Search a 2D Matrix LeetCode

 You are given an m x n integer matrix 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

Example 2:



Input: matrix = [[1,3,5,7],[10,11,16,20],[23,30,34,60]], target = 13

Output: false


Brute Force :

class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
           int rows = matrix.length;
        int cols = matrix[0].length;

        for (int i = 0; i < rows; i++) {
            for (int j = 0; j < cols; j++) {
                if (matrix[i][j] == target) {
                    return true;
                }
            }
        }
        return false;
    }
}



Optimal Approach:-

class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        int rows = matrix.length;
        int cols = matrix[0].length;
        int left = 0, right = rows * cols - 1;

        while (left <= right) {
            int mid = left + (right - left) / 2;
            int row_index=mid / cols;// Mapping 1D index to 2D -get row index
            int col_index=mid % cols;//// Mapping 1D index to 2D -get col index
            int midValue = matrix[row_index][col_index];

            if (midValue == target) {
                return true;
            } else if (midValue < target) {
                left = mid + 1;
            } else {
                right = mid - 1;
            }
        }
        return false;
    }
}




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