Number Stream Median

hardcodingAlgorithmsData Structures

Overview

Design a data structure that supports adding integers from a data stream and finding the median of all elements seen so far.

Implement the MedianFinder class:

  • addNum(num) — adds the integer num to the data structure.
  • findMedian() — returns the median of all elements added so far. If the count is even, return the average of the two middle values.

Your solution will be tested by processing a list of operations.

Implement processMedianOps(operations) where each operation is ["addNum", num] or ["findMedian"], and return an array of results (null for addNum, the median for findMedian).

Constraints

  • -100000 ≤ num ≤ 100000
  • There will be at least one addNum before any findMedian.
  • findMedian must run in $O(1)$ time.
  • addNum should run in $O(\log n)$ time.

Examples

processMedianOps([
  ["addNum", 1],
  ["addNum", 2],
  ["findMedian"],    // → 1.5
  ["addNum", 3],
  ["findMedian"],    // → 2
]);
// → [null, null, 1.5, null, 2]

Notes

  • The classic approach uses two heaps: a max-heap for the lower half and a min-heap for the upper half.
  • JavaScript has no built-in heap — you'll need to implement one or use sorted insertion.
  • Balance the heaps so their sizes differ by at most 1. The median is either the top of the larger heap or the average of both tops.

Solution

Reveal solution
function processMedianOps(operations) {
  // Simple sorted-array approach (O(n) insert, O(1) median)
  const sorted = [];
  const results = [];

  function insert(arr, val) {
    let lo = 0, hi = arr.length;
    while (lo < hi) {
      const mid = (lo + hi) >> 1;
      if (arr[mid] < val) lo = mid + 1;
      else hi = mid;
    }
    arr.splice(lo, 0, val);
  }

  for (const op of operations) {
    if (op[0] === "addNum") {
      insert(sorted, op[1]);
      results.push(null);
    } else {
      const n = sorted.length;
      if (n % 2 === 1) {
        results.push(sorted[Math.floor(n / 2)]);
      } else {
        results.push((sorted[n / 2 - 1] + sorted[n / 2]) / 2);
      }
    }
  }

  return results;
}

Resources

NameTopicDifficulty
Add BinaryAlgorithmseasyBalanced Binary TreeAlgorithmseasyBalanced BracketsAlgorithmseasyBinary SearchAlgorithmseasyBinary Search Tree Lowest Common AncestorAlgorithmseasyBinary Tree Maximum DepthAlgorithmseasyBinary Tree SubtreeAlgorithmseasyBit CountingAlgorithmseasyBit ReversalAlgorithmseasyCount Set Bits in a Binary NumberAlgorithmseasyDiameter of Binary TreeAlgorithmseasyFind Duplicates in ArrayAlgorithmseasyFirst Bad VersionAlgorithmseasyFlip Binary TreeAlgorithmseasyFlood FillAlgorithmseasyLinked List Detect CycleAlgorithmseasyLinked List ReversalAlgorithmseasyLinked Lists Combine Two SortedAlgorithmseasyLongest PalindromeAlgorithmseasyMiddle of the Linked ListAlgorithmseasyMost Common ElementsAlgorithmseasyOptimal Stock TradingAlgorithmseasyPair SumAlgorithmseasyRansom NoteAlgorithmseasyStaircase Climbing CombinationsAlgorithmseasyString AnagramAlgorithmseasyString PalindromeAlgorithmseasy01 MatrixAlgorithmsmediumAccounts MergeAlgorithmsmediumArray Product Excluding CurrentAlgorithmsmediumBinary Search Tree Kth Smallest ElementAlgorithmsmediumBinary Tree Level Order TraversalAlgorithmsmediumBinary Tree Rebuilding from Preorder and Inorder TraversalsAlgorithmsmediumBinary Tree Right Side ViewAlgorithmsmediumCombinations for Target SumAlgorithmsmediumCount Islands in a GridAlgorithmsmediumCourse DependencyAlgorithmsmediumDecode MessageAlgorithmsmediumDisjoint IntervalsAlgorithmsmediumDistinct Paths in GridAlgorithmsmediumEvaluate Reverse Polish NotationAlgorithmsmediumFind All Anagrams in a StringAlgorithmsmediumFind Element in Rotated ArrayAlgorithmsmediumFind the Longest Palindromic SubstringAlgorithmsmediumFind Word in GridAlgorithmsmediumGraph CloneAlgorithmsmediumGraph Count Connected ComponentsAlgorithmsmediumIs the Graph a TreeAlgorithmsmediumK Closest Points to OriginAlgorithmsmediumLetter Combinations of a Phone NumberAlgorithmsmediumLongest Increasing SubsequenceAlgorithmsmediumLongest Non-repeating SubstringAlgorithmsmediumLongest Repeating Substring After ReplacementsAlgorithmsmediumLowest Common Ancestor of a Binary TreeAlgorithmsmediumMatrix RotationAlgorithmsmediumMatrix Spiral TraversalAlgorithmsmediumMatrix ZeroingAlgorithmsmediumMaximum Sum in Contiguous ArrayAlgorithmsmediumMaximum Water Trapped Between WallsAlgorithmsmediumMerge New IntervalAlgorithmsmediumMerge Overlapping IntervalsAlgorithmsmediumMinimum Coins for ChangeAlgorithmsmediumMinimum Height TreesAlgorithmsmediumPalindromic SubstringsAlgorithmsmediumPartition Equal Subset SumAlgorithmsmediumPermutationsAlgorithmsmediumRotting OrangesAlgorithmsmediumSegment WordsAlgorithmsmediumSort ColorsAlgorithmsmediumString Anagram GroupsAlgorithmsmediumString to Integer (atoi)AlgorithmsmediumSubsetsAlgorithmsmediumSum Without AdditionAlgorithmsmediumTask CoordinationAlgorithmsmediumTrie (Prefix Tree)AlgorithmsmediumTriplet SumAlgorithmsmediumValidate Binary Search TreeAlgorithmsmediumBasic CalculatorAlgorithmshardBinary Tree EqualAlgorithmshardBinary Tree Maximum Total PathAlgorithmshardDelete Nth Node from End of Linked ListAlgorithmshardEnd of Array ReachableAlgorithmshardExtraterrestrial LanguageAlgorithmshardFind Missing Number in SequenceAlgorithmshardFind Words in GridAlgorithmshardLargest Rectangle in HistogramAlgorithmshardLinked Lists Combine K SortedAlgorithmshardLongest Common SubsequenceAlgorithmshardLongest Consecutive Number SequenceAlgorithmshardMaximum Product in Contiguous ArrayAlgorithmshardMaximum Profit in Job SchedulingAlgorithmshardMeeting CalendarAlgorithmshardMinimum Meeting Rooms NeededAlgorithmshardNeighborhood TheftAlgorithmshardNeighborhood Theft (Circular)AlgorithmshardNumber Stream MedianAlgorithmshardOcean FlowAlgorithmshardRearrange Linked ListAlgorithmshardShortest Substring Containing CharactersAlgorithmshardSmallest Element in Rotated Sorted ArrayAlgorithmshardTrapping Rain WaterAlgorithmshardWord FinderAlgorithmshardWord LadderAlgorithmshard
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