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ALG:010117Strict greater-than keeps equal tagged keys in order; eight comparisons and six shifts sort the five-record array

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Alg Insertion Sort Stable PrefixAlg Insertion Sort Comparison Shift Count

Correctness proofs and asymptotic complexityAlgorithms · Mixed review

ALG:010218A merge counts every leftover left key, so the seven-key array has thirteen inversions, not three

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Alg Mergesort Inversion Cross CountAlg Mergesort Leftover Left Increment

Divide-and-conquer algorithmsAlgorithms · Mixed review

ALG:010219Quickselect on the nine-key array uses pivot 5 then pivot 7, compares eleven times, and returns 6

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Alg Quickselect Target Side OnlyAlg Quickselect Prescribed Pivot Count

Divide-and-conquer algorithmsAlgorithms · Mixed review

ALG:010220Karatsuba multiplies 1234 by 5678 with three base-100 products; 6164 is not the middle coefficient

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Alg Karatsuba Three Product IdentityAlg Karatsuba Place Value Assembly

Divide-and-conquer algorithmsAlgorithms · Mixed review

ALG:010221The unique maximum subarray of the nine-key instance is the block 2 through 7 and sums to 11

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Alg Max Subarray Crossing OR KadaneAlg Max Subarray Nonempty Unique Block

Divide-and-conquer algorithmsAlgorithms · Mixed review

ALG:010322Huffman merges the two lightest trees; largest-first and raw depth are not WPL

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Huffman Greedy Merge TraceHuffman Sibling Exchange Wpl

Greedy algorithms and exchange proofsAlgorithms · Mixed review

ALG:010323Kruskal accepts a lightest cut edge and rejects every intra-component edge

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Kruskal Component ScanMst Cut Property Safety

Greedy algorithms and exchange proofsAlgorithms · Mixed review

ALG:010424Weighted half-open intervals need a predecessor DP, not a cardinality exchange

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Weighted Interval PredecessorDP Prefix Reconstruction

Dynamic programming and state designAlgorithms · Mixed review

ALG:010425The capacity-8 knapsack optimum is items 2 and 4; fractions and off-by-one cells are not 0/1

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Zero One Knapsack TableKnapsack Take Skip Reconstruction

Dynamic programming and state designAlgorithms · Mixed review

ALG:010426The unique minimum four-matrix product is (A1 A2)(A3 A4) at cost 405

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Matrix Chain Recurrence TableMatrix Chain Split Reconstruction

Dynamic programming and state designAlgorithms · Mixed review

ALG:010527A DAG longest s-t path is a topological max-DP with minus-infinity unreachable labels

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Dag Topo Longest PathUnreachable Minus Infinity Init

Graph optimization and traversal algorithmsAlgorithms · Mixed review

ALG:010528Strong connectivity is mutual reachability: the SCCs of a chain of cycles form a path DAG

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Kosaraju Scc TraceStrong VS One Way Reachability

Graph optimization and traversal algorithmsAlgorithms · Mixed review

ALG:010529A feasible flow of 14 and the source cut of capacity 14 certify the max-flow min-cut value

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Ford Fulkerson ResidualMaxflow Mincut Certificate

Graph optimization and traversal algorithmsAlgorithms · Mixed review

ALG:0106303SAT reduces to Independent Set by clause triangles and complementary conflict edges

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3sat Independent Set ReductionComplementary Conflict Edges

Reductions, NP-completeness, and approximationAlgorithms · Mixed review

ALG:010631Both endpoints of a maximal matching 2-approximate Vertex Cover, tightly on a star

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Maximal Matching Vertex CoverApproximation Factor Two

Reductions, NP-completeness, and approximationAlgorithms · Mixed review