# Minimum number query

I know how to solve it for a problem which handles two queries 1)update an index to a new value 2)minimum element in a range.(using segment tree)

But how to handle for the case like minimum in a range which is greater than K which is some number given in the query

If anyone knows it using fenwick tree/segment tree please explain it clearly.

For a segment tree we will build the tree first but here we dont know the value of k because k is given in the queries .So how to build and update in this case ?

I think you can apply a Merge Sort Tree.

I solved a similar problem a few days ago where I had to find the value closest to `k` in a given range [L, R]. The problem was LRQUER.

In your case you can do the following:

Instead of storing a single value in any node, you can store a range. This range will be the sorted list of the values stored in its children. Then, while querying, you will query in this range. For a single query `[L, R]`, you can find the `upper_bound()` and then return the minimum of all the values found like this.

Edit: To handle point updates, we’ll have to update the corresponding parent nodes too. We can update a node in O(log(n)) time by searching for the previous element and then inserting a new element, using something like `std::set` (because we have to store the elements in sorted order) in C++. If duplicate elements are allowed, then we can use `std::multiset` in C++.

Now, there can be at most O(log(n)) updates in a single update operation because the depth of the tree will be of the order of log(n), making the complexity O(log^2(n)).

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@shubhambhattar but how to handle point updates?