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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 using Iteration
  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

StringsStrings18
❯

  1. 1Reverse Words in a String
  2. 2Find the Largest Odd Number in a Numeric String
  3. 3Find Longest Common Prefix in Array of Strings
  4. 4Check If Two Strings Are Isomorphic - Optimal HashMap Solution
  5. 5Check String Rotation using Concatenation - Optimal Approach
  6. 6Check if Two Strings Are Anagrams - Optimal Approach
  7. 7Sort Characters by Frequency - Optimal HashMap and Heap Approach
  8. 8Find Longest Palindromic Substring - Dynamic Programming Approach
  9. 9Find Longest Palindromic Substring Without Dynamic Programming
  10. 10Remove Outermost Parentheses in String
  11. 11Find Maximum Nesting Depth of Parentheses - Optimal Stack-Free Solution
  12. 12Convert Roman Numerals to Integer - Efficient Approach
  13. 13Convert Integer to Roman Numeral - Step-by-Step for Beginners
  14. 14Implement Atoi - Convert String to Integer in Java
  15. 15Count Number of Substrings in a String - Explanation with Formula
  16. 16Edit Distance Problem
  17. 17Calculate Sum of Beauty of All Substrings - Optimal Approach
  18. 18Reverse Each Word in a String - Optimal Approach

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

Count Subarrays with Given Sum using Prefix Sum and HashMap
Optimal Solution

Topic Contents

ProblemExamplesSolutionVisualizationAlgorithmCodeTimeSpace

Problem Statement

Given an integer array arr and a target sum k, your task is to find the total number of continuous subarrays whose elements add up to exactly k.

A subarray is a sequence of elements that appears in the same order in the array and is contiguous. The same element can be included in multiple subarrays if it appears in different positions.

This problem is common in applications involving range-based queries, financial analysis, and interval sum counting.

Examples❯

Input ArrayTarget Sum (k)Count of SubarraysDescription
[1, 2, 3]32Subarrays: [1, 2], [3]
[1, 1, 1]22Subarrays: [1, 1] (at two different positions)
[3, 4, 7, 2, -3, 1, 4, 2]74Subarrays: [3,4], [7], [4, 2, 1], [1, 4, 2]
[1, -1, 0]03Subarrays: [1, -1], [0], [1, -1, 0]
[]00Empty array has no subarrays
[0, 0, 0]06All possible subarrays (of lengths 1 to 3) sum to 0
[1, 2, 3]100No subarray adds up to 10
[5]51Single element equal to k
[5]30Single element not equal to k

Solution❯

To count how many subarrays sum to a given number k, we can use a clever technique based on prefix sums and a hash map to store frequency of those sums. This approach avoids nested loops and gives us a highly efficient solution with linear time complexity.

Understanding the Core Idea

Imagine you're scanning the array from left to right and keeping track of the sum of all elements you've seen so far. This is called the prefix sum. At any position i, the sum of the subarray from some previous position j to i is simply prefix[i] - prefix[j-1].

Now, if you know that prefix[i] - k has been seen before, that means there exists a subarray that ends at position i and adds up to k.

Different Cases to Consider

  • Exact match: If the current prefix sum is equal to k, it means the subarray starting from index 0 to current index forms a valid subarray.
  • Matching a previous prefix: If you've previously seen a prefix sum of curr_sum - k, it means all subarrays that end at the current index and start after those earlier indices add up to k. You can count how many times that prefix occurred and add that to your answer.
  • Negative numbers and zeroes: The method works even if the array has negative numbers or zeros. For example, in an array like [1, -1, 0] with k = 0, multiple combinations are valid.
  • Empty array: There are no subarrays to count, so the result is 0.
  • All zeros: In arrays like [0, 0, 0], every subarray (length 1 to full length) adds up to 0. This results in multiple overlapping subarrays that all qualify.

Why This Works

By storing how often each prefix sum has appeared, we avoid re-checking every possible subarray. We can just look up how many times we've seen prefix_sum - k in constant time using a hash map. This optimization turns a brute-force O(n²) approach into a fast O(n) solution.

This method is highly effective, scalable, and works for large arrays with positive, negative, or zero values.

Visualization

Algorithm Steps

  1. Given an array arr and a target k.
  2. Initialize a prefix sum curr_sum = 0 and a hash map prefix_count to store frequency of prefix sums.
  3. Initialize count = 0.
  4. Iterate through the array:
  5. → Add current element to curr_sum.
  6. → If curr_sum == k, increment count by 1.
  7. → If curr_sum - k exists in prefix_count, add its frequency to count.
  8. → Update the frequency of curr_sum in prefix_count.
  9. Return the total count.

Code

Python
JavaScript
Java
C++
C
from collections import defaultdict

def count_subarrays_with_sum(arr, k):
    prefix_count = defaultdict(int)
    curr_sum = 0
    count = 0

    for num in arr:
        curr_sum += num
        if curr_sum == k:
            count += 1
        if (curr_sum - k) in prefix_count:
            count += prefix_count[curr_sum - k]
        prefix_count[curr_sum] += 1

    return count

# Sample Input
arr = [1, 1, 1]
k = 2
print("Count of Subarrays:", count_subarrays_with_sum(arr, k))

Time Complexity

CaseTime ComplexityExplanation
Best CaseO(n)Each element is visited exactly once, and all operations (hashmap lookups and updates) take constant time.
Average CaseO(n)On average, the algorithm maintains a prefix sum hashmap and performs constant-time operations per element.
Average CaseO(n)Even in the worst case, the array is traversed only once and hashmap operations remain O(1), resulting in linear time complexity.

Space Complexity

O(n)

Explanation: A hashmap is used to store the frequency of prefix sums, which can grow up to the size of the input array in the worst case.

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