Com S 280 - Algorithms, Integers, Matrices

# Com S 280 - Algorithms, Integers, Matrices - Algorithms...

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Algorithms, Integers, Matrices - Definitions o algorithm: a finite set of precise instructions for performing computation or solving a problem o searching algorithm: the problem of locating an element in a list o linear search algorithm : a procedure for searching a list element by element o binary search algorithm: a procedure for searching an ordered list by successively splitting the list in half o sorting: the reordering of elements of a list into nondecreasing order o greedy algorithm: an algorithm that makes the best choice at each step o )) ( ( ) ( x g O is x f : The fact that ) ( ) ( x g C x f for all k x for some constants C and k o witness to the relationship )) ( ( ) ( x g O is x f : a pair C and k such that ) ( ) ( x g C x f whenever k x o )) ( ( ) ( x g is x f : The fact that ) ( ) ( x g C x f for all k x for some constants C and k o )) ( ( ) ( x g is x f Θ The fact that ) ( x f is ) ( ) ( x and x O o time complexity: the amount of time required for an algorithm to solve a problem o space complexity: the amount of storage space required for an algorithm to solve a problem o worst-case time complexity:

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