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Search a 2D Matrix

Medium
Binary Search

You are given an m x n integer matrix with the following two properties:

  • Each row is sorted in non-decreasing order.
  • The first integer of each row is greater than the last integer of the previous row.

Given an integer target, return true if target is in matrix or false otherwise.

You must write a solution in O(log(m * n)) time complexity.

Example 1

Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 3
Output: true
Explanation: 3 is found in the first row.

Example 2

Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 13
Output: false
Explanation: 13 is not in the matrix.

Constraints

  • •m == matrix.length
  • •n == matrix[i].length
  • •1 <= m, n <= 100
  • •-10^4 <= matrix[i][j], target <= 10^4
Show Hints (3)
Hint 1: The matrix can be treated as a sorted 1D array of length m * n.
Hint 2: Map a 1D index to 2D coordinates: row = index / n, col = index % n.
Hint 3: Alternatively, first binary search to find the row, then binary search within that row.
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