74. Search a 2D Matrix

• Difficulty: Medium

• Topics: Array, Binary Search

• Similar Questions:

  • Search a 2D Matrix II

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

Solutions:

class Solution {
public:
    bool searchMatrix(vector<vector<int>>& matrix, int target) {
        int m = matrix.size();
        if (m == 0) return false;
        int n = matrix[0].size();
        if (n == 0) return false;

        int left = 0;
        int right = m * n - 1;

        while (left <= right) {
            int mid = left + (right - left) / 2;
            auto coord = arrayToMatrix(m, n, mid);
            int row = coord.first;
            int col = coord.second;
            if (matrix[row][col] == target) return true;
            if (matrix[row][col] > target) {
                right = mid - 1;
            } else {
                left = mid + 1;
            }
        }

        return false;
    }

    inline pair<int, int> arrayToMatrix(int m, int n, int index) {
        return {index/n, index%n};
    }

};