Search a 2D Matrix

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Write an efficient algorithm to search for a target value in an m x n matrix where each row is sorted and 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],[23,30,34,60]], target=3 → Output: true
Example 2
Input: matrix=[[1,3,5,7],[10,11,16,20],[23,30,34,60]], target=13 → Output: false

Solution Approach

Treat the matrix as a flat sorted array of m*n elements. Binary search using virtual index mid, and convert to row/col using row=mid/n, col=mid%n.

  • lo=0, hi=m*n-1.
  • mid = (lo+hi)/2; row=mid/n, col=mid%n.
  • If matrix[row][col]==target return true.
  • If < target: lo=mid+1. If > target: hi=mid-1.
Java
class Solution {
    public boolean searchMatrix(int[][] matrix, int target) {
        int m = matrix.length, n = matrix[0].length;
        int lo = 0, hi = m * n - 1;
        while (lo <= hi) {
            int mid = lo + (hi - lo) / 2;
            int val = matrix[mid / n][mid % n];
            if (val == target) return true;
            else if (val < target) lo = mid + 1;
            else hi = mid - 1;
        }
        return false;
    }
}
  • Time Complexity: O(log(M*N))
  • Space Complexity: O(1)