Algorithm analysis is the study of estimating the resources required by an algorithm, particularly its time and space complexity. It helps in identifying the most efficient approach among various methods to solve a problem by using concepts such as asymptotic analysis and big O notation. Overall, it aids in evaluating the algorithm's performance and behavior under different scenarios.

1. ALGORITHM ANALYSIS
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2. OUTLINE
 Algorithm Analysis
 Why do we Need Algorithm Analysis?
 What Does A Better Algorithm Mean?
 Asymptotic Analysis
 Big ‘O’ Notation
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3. INTRODUCTION
 Algorithm analysis is the study to provide theoretical
estimations for the required resources of an algorithm
to solve a specific computational problem i.e.
calculating efficiency.
 Generally the efficiency of an algorithm is related to
the input length that is the number of steps also
known as time complexity or volume of memory
known as space complexity.
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4. WHY DO WE NEED ALGORITHM ANALYSIS
 Knowing the efficiency of an algorithm is
vital on a mission critical task.
 Generally there are multiple approaches or
multiple methods to solve one problem
statement so algorithm. Analysis is performed
to figure out which is a better or optimum
approach out of the different options.

5. WHAT DOES A BETTER ALGORITHM MEAN?
Faster ? (Less execution time) – Time Complexity
Less Memory ? – Space Complexity
Easy to read ?
Less Line of Code?
Less HW/SW needs?
NOTE: algorithm analysis does not give you accurate or
exact values however it gives us estimate which can be
used to study the behavior of the algorithm

6. ASYMPTOTIC ANALYSIS
Definition: Asymptotic analysis of an algorithm is a method of defining the
mathematical boundaries of its runtime performance.
Simple words: it is used to mathematically calculate the running time of any
operation inside an algorithm
 Asymptotic algorithm analysis used to estimate the time complexity function
for arbitrarily large input.
 Using the asymptotic analysis we can easily estimate about the average case
best case and worst case scenarios of an algorithm.
 Time complexity is a computational way to show how the runtime of a
program increases as the size of the input increases.

7. Problem Statement:
Write an algorithm or program to find the sum of N numbers(0-N)
Algorithm 1
function sumOfNumbers(N)
{
sum = 0
for(i = 0 to N)
{
sum = sum + i
}
print(sum)
{

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Problem Statement:
Write an algorithm or program to find the sum of N numbers(0-N)

9. Algorithm 2
function
sumOfNumbers(N)
{
sum = (N*(N+1))/2
print(sum)
{
Problem Statement:
Write an algorithm or program to find the sum of N numbers(0-N)

10. BIG ‘O’ NOTATION
 Big O notation is the formal or mathematical way to
express the upper bound or the worst case scenario of an
algorithm’s running time.
 It measures the worst case time complexity or the largest
amount of time an algorithm can possibly take to
complete.
 Following is the list of some common asymptotic
notations –
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11. BIG ‘O’ NOTATION
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12. CONCLUSION
Understanding Algorithm Analysis and
Asymptotic Algorithm Analysis.
Understanding of Big O Notation, its Importance
and significance.
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