\nIdea is to create a min-heap<\/strong> of characters of size q<\/code>. Each time we extract a character from our heap and add it to s<\/code>, we insert a new character from the string str<\/code> to the heap until the string str<\/code> not empty.<\/p>\n<\/blockquote>\nMethod 1 :<\/h4>\n\nWe can sort the first q<\/code> characters of the string and pick the smallest one and append it to s<\/code>. Now sort the next q<\/code> characters append the smallest one to s<\/code>. Repeat the process untill the string is empty.<\/p>\n<\/blockquote>\nMethod 2 :<\/h4>\n
We need to geneate a min heap of characters of size q<\/code>.<\/p>\n\n\n- In a min-heap<\/strong>, the root always stores the smaller value as compared to its left<\/strong> & right<\/strong> subtree, this condition needs to be true for every node. We need to insert each item one by one such that it’s parent is always smaller than the item itself. If the parent is greater, then we need to swap the current item with its parent. <\/li>\n
- We will insert<\/strong> first
q<\/code> characters from str<\/code> to the heap. Now we will extract<\/strong> a character and print it , and insert a new character from str<\/code>.<\/li>\n- We will stop once we have inserted all the characters from
str<\/code> to the heap.<\/li>\n- Finally, we will extract the characters left in our heap and print. <\/li>\n<\/ul>\n<\/blockquote>\n
extract()<\/strong>: Removes the minimum element from Min-Heap<\/strong>. Time Complexity of this Operation is O(Logn) as this operation needs to maintain the heap property (by calling heapify()<\/strong>) after removing root.<\/p>\nheapify()<\/strong>: Maintains the heap property for each node. If any node does not follow heap property it swaps the node with the node which is smaller, or greater (in case of max-heap<\/strong>), than the node.<\/p>\n\nBelow is the algorithm of above approach.<\/p>\n<\/blockquote>\n
Algorithms :<\/h3>\n
Insert()<\/strong> :<\/p>\n\n\n- Insert the item at the last index, and increment the size by 1.<\/li>\n
- Then, check if the inserted item is smaller than its parent,<\/li>\n
- If yes, then swap the inserted item with its parent.<\/li>\n
- If no, then do nothing.<\/li>\n
- Now, go to step
2<\/code> and repeat untill we reach root (first element).<\/li>\n<\/ol>\n<\/blockquote>\nExtract()<\/strong> :<\/p>\n\n\n- Store the value of the first node of our heap (
temp = heap[0]<\/code> ).<\/li>\n- Replace the root node with the farthest right node (last element).<\/li>\n
- Decrease the size by
1<\/code>. (heap[0] = heap[size-1])<\/code><\/li>\n- Perform heapify<\/strong> starting from the new root. <\/li>\n
- Return the stored value.(temp<\/strong>)<\/li>\n<\/ol>\n<\/blockquote>\n
Heapify ()<\/strong> :<\/p>\n\n\n- \n
if the heap property holds true then you are done.<\/p>\n<\/li>\n
- \n
else if<\/p>\n<\/li>\n
- \n
the replacement node value <= its parent nodes value
\nthen swap them, and repeat step 3.<\/p>\n<\/li>\n
- \n
else<\/p>\n<\/li>\n
- \n
swap the replacement node with the smallest child node, and
\nrepeat step 3.<\/p>\n<\/li>\n<\/ol>\n<\/blockquote>\n
Example:<\/h4>\n
![\"\"](\"https:\/\/prepbytes.com\/blog\/wp-content\/uploads\/2020\/06\/LXSM.png\")
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Solutions:<\/h3>\n\t\t\t\t\t\t
![\"\"](\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1645768140031-Article_487.png\")
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