Introduction to Problem Solving Class 11: Algorithms, Flowcharts, Pseudocode and Decomposition

What Introduction to Problem Solving is about

Weightage: This chapter is part of Unit II, Computational Thinking and Programming - 1, which carries 45 of the 70 theory marks in the school annual exam together with Getting Started with Python, Flow of Control, Strings, Lists, Tuples and Dictionaries and Introduction to Python Modules.Source: CBSE Computer Science (083) syllabus 2026-27, Class XI distribution of marks, Unit II Computational Thinking and Programming - 1

Key concepts

Steps for problem solving

NCERT section NCERT 4.1, 4.2

A computer solves a problem only after a person has worked out the method. The four steps are:
1. Analysing the problem: read the problem statement carefully, list its main parts and decide exactly what the inputs and outputs are and what the solution must do. A wrong understanding leads to a program that does not serve its purpose.
2. Developing an algorithm: write the solution as exact steps in natural language (or as a flowchart or pseudocode), refining it until it handles every case.
3. Coding: translate the algorithm into a high-level language such as Python, following that language's rules, and document the code for later use.
4. Testing and debugging: run the program with many inputs, including unusual ones, to check that it is correct, meets the user's needs and responds in time. Errors found are debugged (removed) and the program is tested again, until no errors remain. The software industry uses unit, integration, system and acceptance testing for large programs.

GIGO (Garbage In, Garbage Out): the output can only be as correct as the input given.

Worked example

A school wants a program that tells each student their grade from total marks. Name the step at which each happens: (a) deciding that the input is marks out of 500 and the output is a grade; (b) running the program with 0, 500 and 499 marks; (c) writing the steps 'if percentage ≥ 90 then grade A ...'; (d) typing the steps in Python.

Try it first, then show the solutionSolution

1. Finding inputs and outputs is analysis.
2. Running with edge values is testing.
3. Writing exact steps is developing the algorithm.
4. Typing in Python is coding.

Answer: (a) Analysing (b) Testing and debugging (c) Developing an algorithm (d) Coding.

Algorithm and its characteristics

NCERT section NCERT 4.3

An algorithm is a finite sequence of exact steps which, when followed, solves a problem; it is like a well-written recipe. It is needed because a programmer must plan the roadmap of a program before coding; with a clear algorithm the code is easier to write, to check and to explain to others. The word comes from the name of the Persian mathematician al-Khwarizmi.

A good algorithm has:

• Precision: each step is stated exactly.
• Uniqueness: the result of each step depends only on the input and the previous steps.
• Finiteness: it always stops after a finite number of steps.
• Input: it receives some input.
• Output: it produces some output.

While writing one, identify the input, the processing to be done and the output wanted.

Worked example

Is this an algorithm? 'Step 1: Set n = 1. Step 2: Print n. Step 3: Add 2 to n. Step 4: Go to Step 2.' Correct it so that it prints the odd numbers up to 9.

Try it first, then show the solutionSolution

1. There is no step that stops it, so it breaks the finiteness rule; it is not a proper algorithm.
2. Add a test: Step 2: While n ≤ 9 repeat Steps 3-4. Step 3: Print n. Step 4: Add 2 to n. Step 5: Stop.

Answer: Not finite as written; adding the test 'while n ≤ 9' makes it print 1, 3, 5, 7, 9 and stop.

Flowcharts

NCERT section NCERT 4.4.1, Table 4.1

A flowchart is a visual representation of an algorithm. Each shape is one kind of step and the arrows show the order:

Symbol	Name	Use
Oval (rounded rectangle)	Terminator	Start and End
Rectangle	Process	A calculation or action, e.g. sum = a + b
Diamond	Decision	A yes/no (true/false) question with two exits
Parallelogram	Input/Output (data)	Read input or print output
Arrow	Flow line (connector)	Order of the steps

Rules: one Start and at least one End; every decision has two labelled exits (Yes/No); arrows go from one shape to the next without crossing where possible; a loop is drawn by an arrow returning to an earlier decision.

Worked example

List, in order, the flowchart shapes for: read the length and breadth of a room, compute the area, display the area.

