SPOJ: MKTHNUM – K-th Number

Problem Link: https://www.spoj.com/problems/MKTHNUM/

Solution Idea: (Merge Sort Tree)

  • At first take input and store the input in a pair array where first element of ith pair is the value ai and second element of ith pair is i.
  • Sort the pair array with with ascending order of ai
  • Build a merge sort tree using the second element of each pair of sorted pair array.
  • Now for each query i,j,k at first check how many number in range i to j inclusive are present in left subtree of current node in merge sort tree. Let the value is x. So if x<=k then it's sure that the answer is in the left subtree. So we will go to left subtree of current node with k. Otherwise we will go to right subtree of current node with k-x;
  • In this manner when we reach to a leaf node we can say that this node contains the index of our answer.


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