Number partitioning | Strongly NP-complete problems

3-partition problem

The 3-partition problem is a strongly NP-complete problem in computer science. The problem is to decide whether a given multiset of integers can be partitioned into triplets that all have the same sum. More precisely: * The input to the problem is a multiset S of n = 3 m  positive integers. The sum of all integers is . * The output is whether or not there exists a partition of S into m triplets S1, S2, …, Sm such that the sum of the numbers in each one is equal to T. The S1, S2, …, Sm must form a partition of S in the sense that they are disjoint and they cover S. The 3-partition problem remains strongly NP-complete under the restriction that every integer in S is strictly between T/4 and T/2. (Wikipedia).

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From playlist Introduction to Algorithms

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From playlist Lines and Planes in Three Dimensions

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From playlist MegaFavNumbers

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From playlist Set Theory

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From playlist Systems of Equations with Three Unknowns

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From playlist CSE547 - Discrete Mathematics - 1999 SBU

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From playlist Problem Solving

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Introduction to Integer Partitions -- Number Theory 28

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From playlist Number Theory v2

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Introduction to Integer Partitions -- Number Theory 28

⭐Support the channel⭐ Patreon: Merch: My amazon shop: 🟢 Discord: ⭐my other channels⭐ Main Channel:

From playlist Number Theory

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From playlist MIT 6.046J / 18.410J Introduction to Algorithms (SMA 5503),

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From playlist Nexus Trimester - 2016 - Fundamental Inequalities and Lower Bounds Theme

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From playlist CSE373 - Analysis of Algorithms - 1997 SBU

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From playlist Rogers-Ramanujan Identities

Related pages

Multiway number partitioning | Disjoint sets | Multiset | Numerical 3-dimensional matching | Pseudopolynomial time number partitioning | Strong NP-completeness | Weak NP-completeness | Cover (topology) | Partition of a set | 3-dimensional matching | Partition problem | Tetris | Rectangle packing