Object Oriented Programming:

• Classes and Objects

• Inheritance and Polymorphism : Overloading and Overriding

• Abstraction and Encapsulation

• Access Modifiers

• Friend and Virtual functions in C++

• static, final, this and super keywords and Interfaces in Java

• Analysis of Algorithms:

  • Growth of functions

  • Asymptotic Notations Omega, Theta,

  • Recursion Tree Method

  • Space Complexity

• • String:

    • Introduction to Strings

  • Searching:

    • Linear Search

    • Binary Search (Iterative and Recursive)

  • Sorting:

    • Stability in Sorting Algorithm

    • Bubble Sort

    • Selection Sort

    • Insertion Sort

    • Quick Sort

    • Different Partition Schemes in QuickSort

    • Merge Sort

    • Lomuto Partition

    • Hoare Partition

    • Heap SOort

    • Counting Sort

    • Radix Sort

    • Bucket Sort

  • Linked List:

    • Drawback of Arrays

    • Introduction to Linked List and Implementation

    • Traversal, Insertion and Deletion

    • Sorted Insertion in Linked List

    • Reversal of Linked List (Iterative and Recursive)

    • Finding Middle

    • Remove Duplicate from Sorted Linked List

  • Circular Linked List:

    • Traversal

    • Insertion (Head, End)

    • Deletion (Head, Kth Node)

  • Doubly Linked List:

    • Traversal

    • Insertion (Head, End)

    • Deletion (Head, End)

    • Reversal

    • Circular Doubly Linked List

  • Stack:

    • Introduction to Stack Data Structure

    • Implement using array

    • Implementation using Linked List

    • Stack Applications

  • Queue:

    • Introduction to Queue Data Structure

    • Implementation using array

    • Implementation using Linked List.

  • Dequeue:

    • Introduction to Deque Data Structure.

    • Implementations using Array

    • Implementation using Linked List

  • Tree:

    • Implementation

    • Traversals: preorder, postorder, inorder, level order(Iterative & Recursive)

    • Binary Tree: Height, Size, Maximum

    • Print Nodes at K Distance

  • BST:

    • Implementation

    • Search

    • Insertion

    • Deletion

    • Floor and Ceil in BST  in CPP and Java

    • Self Balancing BST

    • AVL Tree (Introduction and applications)

    • Red-Black Tree (Introduction and applications)

    • Applications of BST

  • Heap:

    • Implementation

    • Insert

    • Heapify and Extract in Heap

    • Decrease Key, Delete and Build Heap

  • Arrays:

    • Insertion, Deletion, Updation, Shifting

    • Reversal, Sort Check, Maximum, Minimum

  • Recursion

    • Introduction to Recursion

    • Tail Recursion

    • Natural Number Check Using Recursion

    • Palindrome Check Using Recursion

    • Sum of Digits, Rod Cutting and Subsets

    • Tower of Hanoi

  • Hashing:

    • Introduction to Hashing

    • Direct Address Table

    • Collision Handling

    • Chaining

    • Open Addressing

    • Double Hashing

    • Chaining Vs Open Addressing

• C++ STL

  • Introduction to STL

    • Introduction and Application

    • Iterators

    • Templates

    • Function Templates

    • Class Templates

  • Pairs in CPP STL

    • Introduction

    • Problem(With Video Solutions): Sorting an array according to another array

    • Practice Problems

      • This track contains many practice problems for the users which are considered important and must-do as far as Data Structure and Algorithm is concerned.

  • Vectors in CPP STL

    • Introduction

    • Vector Declaration

    • More functions of Vectors 

    • Time Complexities of different operations and passing Vectors to function 

    • Internal Working of Vectors

    • Problems(With Video Solutions):

      • Vector and Vector of Pairs

      • Keeping track of previous indexes after sorting a Vector 

  • Forward_list and list

    • Forward List in C++ STL 

    • List in C++ STL 

    • Problems(With Video Solutions):

      • Josephus Problem using List in STL 

      • Design a Data Structure with Insert/Replace/Print operations 

    • Practice Problems

      • This track contains many practice problems for the users which are considered important and must-do as far as Data Structure and Algorithm is concerned.

