std::map lower_bound is not returning the correct value

Question

Good afternoon, I am trying to use the std::map lower_found member function. However , it keeps returning the wrong answer. Here is an excerpt of my test code. Please explain to me how to make std::map lower bound function properly. Thank you.

class Interval { 
     public:   
         explicit Interval(int item){ 
            mLow = item;
            mHigh = item;
            mStamp = 0;
         }
         Interval(int low, int high, int stamp = 0){ 
            mLow = low;
            mHigh = high;
            mStamp = stamp;

         }
         Interval(void){  
            mLow = 0;
            mHigh = 0;
            mStamp = 0;

         }

         Interval(const Interval& r):
            mLow(r.mLow),
            mHigh(r.mHigh),
            mStamp(r.mStamp)
         {

         }

         bool operator<(const Interval& rhs) const{     
             if (mLow < rhs.mLow){             
                 return true;     
             }     
             return false;   
         } // operator<    
         int low() const { return mLow; }   
         int high() const { return mHigh; }
         int getStamp() const { return mStamp; }
         void setLow(int lower) { mLow = lower; }   
         void setHigh(int higher) { mHigh = higher; }
         void setStamp(int stamp) { mStamp = stamp; }
     private:   
         int mLow;   
         int mHigh; 
         int mStamp;
}; // class Interval 


 int main(int Argc_,char *Argv_[]) {
    int n;
    Interval r;

    std::map<Interval, Interval> Intervals_type;
    r.setLow(0);
    r.setHigh(10);
    r.setStamp(1);
    std::pair< Interval, Interval > tmp(r,r);
    Intervals_type.insert(tmp); 

    r.setLow(10);
    r.setHigh(20);
    r.setStamp(2);
    std::pair< Interval, Interval > tmp2(r,r);
    Intervals_type.insert(tmp2);    


    r.setLow(20);
    r.setHigh(30);
    r.setStamp(3);
    std::pair< Interval, Interval > tmp3(r,r);
    Intervals_type.insert(tmp3);    

    r.setLow(30);
    r.setHigh(40);
    r.setStamp(4);
    std::pair< Interval, Interval > tmp4(r,r);
    Intervals_type.insert(tmp4);    



    n = 36;
    std::map<Interval, Interval>::const_iterator it = 
               Intervals_type.lower_bound(Interval(n));
    if (it == Intervals_type.end()){
        printf(" n = %d not found\n",n);
    }

    return 1;
}

Answer 1

std::map compares with operator < only, so it knows only about Interval::mLow , effectively treating all intervals as [mLow, ∞). You're using the wrong container. It's possible to do it with map but it's harder. Use Boost.Icl instead.

Edit: The best thing you have in STL for this purpose is std::multi_set. Order your intervals by the right end-point:

     bool operator<(const Interval& rhs) const{     
         return mHigh < rhs.mHigh;
     }

Now you can do it this way:

std::multi_set<Interval> cont;
cont.insert(Interval(0,10,1));
cont.insert(Interval(10,20,2));
cont.insert(Interval(20,30,3));
cont.insert(Interval(30,40,4));

std::multi_set<Interval>::const_iterator iter = cont.lower_bound(Interval(36));
if(iter == cont.end() || iter->low() > 36)
    // not found
else
    // found

Answer 2

IIUC, you're dealing with ranges, and you have an invariant on the map that ranges don't overlap. If that's the case, you have to define your operator< so that it deals with ranges, and does something drastic (assertion failure or an exception) in the case of an overlap, to prevent such ranges from being inserted. Assuming a half open range of [low,high) and an assertion that high >= low in the constructor of Interval, something like the following should work:

struct CmpInterval
{
    //  For insertion...
    bool operator<( Interval const& lhs, Interval const& rhs) const
    {
        assert( lhs.low >= rhs.high
                || lhs.high <= rhs.low
                || (lhs.low == rhs.low && lhs.high == rhs.high) );
        return lhs.low < rhs.low;
    }
    //  For find, lower_bound, etc.
    bool operator<( Interval const& lhs, int target ) const
    {
        return lhs.low < target;
    }

    bool operator<( int target, Interval const& rhs ) const
    {
        return target <= rhs.high;
    }
};

The last two are used for lower_bound, find, etc., when you pass a simple integer as key (and not an Interval); together, they define a strict ordering relationship between an int and an Inteval, IFF there are no overlapping intervals, and an equivalence relationship such that all n in an interval [i, j) are equivalent to that range and to each other. (Again, if there are overlapping intervals, there is no equivalence relationship, and the behavior is undefined.)

Answer 3

lower_bound should return the position before the first item that is equal or larger. The largest item in your map is actually smaller so end is returned.

In your operator < you only check mLow. If you want to check that 36 is in the range 30 to 40 then correct your operator <.

Answer 4

The definition of lower_bound is that it returns a location where you could insert the item and still keep the container sorted. Your comparison function only works with the low member; your container has the contents 0,10,20,30 for the lows. The only insertion point for 36 that keeps the container sorted is at the very end.