Try it first, then show the solutionSolution

1. Start: oval.
2. Input length, breadth: parallelogram.
3. area = length × breadth: rectangle.
4. Print area: parallelogram.
5. End: oval.

Answer: Oval → parallelogram → rectangle → parallelogram → oval, joined by arrows.

Pseudocode

NCERT section NCERT 4.4.2

Pseudocode ('not real code') is an informal, language-like description of an algorithm. It is meant for people to read and cannot be run by a computer. There is no fixed standard, but common keywords are INPUT, COMPUTE, PRINT, INCREMENT, DECREMENT, IF/ELSE, WHILE and TRUE/FALSE. Indentation shows which steps belong inside an IF or a loop.

Pseudocode is quicker to write and change than a flowchart and is close to real code, so it is easy to translate into Python. A flowchart shows the flow more clearly at a glance for small problems.

Worked example

Write pseudocode to read the price of an item and the quantity bought, and print the bill amount after a 10% discount.

Try it first, then show the solutionSolution

1. INPUT price
   INPUT qty
   COMPUTE amount = price * qty
   COMPUTE amount = amount - 0.10 * amount
   PRINT amount

Answer: The five lines above: two inputs, two computations, one output.

Flow of control: sequence, selection, repetition

NCERT section NCERT 4.5

The flow of control is the order in which steps run.

• Sequence: the steps run one after another, each exactly once.
• Selection: a condition is tested and one of two (or more) paths is chosen: IF condition THEN ... ELSE .... In a flowchart this is a diamond with Yes and No exits. Several conditions can be tested in turn (IF ... ELSE IF ... ELSE) for more than two choices.
• Repetition (iteration, loop): a set of steps is repeated a fixed number of times or while a condition is true: WHILE condition ... . A loop must change something that the condition tests, or it will never stop.

Worked example

Write pseudocode that reads 5 numbers and prints how many of them are negative.

Try it first, then show the solutionSolution

1. SET count = 0, i = 1
2. WHILE i <= 5
   INPUT n
   IF n < 0 THEN
   INCREMENT count
   INCREMENT i
3. PRINT count
4. This uses all three: sequence (setting values, printing), selection (IF n < 0) and repetition (WHILE i <= 5).

Answer: The pseudocode above; for inputs 4, -2, 0, -7, 3 it prints 2.

Verifying algorithms: the dry run

NCERT section NCERT 4.6

An algorithm must be correct for every possible input, because faulty software in a bank, hospital or spacecraft can do serious harm. To verify it, we go through the steps by hand with sample inputs and note the value of each variable after each step. This is a dry run. It helps to find wrong steps and missing cases.

Choose test inputs carefully: ordinary values, boundary values (such as exactly 60 minutes or exactly the pass mark), and unusual ones (0, negative numbers, equal values). An algorithm that works for one example may fail for another: for instance, adding two durations in hours and minutes is wrong if it forgets to carry 60 minutes into an hour.

Worked example

An algorithm adds two durations given in minutes and seconds: 'total_min = m1 + m2; total_sec = s1 + s2; print total_min, total_sec'. Dry run it for 3 min 40 s + 2 min 35 s, find the error and correct it.

Try it first, then show the solutionSolution

1. total_min = 5, total_sec = 75: output '5 min 75 s', which is not a valid time.
2. Correction: IF total_sec >= 60 THEN total_sec = total_sec - 60 and total_min = total_min + 1.
3. Now the output is 6 min 15 s.

Answer: The algorithm misses the carry when seconds reach 60; with the IF step it gives 6 min 15 s.

Comparing algorithms

NCERT section NCERT 4.7

One problem can have several correct algorithms. To choose, compare how much processing time each needs (time complexity) and how much memory it uses (space complexity). For example, to test whether n is prime you could try dividing by every number from 2 to n - 1, or only by numbers from 2 up to the square root of n: both are correct, but the second does far fewer divisions for a large n, so it is better.

Worked example

How many divisions does each method make, at most, to decide that 97 is prime: (a) divide by 2 to 96; (b) divide by 2 to 9 (since 10 × 10 > 97)?

