Tag: algorithms
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Overview Sorting is the process of arranging a collection of data in a specific order (ascending or descending). Efficient sorting is fundamental to many other algorithms, such as Binary Search. Core Concepts Stability: A sort is stable if it preserves the relative order of records with equal keys. In-Place: An algorithm is in-place if it…
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Overview Search algorithms are methods used to retrieve information stored within some data structure. The efficiency of a search depends heavily on how the data is organized. Core Concepts Linear Search: Checks every element in sequence. Works on unsorted data. Time: $O(n)$. Binary Search: Repeatedly divides a sorted search interval in half. Works only on…
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Overview A Greedy Algorithm is an algorithmic paradigm that builds up a solution piece by piece, always choosing the next piece that offers the most obvious and immediate benefit. It makes a locally optimal choice in the hope that this will lead to a globally optimal solution. Core Concepts Greedy Choice Property: A global optimum…
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Overview Dynamic Programming (DP) is an optimization technique used to solve complex problems by breaking them down into simpler, overlapping subproblems and storing the results of these subproblems to avoid redundant calculations. Core Concepts Optimal Substructure: A problem has optimal substructure if the optimal solution to the problem contains optimal solutions to its subproblems. Overlapping…
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Overview Backtracking is a general algorithmic technique for finding all (or some) solutions to some computational problems, notably constraint satisfaction problems. It incrementally builds candidates for solutions and abandons a candidate (“backtracks”) as soon as it determines that the candidate cannot possibly be completed to a valid solution. Core Concepts State-Space Search: Exploring all possible…
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Overview Recursion is a programming technique where a function calls itself to solve a problem. It is typically used to solve problems that can be broken down into smaller, identical sub-problems. Core Concepts Base Case: The condition under which the recursion stops. Without a base case, the function would call itself infinitely. Recursive Step: The…