![]() ![]() The running time for a recursive subroutine is Statement as being the cost of the more expensive branch.ĭetermining the execution time of a recursive We cannot simply count the cost of the if ![]() To perform an average-case analysis for such programs, Then clause only for the smallest of \(n\) values. If statement might be executed with probability \(1/n\).Īn example would be an if statement that executes the Various branches of an if or switch statement areįor example, for input of size \(n\), the then clause of an There are rare situations in which the probability for executing the ![]() Of the clauses (which is usually, but not necessarily, true).įor switch statements, the worst-case cost is that of the mostįor subroutine calls, simply add the cost of executing the subroutine. The size of \(n\) does not affect the probability of executing one This is also true for the average case, assuming that The cost of an if statement in the worst case is the greater of While loops are analyzed in a manner similar to for Where \(n\) is assumed to be a power of two and again Thus, the total cost of the loop is \(c_3\) times the sum of Until the last time through the loop when \(j = n\). You should see that for the first execution of the outer loop,įor the second execution of the outer loop, \(j\) is 2.Įach time through the outer loop, \(j\) becomes one greater, The cost of the inner loop is different because it costs The outer for loop is executed \(n\) times, but each time The expression sum++ requires constant time call itīecause the inner for loop is executed \(j\) times,īy simplifying rule (4) it has cost \(c_3j\). We work from the inside of the loop outward. The first for loop is a double loop and requires a special The second for loop is just like the one inĮxample 4.6.2 and takes \(c_2 n = \Theta(n)\) time. This code fragment has three separate statements: theįirst assignment statement and the two for loops.Īgain the assignment statement takes constant time If you like my post please follow me to read my latest post on programming and technology.Sum = 0 for ( j = 1 j <= n j ++ ) // First for loop for ( i = 1 i <= j i ++ ) // is a double loop sum ++ for ( k = 0 k < n k ++ ) // Second for loop A = k If L i = T, the search terminates successfully return i.L n−1, and target value T, the following subroutine uses linear search to find the index of the target T in L. Given a list L of n elements with values or records L 0 …. Linear search is rarely practical because other search algorithms and schemes, such as the binary search algorithm and hash tables, allow significantly faster searching for all but short lists. If each element is equally likely to be searched, then linear search has an average case of n+1/2 comparisons, but the average case can be affected if the search probabilities for each element vary. If the algorithm reaches the end of the list, the search terminates unsuccessfully.Ī linear search runs in at worst linear time and makes at most n comparisons, where n is the length of the list. ![]() It sequentially checks each element of the list until a match is found or the whole list has been searched.Ī linear search sequentially checks each element of the list until it finds an element that matches the target value. In computer science, a linear search or sequential search is a method for finding an element within a list. ![]()
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