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Heaps And Maps

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Heap and Map Implementation Details

C :

C does not have support for treemaps being a very basic language. You might have to implement your own version of balanced BST. We suggest you take a look at C++ as well. After all, everything C also works in C++.

C++ :

C++ Standard Template Library provides maps and sets which are implemented > internally using balanced red black trees. We explore maps here for now, although set is very much similar.

Map declaration :
    map<int, int> A; // O(1) declaration which declares an empty tree map.
Insert a new key, value pair K, V:
    A[K] = V; // O(log n). Note that we expect key K to be unique here. If you have keys that will repeat, take a look at multimaps. 
Delete a key K:
    A.erase(K); // O(log n)
Search if a key K exists in map:
    A.find(K) != A.end()  // O(log n)
Search for the value with key K:
     A[K]     // O(log n)
Find minimum key K in the map ( if the map is not empty ) :
    (A.begin())->first     // O(1)
Find maximum key K in the map ( if map is not empty ) :
    (A.rbegin())->first     // O(1)
Iterate over keys in sorted order :
    for (map<int,int>::iterator it = A.begin(); it != A.end(); ++it) {
        // it->first has the key, it->second has the value. 
    }
Find closest key K > x :
    (A.upper_bound(x))->first     // O(log n). Do need to handle the case when x is more than or equal to the max key in the map. 
Find closest key K >= x :
    (A.lower_bound(x))->first     // O(log n). Do need to handle the case when x is more than the max key in the map.
Size ( number of entries in the map ) :
    A.size()
JAVA

Java has TreeMap which is very similar to C++ map. Also implemented using Red Black trees.

Map declaration :
    TreeMap<Integer, Integer> A = new TreeMap<Integer, Integer>(); // O(1) declaration which declares an empty tree map.
Insert a new key, value pair K, V:
    A.put(K, V); // Note that we expect key K to be unique here. If you have keys that will repeat, they will be replaced. 
             // O(log n)
Delete a key K:
    A.remove(K); // O(log n)
Search if a key K exists in map:
    A.containsKey(K)  // O(log n)
Search for the value with key K:
     A.get(K)     // O(log n)
Find minimum key K in the map ( if the map is not empty ) :
    A.firstKey() OR A.firstEntry().getKey()     // O(1)
Find maximum key K in the map ( if map is not empty ) :
    A.lastKey() OR A.lastEntry().getKey()     // O(1)
Iterate over keys in sorted order :
    for (Map.Entry<Integer, Integer> entry : A.entrySet()) {
        // entry.getKey() has the key, entry.getValue() has the value
    } 
Find closest key K >= x :
    A.ceilingEntry(x).getKey()     // O(log n). Do need to handle the case when x is more than the max key in the map.
Find closest key K <= x :
    A.floorEntry(x).getKey()     // O(log n). Do need to handle the case when x is smaller than min key in the map
Size ( number of entries in the map ) :
    A.size() 
PYTHON :

Python does not have a implementation of treemap in standard library ( Sorry python users ). The closes we come to it is with heapq which is implementation of heaps ( http://en.wikipedia.org/wiki/Heap_%28data_structure%29 ) which obviously means that we are restricted in terms of number of things we can do as compared to treemap.

Heap declaration :
    A = []; # declares an empty list / heap. O(1)
            # Note that heaps are internally implemented using lists for which heap[k] <= heap[2*k+1] and heap[k] <= heap[2*k+2] for all k. 
Insert a new key, value pair K, V:
    heapq.heappush(A, (K, V));     // O(log n)
Delete the smallest key K ( Note that deleting random key K will be inefficient ) :
    heapq.heappop(A)[0]
Find minimum key K in the map ( if the map is not empty ) :
    A[0][0]
Size ( number of entries in the map ) :
    len(A) 

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