Finding smallest next bigger element

Question

I have a task which requires me to find the smallest of all bigger elements in an array for all array entries and store the respective indexes in an array and I can't quite figure out the last part of the solution.

This is kind of similar to the problem explained here: https://www.geeksforgeeks.org/smallest-greater-elements-in-whole-array/

The only difference is that only the values right of the array entry are accounted for (j>i), e.g.:

input:  [80; 19; 49; 45; 65; 71; 76; 28; 68; 66]  
output: [-1;  7;  4;  4;  9;  6; -1;  9; -1; -1]

The solution with a self balancing tree makes sense to me. However, I still need to account for the indexing because only the solutions right of the array entry are valid.

Is there a way to map the indexing of the inserted values to the tree entries or to create a second tree with an identical structure but the index of the old array entries instead of the actual values as nodes? I am not sure because the structure of the self-balancing tree of course depends on the values inserted (bigger values right subtree, smaller values left subtree).

EDIT: Actually a second AVL tree propably won't help as I have to check that indexing is bigger AND array entry is bigger while traversing the tree...

Answer 1

The simplest solution is to iterate over the input from right to left, and for each element look up the first greater element in a tree (or any data structure with O(LogN) look-up and insertion), and then add the element to the tree. That way the greater element always comes after the element in the input.

For a C++ version, you can use a std::map where the element's value is the key and the element's index in the input is the value, and use upper_bound to get the next greater value:

#include <iostream>
#include <vector>
#include <map>

void nextValues(std::vector<int> &in, std::vector<int> &out) {
    std::map<int, int> tree;
    for (int i = in.size() - 1; i >= 0; i--) {
        out.insert(out.begin(), tree.upper_bound(in[i])->second - 1);
        tree.insert(std::pair<int, int>(in[i], i + 1));
    }
}

int main() {
    std::vector<int> a = {80,19,49,45,65,71,76,28,68,66};
    std::vector<int> b;
    nextValues(a, b);
    for (int i : b) std::cout << (int) i << ","; // -1,7,4,4,9,6,-1,9,-1,-1
    return 0;
}