  • Deque

    • Introduction

    • Problems(With Video Solutions):

      • Sliding Window Maximum

      • Design a Data Structure with Min/Max operations in O(1) time

    • Practice Problems

      • This track contains many practice problems for the users which are considered important and must-do as far as Data Structure and Algorithm is concerned.

  • Stack

    • Introduction and Various Operations

      • push()

      • pop()

      • top()

      • size()

      • empty()

    • Problems(With Video Solutions):

      • Reverse items using Stack 

      • Balanced Parenthesis 

      • Stock Span Problem

      • Previous Greater Elements

      • Next Greater Elements

    • Practice Problems

      • This track contains many practice problems for the users which are considered important and must-do as far as Data Structure and Algorithm is concerned.

  • Queue

    • Introduction and Various Operations

      • push()

      • pop()

      • front()

      • back()

      • empty()

      • size()

    • Problems(With Video Solutions):

      • Reverse first K items in a Queue

    • Practice Problems

      • This track contains many practice problems for the users which are considered important and must-do as far as Data Structure and Algorithm is concerned.

  • Priority Queue

    • Introduction and Various Operations

      • push()

      • pop()

      • top()

      • empty()

      • size()

      • Creating Min Heap based Priority Queue

    • Problems(With Video Solutions):

      • Sort an array using Priority Queue

      • K Largest Elements in an array

      • Buy maximum items with given money

      • Find K most frequent elements

    • Practice Problems

      • This track contains many practice problems for the users which are considered important and must-do as far as Data Structure and Algorithm is concerned.

  • Set & MultiSet

    • Set in C++ STL

      • Introduction and Implementation

      • insert()

      • begin()

      • end()

      • rbegin()

      • rend()

      • erase()

      • clear()

      • find()

      • Internal Working

      • Time Complexities

    • Problems on Set(With Video Solutions):

      • Design a Data Structure that supports the below operations:

      • insert()

      • delete()

      • search()

      • getFloor()

      • getCeiling()

    • Multiset in C++ STL with few operations

    • Practice Problems

      • This track contains many practice problems for the users which are considered important and must-do as far as Data Structure and Algorithm is concerned.

  • Map and MultiMap

    • Introduction to Map

      • insert()

      • operator()

      • size()

      • empty()

      • clear()

      • begin()

      • end()

      • Internal Working

      • Time Complexities

    • Problem:

      • Design a data structure for item prices. The operations are add(), find(), findGreater(), findSmaller() and printSorted()

      • Count greater elements for every array element.

    • Multimap in C++ STL with few functional operations

    • Problem(With Video Solutions):

      • Design a data structure for prices with duplicates allowed. The operations are add(), find(), findGreater(), findSmaller() and printSorted

    • Practice Problems

      • This track contains many practice problems for the users which are considered important and must-do as far as Data Structure and Algorithm is concerned.

  • Unordered_set

    • Introduction to Set

      • insert()

      • begin()

      • size()

      • end()

      • clear()

      • find()

      • Internal Working

      • Time Complexities

    • Problems(With Video Solutions):

      • Print Unique Elements of Array 

      • Print duplicate elements of the array 

    • Practice Problems

      • This track contains many practice problems for the users which are considered important and must-do as far as Data Structure and Algorithm is concerned.

  • Unordered_Map

    • Introduction

    • Problems(With Video Solutions):

      • Design a DS for storing user balance 

      • Find Winner of Election 

    • Practice Problems

      • This track contains many practice problems for the users which are considered important and must-do as far as Data Structure and Algorithm is concerned.

  • Non Mutating STL Algorithms

    • Explanation along with Time Complexities of

      • max_element()

      • min_element()

      • accumulate()

      • count()

      • find()

      • binary_search()

      • lower_bound()

      • upper_bound()

      • rotate()

      • fill()

      • is_permutation()

      • rand()

    • Practice Problems

      • This track contains many practice problems for the users which are considered important and must-do as far as Data Structure and Algorithm is concerned.

