Sponsored
Sponsored
This approach uses a Binary Indexed Tree (BIT) data structure to efficiently count the number of elements less than and greater than the current element during the insertion process.
We maintain a BIT to store the frequency of each element from the instructions array. For each element, we calculate the cost as the minimum of the count of elements that are less than it and the count of elements that are greater than it that have been inserted so far. We use BIT to efficiently calculate prefix sums, which helps in calculating these counts.
Time Complexity: O(n log n), where n is the number of instructions. The operations of update and query on the BIT are O(log n).
Space Complexity: O(n), to store the BIT.
1import java.util.*;
2
3public class CreateSortedArray {
4 private static final int MAX = 100001;
5
Java implementation uses a static BIT array and applies similar techniques as C/C++ implementations. Methods including update and query provide the mechanism for maintaining the frequency of elements and calculating the insertion costs.
This approach employs a Segment Tree to perform range query operations to efficiently count the number of elements less than and greater than the current element during insertion. The Segment Tree helps maintain the frequency of elements within a range and can provide range sum in logarithmic time, allowing for quick calculations of the insertion cost.
Time Complexity: O(n log n), where n is the number of instructions. The Segment Tree operations take O(log n).
Space Complexity: O(n), to store the Segment Tree.
The C implementation uses a Segment Tree to efficiently count elements in a range for insertion cost calculation. The update function alters the Segment Tree to reflect changes in element frequency, while query retrieves summations of elements over a range.