ProgramGuru

DSA Visualizations /

Overview of TechniquesOverview of Techniques14
❯

  1. 1Overview of DSA Problem Solving Techniques
  2. 2Brute Force Technique in DSA
  3. 3Greedy Algorithm Technique in DSA
  4. 4Divide and Conquer Technique in DSA
  5. 5Dynamic Programming Technique in DSA
  6. 6Backtracking Technique in DSA
  7. 7Recursion Technique in DSA
  8. 8Sliding Window Technique in DSA
  9. 9Two Pointers Technique
  10. 10Binary Search Technique
  11. 11Tree / Graph Traversal Technique in DSA
  12. 12Bit Manipulation Technique in DSA
  13. 13Hashing Technique
  14. 14Heaps Technique in DSA

SortingSorting10
❯

  1. 1Bubble Sort
  2. 2Selection Sort
  3. 3Insertion Sort
  4. 4Merge Sort
  5. 5Quick Sort
  6. 6Heap Sort
  7. 7Radix Sort
  8. 8Counting Sort
  9. 9Bucket Sort
  10. 10Shell Sort

ArraysArrays32
❯

  1. 1Find Maximum and Minimum in Array using Loop
  2. 2Find Second Largest in Array
  3. 3Find Second Smallest in Array
  4. 4Reverse Array using Two Pointers
  5. 5Check if Array is Sorted
  6. 6Remove Duplicates from Sorted Array
  7. 7Left Rotate an Array by One Place
  8. 8Left Rotate an Array by K Places
  9. 9Move Zeroes in Array to End
  10. 10Linear Search in Array
  11. 11Union of Two Arrays
  12. 12Find Missing Number in Array
  13. 13Max Consecutive Ones in Array
  14. 14Find Kth Smallest Element
  15. 15Longest Subarray with Given Sum (Positives)
  16. 16Longest Subarray with Given Sum (Positives and Negatives)
  17. 17Find Majority Element in Array (more than n/2 times)
  18. 18Find Majority Element in Array (more than n/3 times)
  19. 19Maximum Subarray Sum using Kadane's Algorithm
  20. 20Print Subarray with Maximum Sum
  21. 21Stock Buy and Sell
  22. 22Rearrange Array Alternating Positive and Negative Elements
  23. 23Next Permutation of Array
  24. 24Leaders in an Array
  25. 25Longest Consecutive Sequence in Array
  26. 26Count Subarrays with Given Sum
  27. 27Sort an Array of 0s, 1s, and 2s
  28. 28Two Sum Problem
  29. 29Three Sum Problem
  30. 304 Sum Problem
  31. 31Find Length of Largest Subarray with 0 Sum
  32. 32Find Maximum Product Subarray

Arrays - Binary SearchArrays - Binary Search28
❯

  1. 1Binary Search in Array<br><span class="highlight">Using Iteration</span>
  2. 2Find Lower Bound in Sorted Array
  3. 3Find Upper Bound in Sorted Array
  4. 4Search Insert Position in Sorted Array (Lower Bound Approach)
  5. 5Floor and Ceil in Sorted Array
  6. 6First Occurrence in a Sorted Array
  7. 7Last Occurrence in a Sorted Array
  8. 8Count Occurrences in Sorted Array
  9. 9Search Element in a Rotated Sorted Array
  10. 10Search in Rotated Sorted Array with Duplicates
  11. 11Minimum in Rotated Sorted Array
  12. 12Find Rotation Count in Sorted Array
  13. 13Search Single Element in Sorted Array
  14. 14Find Peak Element in Array
  15. 15Square Root using Binary Search
  16. 16Nth Root of a Number using Binary Search
  17. 17Koko Eating Bananas
  18. 18Minimum Days to Make M Bouquets
  19. 19Find the Smallest Divisor Given a Threshold
  20. 20Capacity to Ship Packages within D Days
  21. 21Kth Missing Positive Number
  22. 22Aggressive Cows Problem
  23. 23Allocate Minimum Number of Pages
  24. 24Split Array - Minimize Largest Sum
  25. 25Painter's Partition Problem
  26. 26Minimize Maximum Distance Between Gas Stations
  27. 27Median of Two Sorted Arrays of Different Sizes
  28. 28K-th Element of Two Sorted Arrays

StringsStrings2
❯

  1. 1Remove Outermost Parentheses in String
  2. 2Edit Distance Problem

MatrixMatrix3
❯

  1. 1Set Matrix Zeroes
  2. 2Rotate Matrix by 90 Degrees Clockwise
  3. 3Print Matrix in Spiral Manner

Matrix - Binary SearchMatrix - Binary Search5
❯

  1. 1Row with Maximum Number of 1's
  2. 2Search in a Sorted 2D Matrix
  3. 3Search in Row and Column-wise Sorted Matrix
  4. 4Find Target in 2D Matrix
  5. 5Matrix Median

