Silver

Introduction to Prefix Sums

Somewhat Frequent

Computing range sum queries in constant time over a fixed 1D array.
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More on Prefix Sums

Not Frequent

Max subarray sum, prefix sums in two dimensions, and a more complicated example.
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Custom Comparators and Coordinate Compression

Somewhat Frequent

Using a custom comparator to sort custom objects or values in a non-default order, and compressing values from a large range to a smaller one.
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Two Pointers

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Iterating two monotonic pointers across an array to search for a pair of indices satisfying some condition in linear time.

More Operations on Sorted Sets

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Finding the next element smaller or larger than a specified key in a set, and using iterators with sets.
Updated: 5 days ago

(Optional) C++ Sets with Custom Comparators

Rare

Incorporating custom comparators into standard library containers.

Greedy Algorithms with Sorting

Somewhat Frequent

Solving greedy problems by sorting the input.
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Binary Search

Somewhat Frequent

Binary searching on arbitrary monotonic functions and built-in functions for binary search.
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Graph Traversal

Very Frequent

Traversing a graph with depth first search and breadth first search.
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Flood Fill

Somewhat Frequent

Finding connected components in a graph represented by a grid.
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Introduction to Tree Algorithms

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Introducing a special type of graph: trees.
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Introduction to Functional Graphs

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Directed graphs in which every vertex has exactly one outgoing edge.
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Intro to Bitwise Operators

Somewhat Frequent

Six bitwise operators and the common ways they are used.

Additional Practice for USACO Silver

Final tips for Silver and additional practice problems.