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Count of Smaller Numbers After Self [Hard] — Merge Sort
Count elements smaller than each element to its right using a modified merge sort that counts inversions during the merge step.
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Divide-conquer
12 articles
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Median of Two Sorted Arrays [Hard] — Binary Search on Partition
Find the median of two sorted arrays in O(log(min(m,n))) by binary searching for the correct partition point.
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Reverse Pairs [Hard] — Merge Sort with Cross-Half Counting
Count pairs (i,j) where i<j and nums[i]>2*nums[j] using modified merge sort to count cross-half pairs before merging.
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Kth Element of Two Sorted Arrays — Binary Search Elimination
Find the kth smallest element from two sorted arrays in O(log(m+n)) using binary elimination of k/2 elements per step.
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Sort List — Top-Down Merge Sort
Sort a linked list in O(n log n) time and O(log n) space using top-down merge sort with fast/slow split.
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Convert Sorted List to BST — Fast/Slow + Recursion
Convert a sorted linked list to a height-balanced BST by repeatedly finding the middle node as root.
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Merge K Sorted Lists — Min-Heap or Divide and Conquer
Merge k sorted linked lists into one sorted list using a min-heap for O(n log k) time complexity.
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Construct Binary Tree from Preorder and Inorder — HashMap Index
Build a binary tree from preorder and inorder traversals by using the preorder root and inorder index to split left/right subtrees.
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Construct Quad Tree
Build a quad tree from a 2D grid by recursively checking if a region is uniform and splitting into four quadrants.
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4Sum II [Medium] — Split and Hash
Count tuples (i,j,k,l) where nums1[i]+nums2[j]+nums3[k]+nums4[l]=0 by hashing all pairs from first two arrays.
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Google — Count Inversions (Modified Merge Sort)
Count the number of inversions in an array (pairs where i < j but arr[i] > arr[j]) using modified merge sort in O(n log n). Google uses this to test deep algorithm understanding.
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Amazon — Find Median of Two Sorted Arrays (Binary Search)
Find the median of two sorted arrays in O(log(min(m,n))) time using binary search on partition points. A classic hard problem testing deep binary search understanding.
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