  • Mutating STL Algorithm

    • Explanation along with Time Complexities of

      • sort()

      • reverse()

      • next_permutation()

      • prev_permutation()

      • make_heap()

      • merge()

    • Problems(With Video Solutions):

      • The Thief problem 

      • Fractional knapsack problem 

      • Chocolate Distribution problem 

      • Sort array elements by frequency 

    • Practice Problems

      • This track contains many practice problems for the users which are considered important and must-do as far as Data Structure and Algorithm is concerned.

• Java Collections

  • Collection Overview

    • Introduction to Java Collections Framework

    • Collections hierarchy

    • Generics

    • Wildcards

    • toArray() Methods

    • Collections Interface

    • Iterators

    • Collections Bulk operations

    • Iterating through Collections

  • Java Lambda Expressions

    • Introduction to Lambda Expressions and ways to use them

    • Introduction to Method References and examples

    • Syntax of Lambda Expressions

    • Practice Problems

      • Practice problems on Lambda Expressions

  • Java Streams

    • Introduction to Streams in Java

    • Various Applications of Streams

    • The Stream hierarchy and methods

    • Examples on Streams

    • Practice Problems

      • Practice problems on Streams

  • ArrayList

    • Introduction to List Interface

    • Using List Iterator

    • Introduction to ArrayLists

    • Implementation

    • ArrayList Methods

    • Traversal

    • Problems with video explanation

      • List of smaller elements

    • Practice Problems

      • Practice problems on implementation, iterator, methods, and using ArrayList to solve dsa problems

  • Linked List

    • Introduction and implementation of LinkedList in Java

    • Problems with video explanation

      • Josephus Problem using LinkedList

      • Design a DS for remove and print

    • Practice Problems

      • Practice problems on implementation, traversal, and use of LinkedList,

  • Stack

    • Introduction to Stack

    • Implementation

    • Methods

    • Traversal

    • Problems with video explanation

      • Reverse order of items

      • Check for balanced parentheses

      • Stock span

      • Previous greater element

      • Next greater element

    • Practice Problems

      • Practice problems on implementation, methods, and using Stacks to solve dsa problems

  • Queue

    • Introduction to Queue Interface

    • Implementation and usage

    • Methods

    • Traversal

    • Problems with video explanation

      • Reverse first k items

    • Practice Problems

      • Practice problems on implementation, methods, and using Queue to solve dsa problems

  • Deque

    • Introduction to Deque

    • Implementation and usage

    • ArrayDeque

    • Methods

    • Traversal

    • Practice Problems

      • Practice problems on implementation, methods, and using ArrayDeque to solve dsa problems

  • PriorityQueue

    • Introduction to PriorityQueue

    • Implementation and usage

    • Methods

    • Traversal

    • Problems with video explanation

      • Purchasing maximum items

      • K largest elements

      • Find k most frequent

      • Find k most frequent in Linear time

    • Practice Problems

      • Practice problems on implementation, methods, and using PriorityQueue to solve dsa problems

  • HashSet and LinkedHashSet

    • Introduction to HashSet

    • Introduction to LinkedHashSet

    • Implementation and usage

    • Methods

    • Traversal

    • Problems with video explanation

      • Print distinct elements

      • Print repeating elements

    • Practice Problems

      • Practice problems on implementation, methods, and using HashSet to solve dsa problems

  • TreeSet

    • Introduction to TreeSet

    • Implementation and usage

    • Methods

    • Traversal

    • Problems with video explanation

      • Ceiling on right

      • Count greater element

    • Practice Problems

      • Practice problems on implementation, methods, and using TreeSet to solve dsa problems

  • HashMap and LinkedHashMap

    • Introduction to HashMap

    • Introduction to LinkedHashMap

    • Implementation and usage

    • Methods

    • Traversal

    • Problems with video explanation

      • DS for balance

      • Print frequencies in order

    • Practice Problems

      • Practice problems on implementation, methods, and using HashMap to solve dsa problems

  • TreeMap

    • Introduction to TreeMap

    • Implementation and usage

    • Methods

    • Traversal

    • Problems with video explanation

      • Design a data structure for item prices

      • Design a data structure for item prices with duplicates allowed

    • Practice Problems

      • Practice problems on implementation, methods, and using TreeMap to solve dsa problems

