Kth Smallest Element in a Sorted Matrix

Description

Given a n x n matrix where each of the rows and columns are sorted in ascending order, find the kth smallest element in the matrix.

Note that it is the kth smallest element in the sorted order, not the kth distinct element.

Example:

matrix = [
   [ 1,  5,  9],
   [10, 11, 13],
   [12, 13, 15]
],
k = 8,
return 13.

Note:
You may assume k is always valid, 1 ≤ k ≤ n².

Solution(javascript)

const swap = (a, b, arr) => { // eslint-disable-line
  if (a !== b) {
    const temp = arr[a]
    arr[a] = arr[b] // eslint-disable-line
    arr[b] = temp // eslint-disable-line
  }
}

const Heap = compareFn => (arr = []) => {
  const left = index => 2 * index + 1
  const right = index => 2 * index + 2
  const parent = index => Math.floor((index - 1) / 2)
  const size = () => arr.length

  // log(n)
  const heapify = (index) => {
    const l = left(index)
    const r = right(index)
    let current = index
    if ((l < size()) && compareFn(arr[current], arr[l]) > 0) {
      current = l
    }
    if ((r < size()) && compareFn(arr[current], arr[r]) > 0) {
      current = r
    }
    if (current !== index) {
      swap(current, index, arr)
      heapify(current)
    }
  }
  // log(n)
  const heapifyUp = (index) => {
    const p = parent(index)
    if (p >= 0 && compareFn(arr[p], arr[index]) > 0) {
      swap(p, index, arr)
      heapifyUp(p)
    }
  }
  // O(n)
  const buildHeap = () => {
    for (let i = Math.floor(arr.length / 2); i >= 0; i--) {
      heapify(i)
    }
  }
  const extract = () => {
    swap(0, arr.length - 1, arr)
    const top = arr.pop()
    heapify(0)
    return top
  }
  const remove = (item) => {
    const index = arr.findIndex(x => compareFn(x, item) === 0)
    if (index === -1) {
      return
    }
    arr[index] = arr.pop() // eslint-disable-line
    const p = parent(index)
    if (p < 0 || compareFn(p, arr[index]) < 0) {
      heapify(index)
    } else {
      heapifyUp(index)
    }
  }
  buildHeap()
  return {
    getHeap: () => arr,
    peek: () => {
      if (arr.length === 0) {
        return null
      }
      return arr[0]
    },
    add: (item) => {
      arr.push(item)
      heapifyUp(arr.length - 1)
    },
    extract,
    remove,
    size,
  }
}

/**
 * @param {number[][]} matrix
 * @param {number} k
 * @return {number}
 */
const kthSmallest = function (matrix = [], k) {
  const minHeap = Heap((a, b) => a.val - b.val)(
    matrix.map((arr, rowIndex) => ({
      val: arr[0],
      rowIndex,
      columnIndex: 0,
    })),
  )
  for (let i = 1; i < k; i++) {
    const { rowIndex, columnIndex } = minHeap.extract()
    if (matrix[rowIndex][columnIndex + 1] !== undefined) {
      minHeap.add({
        val: matrix[rowIndex][columnIndex + 1],
        rowIndex,
        columnIndex: columnIndex + 1,
      })
    }
  }
  return minHeap.extract().val
}