An analysis of algorithm is a set of mathematical sequence that can be defined by a set of programming languages that is utilizes certain logic commands that are needed by a computer to complete a defined task. Algorithms can be found just about anywhere, embedded within, any and every computer program or software that one has ever used.
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1) When analysing the algorithms, we have to employ statistical strategies in which analyze algorithms separately regarding certain implementations, computer or data.
Example: Nested Loop
|j = 0 // if j equal to 0|
sum = 0; //and sum equal to 0
while (k <= m) // if k less than equal to m
l = 1
while (l <= m) // if l less than equal to m
sum+1; // then sum plus one
l = l+1; //increment with 1
k = k+1; //increment with 1
TOTAL COST = C0 + C1 + ( T + 1 )*C2 + T*C3 + T*(T + 1)*C4 + T*C5 + T*T*C6 + T*C7 // For this algorithm- time required is proportional to n power2
c = (c + 1); count: c //time taken for each process, but it is constant
|c = (c + 1); cost: cost1|
s = (s + c); cost: cost2, sum: s
-> Total cost = (cost1 + cost2)
|if (n < 0)|
absval = n;
TOTAL COST <= C0 + MAX(C1, C2)
Space Complexity : the space complexity of an algorithm is define as it is the volume of memory it desires to run to completion.
S(P) = c+ Sp (instance features) where,
c= space for (instructions, basic variables, fixed volume aggregates)
Sp = (variable component is based on problem instance factors)
Time Complexity: The time complexity of an algorithm is define as it is the volume of memory it desires to run to completion.
T(P) = compile_time + run_time(execution_time)
Compile_time is constant or Executed the same program as many times, therefore run_time of a program(tp) is important that is depends upon instance characteristics
There are various ways to classify algorithms. Some of the popular methodologies are: