74. Search a 2D Matrix

Problem:

Write an efficient algorithm that searches for a value in an m x n matrix. This matrix has the following properties:

• Integers in each row are sorted from left to right.
• The first integer of each row is greater than the last integer of the previous row.

Example 1:

Input:
matrix = [
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]
target = 3
Output: true

Example 2:

Input:
matrix = [
  [1,   3,  5,  7],
  [10, 11, 16, 20],
  [23, 30, 34, 50]
]
target = 13
Output: false

Solution:

ONE

Search from top-left to bottom-right. O(n).

/**
 * @param {number[][]} matrix
 * @param {number} target
 * @return {boolean}
 */
var searchMatrix = function(matrix, target) {
  const height = matrix.length
  if (height <= 0) { return false }
  const width = matrix[0].length
  if (width <= 0) { return false }

  let i = 0
  let j = width - 1
  while (i < height && j >= 0) {
    const diff = matrix[i][j] - target
    if (diff > 0) {
      j--
    } else if (diff < 0) {
      i++
    } else {
      return true
    }
  }

  return false
};

TWO

Binary search. O(logn).

View the matrix as an sorted array that is cut into n slices.

Take the algorithm from 35. Search Insert Position.

/**
 * @param {number[][]} matrix
 * @param {number} target
 * @return {boolean}
 */
var searchMatrix = function(matrix, target) {
  const height = matrix.length
  if (height <= 0) { return false }
  const width = matrix[0].length
  if (width <= 0) { return false }

  let s = 0
  let e = width * height - 1
  while (s <= e) {
    const mid = Math.floor((s + e) / 2)
    const diff = matrix[Math.floor(mid / width)][mid % width] - target
    if (diff < 0) {
      s = mid + 1
    } else if (diff > 0) {
      e = mid - 1
    } else {
      return true
    }
  }

  return false
};