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

Binary Search TreesBinary Search Trees14
❯

  1. 1Find a Value in a Binary Search Tree
  2. 2Delete a Node in a Binary Search Tree
  3. 3Find the Minimum Value in a Binary Search Tree
  4. 4Find the Maximum Value in a Binary Search Tree
  5. 5Find the Inorder Successor in a Binary Search Tree
  6. 6Find the Inorder Predecessor in a Binary Search Tree
  7. 7Check if a Binary Tree is a Binary Search Tree
  8. 8Find the Lowest Common Ancestor of Two Nodes in a Binary Search Tree
  9. 9Convert a Binary Tree into a Binary Search Tree
  10. 10Balance a Binary Search Tree
  11. 11Merge Two Binary Search Trees
  12. 12Find the kth Largest Element in a Binary Search Tree
  13. 13Find the kth Smallest Element in a Binary Search Tree
  14. 14Flatten a Binary Search Tree into a Sorted List

Search Target in a 2D Sorted Matrix
Binary Search Approach

Topic Contents

ProblemExamplesSolutionCodeTime ComplexitySpace Complexity

Problem Statement

You are given a 2D matrix of size N × M where:

Your task is to determine whether a given target value exists in the matrix or not.

If the target is found, return true; otherwise, return false.

Examples❯

MatrixTargetResultDescription
[[1, 3, 5], [7, 9, 11], [13, 15, 17]]9true9 is present in the second row
[[1, 3, 5], [7, 9, 11], [13, 15, 17]]6false6 is not present anywhere in the matrix
[[5, 10, 15], [20, 25, 30]]5true5 is the first element
[[5, 10, 15], [20, 25, 30]]30true30 is the last element
[[5, 10, 15], [20, 25, 30]]35falseTarget is greater than all elements
[[5, 10, 15], [20, 25, 30]]1falseTarget is smaller than all elements
[[10]]10trueSingle element matrix, target matches
[[10]]5falseSingle element matrix, target does not match
[]10falseEmpty matrix, nothing to search

Solution❯

To search for a number in a special type of 2D matrix where each row is sorted and the first element of every row is greater than the last of the previous row, we can treat the matrix like a flattened sorted 1D array.

Imagine laying out all the rows into a single list and then applying binary search on that list. Since the matrix behaves like a sorted list, we can efficiently find whether the target exists using this approach.

Handling Different Cases

1. Normal Case: For a matrix like [[1, 3, 5], [7, 9, 11], [13, 15, 17]] and target = 9, we start our search from the middle element. If it’s not a match, we reduce our search space to the left or right half depending on comparison, just like binary search in arrays.

2. Edge Case (target is smallest or largest): If the target is the smallest number, it will be at the top-left corner. If it’s the largest, it will be at the bottom-right corner. Both are valid positions and must be included in the search.

3. Single Element Matrix: If the matrix has only one element, we directly compare it with the target. It’s the simplest base case.

4. Empty Matrix: If the matrix is empty (i.e., has no rows), there’s nothing to search, and we return false immediately.

Why Binary Search Works

Since the matrix is globally sorted (across rows and columns), binary search lets us eliminate half of the matrix in every step. By converting the single index into 2D coordinates row = mid / M and col = mid % M, we can access the matrix element in constant time.

This approach works in O(log(N × M)) time and is highly efficient even for large matrices.

Algorithm Steps

  1. Let start = 0, end = N * M - 1.
  2. While start ≤ end:
  3. → Compute mid = (start + end) / 2.
  4. → Convert mid to row = mid / M and col = mid % M.
  5. → Compare mat[row][col] with target.
  6. If equal, return true.
  7. If target < mat[row][col], move left (end = mid - 1).
  8. If target > mat[row][col], move right (start = mid + 1).
  9. If loop ends, return false (not found).

Code

Java
Python
JavaScript
C
C++
C#
Kotlin
Swift
Go
Php
public class MatrixSearch {
  public static boolean searchMatrix(int[][] mat, int target) {
    int rows = mat.length;
    int cols = mat[0].length;
    int start = 0;
    int end = rows * cols - 1;

    while (start <= end) {
      int mid = start + (end - start) / 2;
      int row = mid / cols;    // Map 1D index to 2D row
      int col = mid % cols;    // Map 1D index to 2D col

      if (mat[row][col] == target) {
        return true;
      } else if (mat[row][col] < target) {
        start = mid + 1;
      } else {
        end = mid - 1;
      }
    }
    return false;
  }

  public static void main(String[] args) {
    int[][] mat = {
      {1, 4, 7},
      {8, 11, 15},
      {17, 20, 23}
    };
    int target = 11;
    System.out.println("Found? " + searchMatrix(mat, target));
  }
}

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(1)When the target is found in the first mid calculation.
Average CaseO(log(N * M))The binary search reduces the search space by half in each iteration over the virtual flattened array.
Average CaseO(log(N * M))All elements are searched using binary search till the last comparison.

Space Complexity

O(1)

Explanation: No extra space is used; the algorithm uses a constant number of variables.

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