  • String

    • Introduction to Strings

    • Introduction to StringBuilder and StringBuffer

    • Implementation and usage

    • Methods

    • Traversal

    • Problems with video explanation

      • Pangram checking

      • Pattern searching

      • Find one extra character

    • Practice Problems

      • Practice problems on implementation, methods, and using Strings to solve dsa problems

  • Comparator and Comparable

    • Introduction to Comparable Interface

    • Introduction to Comparator Interface

    • Methods of Comparator Interface and Examples on it

    • Practice Problems

      • Practice problems on using Comparator to sort effectively

  • Arrays Class

    • Introduction to Arrays and the Arrays Class

    • Implementation and usage

    • Methods like

      • fill()

      • BinarySearch()

      • equals()

      • mismatch()

      • compare()

      • asList()

      • toString()

    • Traversal

    • Practice Problems

      • Practice problems on implementation and methods

  • Collections Class

    • Introduction to Collections Class

    • Methods like fill(), reverse(), binarySearch(), max(), min(), frequency()

    • Practice Problems

      • Practice problems on methods

  • Sorting

    • Introduction to sorting in Java

    • Arrays.sort()

    • Collections.sort()

    • Comparable Interface

    • Problems with video explanation

      • The thief problem

      • Chocolate distribution problem

      • Keep indices after sorting

      • Sort an array according to other

      • Sort students by marks

      • Sort elements by frequency

      • Sort elements by frequency in Linear Time

    • Practice Problems

      • Practice problems on various sorting algorithms, and comparator sort

• Mathematics

  • Count Digits

  • Palindrome Numbers

  • Factorial of Numbers

  • GCD of Two Numbers

  • LCM of Two Numbers

  • Check for Prime

  • Prime Factors

  • Sieve of Eratosthenes

  • Computing Power

• Recursion

  • Josephus Problem

  • Subset Sum Problem

• Arrays: 

  • Kadane’s Algorithm

  • Shuffling Algorithms

  • Sliding Window

  • Prefix Sum Technique

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• Matrix: 

  • Multidimensional Array in CPP and Java

  • Search, Transpose and Rotate

  • Pattern Traversal: Snake, Spiral, Boundary

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• Searching:

  • Two Pointer Approach

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• Sorting: 

  • Union And Intersection of Sorted Arrays

  • Inversions Count

  • Tail Call elimination Quick Sort

  • Cycle Sort

  • Merge of Overlapping Intervals

  • Overview of Sorting Algorithms

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• Hashing:

  • Double Hashing

  • Find frequencies of array 

  • Count Distinct element in Every Window 

  • Intersection and Union via Hashing

  • Frequencies of Array Elements

  • Distinct Elements in Window

  • Counting Occurences

  • Check for a Pair with given Sum 

  • Longest Consecutive Subsequence 

  • Subsequence Problems

  • Subarray Problems

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• Strings:

  • Creation, Updation

  • Reverse, Pangram, Case conversion

  • Validation, Length

  • Palindrome Check

  • Overview of Pattern Searching

  • Pattern Matching Algorithms:

    • Rabin Karp Algorithm

    • KMP Algorithm

  • Rotations Check of two Strings

  • Anagram

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• Linked List:

  • Doubly Linked List

  • Circular Linked List

  • Loop in Linked List (Detection and Removal)

  • Loop Detection Algorithms

  • Union and Intersection of LinkedLists

  • Reverse in Groups

  • LRU Cache Design

  • Palindrome LinkedList

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• Stack:

  • Infix, Postfix, Prefix (Introduction)

  • Infix to PostFix (Simple Solution)

  • Infix to PostFix (Efficient Solution)

  • Evaluation of Postfix

  • Infix to Prefix (Simple Solution)

  • Infix to Postfix (Efficient Solution)

  • Evaluation of Prefix

  • Implementing Two Stacks in Single Array

  • Implementing K stacks in Single Array

  • Largest Rectangular Area in Histogram

  • Design a Stack that supports getMin() operation

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• Queue and Deque:

