Binary TreesBinary Trees36

  1. 1Preorder Traversal of a Binary Tree using Recursion
  2. 2Preorder Traversal of a Binary Tree using Iteration
  3. 3Postorder Traversal of a Binary Tree Using Recursion
  4. 4Postorder Traversal of a Binary Tree using Iteration
  5. 5Level Order Traversal of a Binary Tree using Recursion
  6. 6Level Order Traversal of a Binary Tree using Iteration
  7. 7Reverse Level Order Traversal of a Binary Tree using Iteration
  8. 8Reverse Level Order Traversal of a Binary Tree using Recursion
  9. 9Find Height of a Binary Tree
  10. 10Find Diameter of a Binary Tree
  11. 11Find Mirror of a Binary Tree - Todo
  12. 12Inorder Traversal of a Binary Tree using Recursion
  13. 13Inorder Traversal of a Binary Tree using Iteration
  14. 14Left View of a Binary Tree
  15. 15Right View of a Binary Tree
  16. 16Top View of a Binary Tree
  17. 17Bottom View of a Binary Tree
  18. 18Zigzag Traversal of a Binary Tree
  19. 19Check if a Binary Tree is Balanced
  20. 20Diagonal Traversal of a Binary Tree
  21. 21Boundary Traversal of a Binary Tree
  22. 22Construct a Binary Tree from a String with Bracket Representation
  23. 23Convert a Binary Tree into a Doubly Linked List
  24. 24Convert a Binary Tree into a Sum Tree
  25. 25Find Minimum Swaps Required to Convert a Binary Tree into a BST
  26. 26Check if a Binary Tree is a Sum Tree
  27. 27Check if All Leaf Nodes are at the Same Level in a Binary Tree
  28. 28Lowest Common Ancestor (LCA) in a Binary Tree
  29. 29Solve the Tree Isomorphism Problem
  30. 30Check if a Binary Tree Contains Duplicate Subtrees of Size 2 or More
  31. 31Check if Two Binary Trees are Mirror Images
  32. 32Calculate the Sum of Nodes on the Longest Path from Root to Leaf in a Binary Tree
  33. 33Print All Paths in a Binary Tree with a Given Sum
  34. 34Find the Distance Between Two Nodes in a Binary Tree
  35. 35Find the kth Ancestor of a Node in a Binary Tree
  36. 36Find All Duplicate Subtrees in a Binary Tree

Find the Row with Maximum 1's in a Binary Matrix
Optimal Approach using Binary Search



Problem Statement

Given a binary matrix of size n x m, where each row is sorted (0s appear before 1s), your task is to find the index of the row that contains the maximum number of 1's.

Examples

MatrixOutputDescription
[[0, 0, 1, 1], [0, 1, 1, 1], [0, 0, 0, 1]]1Row 1 has 3 ones, more than any other row.
[[0, 0, 0], [0, 0, 1], [0, 1, 1]]2Row 2 has 2 ones, the highest among all.
[[0, 0, 0], [0, 0, 0], [0, 0, 0]]-1No row contains a 1.
[[1, 1, 1], [1, 1, 1], [1, 1, 1]]0All rows have 3 ones, return the first row index.
[]-1Matrix is empty, so no rows to check.
[[0, 1, 1], [0, 1, 1], [0, 1, 1]]0All rows have 2 ones, return index of the first.
[[0, 0, 1], [1, 1, 1], [0, 1, 1]]1Row 1 has 3 ones, which is the maximum.
[[0, 0], [0, 0], [1, 1]]2Only row 2 has ones.

Solution

To find the row with the maximum number of 1's in a sorted binary matrix, we can take advantage of the fact that each row is already sorted — meaning all the 0s appear before the 1s in each row.

The goal is to determine which row contains the most 1's, and if there’s a tie, return the first such row (i.e., the row with the smallest index).

Understanding Different Scenarios:

  • If a row has 0 ones (e.g., [0, 0, 0]), we simply move to the next row.
  • If a row has all ones (e.g., [1, 1, 1]), then this row has the maximum possible count of 1's — we can even stop searching further because no row can have more.
  • If multiple rows have the same number of 1’s, we return the index of the first row that achieves that maximum.
  • If no rows have 1's at all, we return -1 because there’s no valid answer.
  • If the matrix is empty (i.e., has no rows), we also return -1.

How Binary Search Helps

Since each row is sorted, we don’t have to scan the entire row to count the number of 1’s. Instead, we can use binary search to quickly find the first occurrence of 1 in each row. Once we know the position of the first 1, we can calculate how many 1’s are present in that row (which is simply m - index_of_first_1).

By applying this to each row and keeping track of the row that gives the highest count, we can find the answer efficiently. At the end, we return the row index with the maximum 1's.

This method works well even for large matrices because binary search keeps the time complexity low (around O(n log m) where n is the number of rows and m is the number of columns).

Algorithm Steps

  1. Initialize maxOnesRow = -1 and maxOnes = 0.
  2. For each row, do binary search to find the index of first 1.
  3. If number of 1s in the row = m - index_of_first_1 is more than maxOnes, update both maxOnes and maxOnesRow.
  4. After checking all rows, return maxOnesRow.

Code

Java
Python
JavaScript
C
C++
C#
Kotlin
Swift
Go
Php
public class MaxOnesRowFinder {
  public static int rowWithMaxOnes(int[][] matrix) {
    int n = matrix.length, m = matrix[0].length;
    int maxOnesRow = -1;
    int maxOnes = 0;

    for (int i = 0; i < n; i++) {
      int firstOneIndex = findFirstOne(matrix[i], m);
      if (firstOneIndex != -1) {
        int onesCount = m - firstOneIndex;
        if (onesCount > maxOnes) {
          maxOnes = onesCount;
          maxOnesRow = i;
        }
      }
    }
    return maxOnes == 0 ? -1 : maxOnesRow;
  }

  private static int findFirstOne(int[] row, int m) {
    int low = 0, high = m - 1, index = -1;
    while (low <= high) {
      int mid = low + (high - low) / 2;
      if (row[mid] == 1) {
        index = mid;
        high = mid - 1; // Look for earlier 1
      } else {
        low = mid + 1;
      }
    }
    return index;
  }

  public static void main(String[] args) {
    int[][] matrix = {
      {0, 0, 1, 1},
      {0, 1, 1, 1},
      {0, 0, 0, 1}
    };
    System.out.println("Row with max 1's: " + rowWithMaxOnes(matrix));
  }
}

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(n)If all 1s are at the beginning of each row, the binary search terminates quickly for each.
Average CaseO(n log m)Binary search is applied to each of the n rows, with log m steps per row.
Average CaseO(n log m)Each row takes log m time to search in worst-case when 1s are at the end.

Space Complexity

O(1)

Explanation: No extra space used other than a few variables.



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