Try it first, then show the solutionSolution

1. (a) 2 to 96 is 95 divisions.
2. (b) 2 to 9 is 8 divisions.
3. If n had a factor larger than its square root, it would also have one smaller, so (b) is enough.

Answer: (a) 95 (b) 8; method (b) is far more efficient.

Coding

NCERT section NCERT 4.8, 4.2.4

In coding, the finished algorithm is written in a programming language by following its syntax: the rules for spelling, word order and punctuation of statements. Machine language (0s and 1s) is what the computer runs but is very hard to write, so we write source code in a high-level language and use a compiler or interpreter to translate it. The choice of language depends on things such as the platform (operating system) and whether the program is a desktop, mobile or web application.

Two kinds of error to know: a syntax error breaks the language's rules and the program does not run (no output); a logical error lets the program run but gives wrong output, and is found by testing and dry runs.

Worked example

Classify the error: (a) the average of three marks is computed as a + b + c / 3; (b) a print statement is missing its closing bracket.

Try it first, then show the solutionSolution

1. (a) The program runs but divides only c by 3 (division before addition): wrong output, so a logical error. Fix: (a + b + c) / 3.
2. (b) Breaks the language rules, so the program cannot run: syntax error.

Answer: (a) Logical error (b) Syntax error.

Decomposition

NCERT section NCERT 4.9

Some problems are too complex to solve in one go. Decomposition means breaking a complex problem into smaller sub-problems, solving each separately (often by different people), testing each, and then combining them into the full solution: 'divide and conquer'. Each sub-problem can be studied in detail, and a sub-problem may itself be broken down further.

A railway reservation system, for example, can be split into train and seat details, searching trains, booking and payment, cancellation and refunds, and printing tickets. Other examples are planning a school event, weather forecasting and a delivery management system.

Worked example

Decompose 'run the school's annual sports day' into at least five sub-problems.

Try it first, then show the solutionSolution

1. Event list and schedule.
2. Student registration for events.
3. Ground, equipment and volunteers.
4. Recording results and points.
5. Prizes and the closing ceremony.
6. Each team handles one part; the parts are put together on the day.

Answer: Schedule; registration; ground and equipment; results; prizes and ceremony (any five reasonable parts).

Introduction to Problem Solving in real life

Each concept, met in an everyday situation. Read the situation, answer the question in your own words, then compare with the model answer. The one-line hook is what to remember.

Topics in this chapter

• Algorithms, Flowcharts and Pseudocode for Problem Solving
• Dry Run, Comparing Algorithms and Decomposition

Introduction to Problem Solving: syntax and key facts

Steps of problem solving

1. 1.Analyse
2. 2.Algorithm
3. 3.Code
4. 4.Test and debug

Return to an earlier step whenever testing shows a fault.

Good algorithm

Precision, Uniqueness, Finiteness, Input, Output

Also identify input, processing and output first.

Flowchart symbols

Oval: start/end; rectangle: process; diamond: decision; parallelogram: input/output; arrow: flow

A decision has exactly two exits, Yes and No.

Pseudocode keywords

INPUT, COMPUTE, PRINT, INCREMENT, DECREMENT, IF/ELSE, WHILE, TRUE/FALSE

Indent the steps inside IF and WHILE.

Flow of control

Sequence, selection, repetition

Every algorithm is built from these three.

Comparing algorithms

Time complexity (processing time) and space complexity (memory)

Fewer steps for the same result is better.

Introduction to Problem Solving: diagrams to practise

Practise each one on paper: draw it from the checklist, then tick off every label.

How the school exam asks Introduction to Problem Solving

The question patterns to expect, and the method that works for each.

Tricks to remember Introduction to Problem Solving

Short memory aids. Say each one aloud once, then use it on a question the same day.

• A-A-C-T

  Analyse, Algorithm, Code, Test: 'All Answers Come from Testing'.

  Use it when: Listing the four steps in order.

• PUFIO

  Precision, Uniqueness, Finiteness, Input, Output.

  Use it when: Characteristics of a good algorithm.