  • Stack using Queue

  • Reversal

  • Maximum of all Subarrays of Size K

  • Generate numbers using given digits

  • Design a data structure with min/max operations

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• Tree:

  • Line By Line Level Order Traversal

  • Printing Left, Right, Top and Bottom Views

  • Binary Tree to Doubly Linked List

  • Binary Tree from Inorder and Postorder Traversal

  • Maximum Width

  • Child Sum Property

  • Convert Binary Tree to Doubly LinkedList

  • Burning a Tree from Leaf

  • Diameter

  • LCA

  • Serialize and Deserialize

  • Count Nodes in Complete Binary Tree

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• Binary Search Tree:

  • Top View

  • Bottom View

  • Vertical Sum

  • Vertical Traversal

  • Fix BST With Two Nodes Swapped

  • Check For BST

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• Heap:

  • Heap Sort

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• Graph:

  • Graph Representation: Adjacency List

  • Adjacency List Implementation in CPP

  • Adjacency List Implementation in Java

  • Adjacency List and Matrix Comparison

  • Breadth First Search and application

  • Depth First Search and application

  • Detect Cycle in Undirected Graph

  • Detect Cycle in Directed Graph

  • Topological Sorting

  • Shortest Path Problems

  • Prim's Algorithm Introduction and Implementation in CPP and Java

  • Dijkstra’s Algorithm Introduction and Implementation in CPP and Java

  • Bellman Ford Algorithm

  • Kosaraju’s Algorithm

  • Articulation Point

  • Bridges in Graph

  • Tarjan’s Algorithm

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• Greedy Algorithm:

  • Introduction

  • Activity Selection Problem in CPP and Java

  • Fractional Knapsack in CPP and Java

  • Job Sequencing Problem

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• BackTracking:

  • Concept of Backtracking

  • Problems: Rat In Maze, N Queen, Sudoku

  • More Problems for Practice.

• Dynamic Programming:

  • Introduction

  • Memoization

  • Tabulation

  • LCS and its variations

  • Coin Change

  • KnapSack

  • LIS and its variations

  • Egg Drop Puzzle

  • Subset Sum

  • Matrix Chain Multiplication

  • Palindrome Partitioning

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• Trie:

  • Introduction

  • Insert, Search, Delete

  • Video Solutions for some standard and complex problems

  • More Problems for Practice.

• Segment Tree:

  • Introduction 

  • Construction

  • Range and Update Query

  • More Problems for Practice.

• Disjoint-Set

  • Introduction

  • Union-Find

  • Union By Rank

  • Path Compression

  • Kruskal’s Algorithm

  • More Problems for Practice

Object oriented Analysis and Design Concepts

• Introduction to Object and Classes. 

• Software Development Process.  

• UML and its importance.

• Class Diagrams & Object Diagrams 

• Use-case Diagrams

Object-oriented Analysis and Design Case Studies: Complete step by step design and analysis of below case studies.

• BookMyShow : Movie ticket booking application. 

• MyFlipCart : Complete e-commerce application.

• ParkingLot : Automated Solution for Parking-Lots. 

• BlackJack : Most popular card game in casinos.

• Chess Game

• Live Cricket Commentary System

Operating System

• Operating System and its Types

• Multiprogramming, Multiprocessing, Multithreading

• Process Management and Scheduling

• Process Synchronization.

• Deadlock

• Memory Management 

• Virtual Memory

Database Management System

• Introduction to DBMS

• Architectures

• ER Model

• Relational Model

• Keys in Relational Model

• Database Normalization 

• Normal Forms

• Concurrency Control

• Indexing in Database

• B+ Tree Introduction

• SQL

Computer Networks:

