Algorithms
Sliding Window
Solve fixed-window problems: maximum sum of k elements, moving averages, and O(n) updates as the window slides.
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Algorithms
Two Pointers
Scan a sorted array or string from both ends at once to find pairs, remove duplicates, or reverse data in O(n).
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Searching
Binary Search
Cut a sorted range in half on every step to find a value or boundary in O(log n) instead of checking one by one.
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Graph
Depth-First Search
Explore as far as possible down one path before backtracking, used to walk trees, graphs, and grids.
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Graph
Breadth-First Search
Explore level by level from a starting point, the go-to way to find the shortest path in an unweighted graph.
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Algorithms
Dynamic Programming
Break a problem into overlapping subproblems and reuse their answers to avoid recomputing the same work.
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Algorithms
Backtracking
Try a choice, keep going, and undo it if it fails, used to generate permutations, combinations, and valid layouts.
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Algorithms
Greedy Algorithms
Make the locally best choice at each step and never look back, useful when local optima add up to a global optimum.
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Sorting
Bubble Sort
Repeatedly swap neighboring out-of-order elements until the whole list is sorted, simple but slow on large lists.
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Sorting
Merge Sort
Split the list in half, sort each half, then merge them back together in order, giving reliable O(n log n) time.
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Sorting
Quick Sort
Pick a pivot, move smaller elements left and larger ones right, then repeat on each side to sort in place.
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Sorting
Insertion Sort
Build the sorted list one element at a time, inserting each new element into its correct position as you go.
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Graph
Dijkstra's Algorithm
Find the shortest path from a starting node to every other node in a graph where edges have non-negative weights.
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Graph
Bellman-Ford Algorithm
Find the shortest path from a starting node even when some edges have negative weights, and detect negative cycles.
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Graph
Topological Sort
Order the nodes of a graph so every task comes after everything it depends on, used for scheduling and build order.
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Graph
Union-Find (Disjoint Set)
Track which nodes belong to the same group and merge groups quickly, used to detect cycles and build networks.
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Graph
Kruskal's Algorithm
Build the cheapest network connecting all nodes by adding the smallest edges first, skipping any that form a cycle.
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Graph
Prim's Algorithm
Build the cheapest network connecting all nodes by growing a tree one node at a time, always picking the cheapest edge out.
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Algorithms
Recursion
Solve a problem by having a function call itself on a smaller version of the same problem until it hits a base case.
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Sorting
Selection Sort
Repeatedly find the smallest remaining element and move it into place, simple to write but slow on large lists.
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Sorting
Heap Sort
Build a heap from the list, then repeatedly pull out the largest element to sort in place in O(n log n).
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Sorting
Counting Sort
Count how many times each value appears, then rebuild the list in order, sorting in O(n) when values fall in a small range.
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Algorithms
Prefix Sum
Precompute running totals so the sum of any range can be answered instantly instead of adding it up every time.
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Algorithms
Kadane's Algorithm
Track the best running sum ending at each position to find the maximum sum of a contiguous subarray in one pass.
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