• Shapes by job

  Oval = open/close, rectangle = work, diamond = decide, parallelogram = pass data in or out.

  Use it when: Flowchart symbols.

• S-S-R

  Sequence, Selection, Repetition: 'Step, Steer, Repeat'.

  Use it when: Flow of control.

Introduction to Problem Solving: exam-level solved questions

Ordered from exam level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section E style)

Read the situation, then answer every part. In a school exam set on the board pattern this is a 4-mark question split into 1 + 1 + 1 + 1 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Introduction to Problem Solving

The slips examiners see most often, and what to write instead.

• ✗Mistake: Using a rectangle for input or output

  Input and output use the parallelogram; the rectangle is for processing.

  Wrong working

  [ Read marks ] drawn as a rectangle

  Right working

  / Read marks / drawn as a parallelogram

  ✓Do this: Check each box: data in or out → parallelogram.

  Usually costs: Half to 1 mark

• ✗Mistake: Decision box with one exit or unlabelled exits

  A decision always has a Yes and a No path.

  Wrong working

  <n > 0?> with a single arrow onward

  Right working

  <n > 0?> with arrows labelled Yes and No

  ✓Do this: Label both exits of every diamond.

  Usually costs: 1 mark

• ✗Mistake: A loop whose condition never becomes false

  The variable tested must change inside the loop, or the algorithm is not finite.

  Wrong working

  i = 1
  WHILE i <= 10
  PRINT i

  Right working

  i = 1
  WHILE i <= 10
  PRINT i
  INCREMENT i

  ✓Do this: After writing a loop, find the step that moves it towards stopping.

  Usually costs: 1 mark

• ✗Mistake: Mixing up syntax and logical errors

  A syntax error stops the program running; a logical error gives wrong output.

  Wrong working

  Writing area = l + b is a syntax error.

  Right working

  area = l + b runs but gives a wrong value: logical error.

  ✓Do this: Ask: does it run? If yes but the answer is wrong, it is logical.

  Usually costs: 1 mark

• ✗Mistake: Writing Python code when pseudocode is asked

  Pseudocode should be readable steps without language rules; marks go for the logic and keywords.

  Wrong working

  n = int(input())
  if n % 2 == 0: print('Even')

  Right working

  INPUT n
  IF n MOD 2 = 0 THEN PRINT 'Even' ELSE PRINT 'Odd'

  ✓Do this: Use the pseudocode keywords and plain operators.

  Usually costs: Half mark

NCERT exercise guide: Introduction to Problem Solving

What each exercise in the NCERT chapter tests, how to approach it, and a question of the same kind solved step by step. Questions here are written in our own words.

Practice questions on Introduction to Problem Solving

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQExam level

   Which flowchart symbol is used to show input or output? (a) Rectangle (b) Diamond (c) Parallelogram (d) Oval

   Hint

   Also called the data symbol.

   Answer

   (c) Parallelogram

2. Q2 · 2 marks · Short answerExam level

   List the four steps of problem solving in order.

   Hint

   Before coding there are two steps.

   Answer

   Analysing the problem, developing an algorithm, coding, testing and debugging.

3. Q3 · 2 marks · Short answerExam level

   What is decomposition? Give one advantage.

   Hint

   Divide and conquer.

   Answer

   Breaking a complex problem into smaller sub-problems that are solved separately and then combined. Advantage: each part is simpler and can be solved and tested independently, even by different people.

4. Q4 · 2 marks · Short answerHarder exam level

   Dry run and give the output:
   SET n = 5, f = 1
   WHILE n > 1
   f = f * n
   n = n - 1
   PRINT f

   Hint

   5 × 4 × 3 × 2.

   Answer

   120

5. Q5 · 1 mark · MCQHarder exam level

   Assertion (A): Pseudocode can be run directly on a computer. Reason (R): Pseudocode uses keywords like INPUT and PRINT. Choose (a) both true, R explains A (b) both true, R does not explain A (c) A false, R true (d) both false.

   Hint

   Pseudo = not real.

   Answer

   (c) A is false (pseudocode is for people and cannot be executed); R is true.