• Introduction to Computer Networks

• TCP/IP vs OSI Model

• Circuit Switching vs Packet Switching

• Flow Control Protocols 

• IP and Classful Addressing

• Classless Addressing

• Routing Protocols

• ARP & DHCP

• Transport Layer

• TCP & UDP

• Application Layer

Subject Wise Most Asked Interview Questions

QUANTITATIVE ANALYSIS

• Number System - Numbers, Prime & Composite Numbers, Co-Prime numbers, ....
• Divisibility Test - Divisibility, Factor, Prime Factor, Divisibility Rules(2, 3, 4, …., 10, 11)
• HCF and LCM - Listing Multiples, Prime Factorization, Division method, etc.
• Decimals Fractions - Fractions, Decimals, Decimal Fractions, Recurring Decimals.
• Squares & Cubes - Square, Cube, Square Root, Cube Root
• Average - Mean, Median and Mode
• Age - Various techniques to solve age problems.
• Log - Log Function, Common Log, Natural Log, Binary Log, Laws of Logarithms.
• Percentage - Percentage, Fractions of Percentages, Expenditure, Price, Consumption, Population, Depreciation, …
• Profit, Loss & Discount - CP, SP, MP, Profit, Loss, Discount, …
• Ratio And Proportion - Ratio, Proportion, Compounded Ratio, Mean Proportional, Componendo, Dividendo, Directly Proportional, Inversely Proportional.
• Partnership -Various types of Partnership and Partners.
• Pipe and Cistern | Part 1
• Pipe and Cistern | Part 2
• Time And Work - Problems on Time, Work and Efficiency.
• Work and Wages | Part 1 
• Work and Wages | Part 2 
• Speed, Distance and Time | Part 1 
• Speed, Distance and Time | Part 2 
• Boats and Streams - Downstream, Upstream, Average Speed,...
• Trains - Problems in same and opposite Direction.
• Simple Interest 
• Compound Interest | Part 1 
• Compound Interest | Part 2 
• Area - Rectangle, Square, Triangle etc.
• Volume - Cube, Cuboid, Cylinder, Cone, Sphere, Hemisphere, 
• Race - Race, Winner, Dead Heat Race, etc.
• Clocks - Problems related to angle between hands.
• Calendars - Day, Week, Month, Year, Leap Year, Non-Leap year, Odd days etc.
• Height Distance - Heights, Height, Distance, Angle of Elevation, Depression, Trigonometry Ratio, Conversion
• Series  And Sequence - AP, GP, HP.
   

LOGICAL and VERBAL REASONING

• LOGICAL REASONING - 

  • Introduction, 

  • Data Sufficiency, 

  • Data Interpretation, 

  • Blood Relations, 

  • Sequence and Series, 

  • Direction Test, 

  • Mathematical Operations, 

  • Syllogism.

• VERBAL APTITUDE -

  • Verbal Ability

  • Reading Comprehension

  • Vocabulary Section 

  • Vocabulary Reasoning Section 

• BASICS OF GRAMMAR 1 -

  • Section

  • Clause

  • Phrase

  • Parts of Speech

  • Nouns

  • Gerunds

  • Pronouns

  • Verbs

  • Adjectives.

  • Adverbs

• BASICS OF GRAMMAR 2 -

  • Prepositions

  • Conjunctions

  • Subordinating Conjunctions

  • Tenses

  • Interjections

• ARTICLE -

• ACTIVE VOICE & PASSIVE VOICE -

  • Use with Tenses

• CLOSET TESTS -

  • Problem Solving

• PASSAGE FORMATION -

  • Problem Solving

• SENTENCE FORMATION -

  • Problem Solving

• SENTENCE COMPLETION-

  • Problem Solving

• SUBJECT VERB and AGREEMENT -

  • General Rule

  • Multiple Subjects

  • Inverted Sentences

  • There is & There are

  • Collective Nouns

  • Or and Nor

  • Indefinite Pronouns

  • Number Of and Percentage Of

• DETERMINERS

  • Demonstration and Use

• MODIFIERS

  • General Rules

  • Problem Solving

  • Dangling Modifiers

• PARALLEL STRUCTURE

  • General Rules

  • Problems with Articles, Infinitives, and Prepositions.

  • Conjunction Pairs

  • Comparing and Contrasting

• GRAMMAR EXERCISE -

  • Subject-Verb Agreement

  • Pronouns

  • Verbs

  • Parallel Structure

  • Modifiers

  • Adjectives and Adverbs

• ERROR SPOTTING

  • Types of Errors

  • Problem Solving

• PARAJUMBLES

  • Problem Solving

• VERBAL ANALOGIES

  • Problem Solving