What is the time complexity for building a segment tree for an array of size n?
# | User | Rating |
---|---|---|
1 | ecnerwala | 3648 |
2 | Benq | 3580 |
3 | orzdevinwang | 3570 |
4 | cnnfls_csy | 3569 |
5 | Geothermal | 3568 |
6 | tourist | 3565 |
7 | maroonrk | 3530 |
8 | Radewoosh | 3520 |
9 | Um_nik | 3481 |
10 | jiangly | 3467 |
# | User | Contrib. |
---|---|---|
1 | maomao90 | 174 |
2 | awoo | 164 |
2 | adamant | 164 |
4 | TheScrasse | 159 |
4 | nor | 159 |
6 | maroonrk | 156 |
7 | -is-this-fft- | 150 |
8 | SecondThread | 147 |
9 | orz | 146 |
10 | pajenegod | 145 |
What is the time complexity for building a segment tree for an array of size n?
Name |
---|
O(n). Because in each recursuion call you recurse twice for subtasks of size n / 2 and do O(1) operations (that's if you're building segment tree for simple operation like sum or max).
T(n) = 2T(n / 2) + O(1) = O(n) (by Master-theorem)
Another way to see this — segment tree has n nodes on lowest level, n / 2 nodes on second level, n / 4 on third, ..., 1 on top level = 2 * n nodes = O(n) nodes, and in all of them you do O(1) operations.
Also, you can appreciate segtree visualization here. :D
2N memory and operations required. [N; N + N — 1] leaves + [1; N — 1] internal nodes and root.