Map a range of values to a single value

I need to map values ranging between lowerBound and upperBound to a certain value.

Illustrative Example:

For example, imagine I have GPS system which has users subscribed to it. This system is able to provide me the distance of the user from a certain point. Based on the distance of the user I want to assign them an ID.

Thus users in distance from

• 1 to 100 get ID: 8.4
• 101 to 200 get ID: 7.2
• 201 to 300 get ID: 3.6
• 401 to 600 get ID: 4.1

and so on...

My approach:

So what I did, I created an std::map by initializing it as follows:

   std::map<int, double> distanceToIdMap; 

   distanceToIdMap =
    {
            {100, 8.4},
            {200, 7.2},
            {300, 3.6},
    };

Then I use this code to get the ID for the given distance:

double roundUpToHundred = std::ceil(realDistance / 100.0) * 100;
double powerForDistance = distanceToIdMap.at(roundUpToHundred);

However my approach breaks down for the 401 to 600 distance, because by ceiling to the nearest hundred for a distance of 400+ I get the value 500 for which I don't have an entry in the map. Of course the trivial solution would be to add an entry for 500 to the distanceToIdMap but that is not how I want to handle this problem.

I would like to have a map with {(lowerbound, upperbound) , correspondingID} structure so I can address cases where an ID covers distance spanning more than 100m. And a given can check if the lowerBound < realDistance < upperBound and then provide the ID.