[Algorithm] How to use Max Heap to maintain K smallest items

Let's say we are given an array:

[4,1,5,2,3,0,10]

We want to get K = 3 smallest items from the array and using Max heap data structure.

 

So this is how to think about it.

1. We take first K items put it into Max Heap:

     5

  /     \

4          1

 

2. Then we move forward to next element '2' in the array, we check

• Whether 2 is smaller than current max item in heap, which is '5', if yes, then replace 5 with 2
• Then re-arrange the heap

     4

   /    \        

 2         1

3. Repeat the process for items [3,0]

     3　　　　　　　　2

   /    \                   /　　\

 2         1              0　　　　1

4. When the item is '10' which is larger than current max '2', we just ingore it.

5. In the end, we got K smallest items, we just need to print it out. (K smallest items are not ncessary in order)