Problem:
Suppose that we are given a sequence of n values x1, x2, ..., xn and seek to quickly answer repeated queries of the form:
given i and j, find the smallest value in xi, ...., xj.
1. Design a data structure that uses O(n2) space and answers queries in O(1) time.
N*N matrix
2. Design a data structure that uses O(n) space and answer s queries in O(log n) time. For partial credit, your data structure can use O(n log n) space and O(log n) query time.
Solution
Maintain a binary tree. At each node record the smallest value of the tree rooted at the specific node.
On query for (i, j);
1. Find where i and j departs, ie. the common root with the highest level. That's easy.
2. From this common root, continue to find i and j.
For each nodeA along i's path,
if the path goes left from nodeA, add nodeA->min and nodeA->right->min to the candidates.
if the path goes right, nothing is done but go right.
For each nodeA along the j's path,
if the path goes right from nodeA, add nodeA->min and nodeA->left->min to the candidates.
if the path goes left from nodeA, nothing done but go left.
I don't know complex data structure now, but this gives an answer