcode] - 96 Unique Binary Search Trees

2015-10-03 15:36 477 查看
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


class Solution {
public:
  int numTrees(int n) {
    if (n <= 2) return n;
    vector<int>nums(n + 1);
    nums[0] = 1;
    for (int i = 1; i <= n; ++i ) {
      if (i < 3) {
        nums[i] = i;
        continue;
      }
      for (int j = 1; j <= i; ++j) {
        nums[i] += nums[j - 1] * nums[i - j];
      }
    }
    return nums
;
  }
};
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