6. Q6 · 3 marks · Short answerHarder exam level

   Write pseudocode to input marks out of 100 and print 'Distinction' for 75 and above, 'Pass' for 33 to 74 and 'Fail' below 33. Which three inputs would you use to test the boundaries?

   Hint

   Test exactly at the cut-offs.

   Answer

   INPUT m
   IF m >= 75 THEN PRINT 'Distinction'
   ELSE IF m >= 33 THEN PRINT 'Pass'
   ELSE PRINT 'Fail'
   Test with 75, 33 and 32 (and 74).

7. Q7 · 2 marks · Short answerHarder exam level

   Predict the output:

   count = 0
   n = 1
   while n < 50:
       n = n * 3
       count = count + 1
   print(n, count)

   Hint

   1, 3, 9, 27, 81.

   Answer

   81 4

8. Q8 · 2 marks · Short answerHOTS / competency

   An algorithm checks if a year is a leap year with 'IF year MOD 4 = 0 THEN leap'. Give a year for which it gives the wrong answer and say what is missing.

   Hint

   Century years.

   Answer

   1900 (divisible by 4 but not a leap year). Missing rule: a century year is a leap year only if it is divisible by 400 (so 2000 is a leap year, 1900 is not).

9. Q9 · 2 marks · Short answerExam level

   Why is testing done with many inputs and not just one? Explain with an example.

   Hint

   A program can be right for one input and wrong for another.

   Answer

   A program can work for one input but fail for another. For example, a time-adding program may give 5 min 50 s correctly but print 6 min 75 s when the seconds pass 60. Testing many and boundary inputs finds such faults.

10. Q10 · 3 marks · Short answerHOTS / competency

    Two algorithms search for a roll number in a list of 1000 sorted numbers: one checks every number from the start; the other repeatedly checks the middle and discards half. At most how many checks does the second need, roughly? Which is better?

    Hint

    Halve 1000 until 1 is left.

    Answer

    About 10 checks (1000 → 500 → 250 → ... → 1, since 2^10 = 1024), against up to 1000 for the first. The halving method takes far less time.

11. Q11 · 3 marks · Short answerHOTS / competency

    Rewrite as pseudocode with a loop: 'Read numbers one by one until the user enters 0, then print how many numbers were entered (not counting the 0).'

    Hint

    Read once before the loop.

    Answer

    SET count = 0
    INPUT x
    WHILE x != 0
    INCREMENT count
    INPUT x
    PRINT count

12. Q12 · 1 mark · Very short answerExam level

    Name the error type: (a) the program prints the area of a circle as 2πr; (b) the keyword 'while' is written 'whiel'.

    Hint

    Does it run?

    Answer

    (a) Logical error (b) Syntax error.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.What does GIGO stand for?Show answer

   Garbage In, Garbage Out.

2. 2.Which flowchart symbol is used for a decision?Show answer

   A diamond.

3. 3.What is a dry run?Show answer

   Working through an algorithm by hand with sample inputs to check it.

4. 4.Name the three kinds of flow of control.Show answer

   Sequence, selection and repetition.

5. 5.What does 'pseudo' mean in pseudocode?Show answer

   Not real.

6. 6.Which characteristic of an algorithm says it must stop?Show answer

   Finiteness.

7. 7.What two things are compared when choosing between algorithms?Show answer

   Time (processing time) and space (memory) needed.

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Steps: analyse, develop an algorithm, code, test and debug.
• ☐Algorithm: finite, exact steps that solve a problem; precise, unique, finite, has input and output.
• ☐Flowchart: oval start/end, rectangle process, diamond decision, parallelogram input/output, arrows.
• ☐Pseudocode: human-readable, not executable; INPUT, COMPUTE, PRINT, IF/ELSE, WHILE.
• ☐Flow of control: sequence, selection, repetition.
• ☐Dry run = tracing by hand; test boundary and unusual inputs.
• ☐Compare algorithms by time and memory needed.
• ☐Decomposition: split a complex problem into smaller ones, solve, test and combine.

Introduction to Problem Solving: frequently asked questions