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Exact analysis of insertion sort:
Let us assume the following pseudocode to analyse the exact runtime complexity of insertion sort.
Tj is the time taken to execute the statement through jth iteration.
The statement at line 4 will execute Tj number of times.
The statements at lines 5 & 6 will execute Tj - 1 number of times (one step less) each
Line 7 will execute for (n-1) times
Thus, total time is the sum of time taken for every line multiplied through their cost factor.
Three cases can emerge based on the initial configuration of the input list. First case is where the list was sorted already; second case is the case in which the list is sorted in reverse order and third case is the case where in the list is in random order (unsorted). The best case scenario will emerge while the list is sorted already.
Graph terminologies : Adjacent vertices: Two vertices a & b are said to be adjacent if there is an edge connecting a & b. For instance, in given Figure, vertices 5 & 4 are adj
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Thus far, we have been considering sorting depend on single keys. However, in real life applications, we may desire to sort the data on several keys. The simplest instance is that
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what is the impoartance of average case analysis of algorithm
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