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The problem is named after Flavius Josephus, a Jewish historian and leader who lived in the 1st century. According to Josephus's firsthand account of the siege of Yodfat, he and his 40 soldiers were trapped in a cave by Roman soldiers. They chose suicide over capture, and settled on a serial method of committing suicide by drawing lots.
A good example that highlights the pros and cons of using dynamic arrays vs. linked lists is by implementing a program that resolves the Josephus problem. The Josephus problem is an election method that works by having a group of people stand in a circle. Starting at a predetermined person, one may count around the circle n times.
The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
This article says, “Josephus had an accomplice; the problem was then to find the places of the two last remaining survivors (whose conspiracy would ensure their survival). It is alleged that he placed himself and the other man in the 31st and 16th place respectively (for k = 3 below).”
Variant of the Josephus problem with 15 Christians and 15 Turks and a step size of 9, visualised by CMG Lee. Time progresses inwards along the spiral, green dots denoting live soldiers, grey dead soldiers, and crosses killings.
They use that information to identify public policy problems, develop programs to address those problems and then evaluate whether or not the programs are working using an evidence-based approach ...
Josephus problem table: Image title: Claude Gaspar Bachet de Méziriac's interpretation of the Josephus problem with 41 soldiers and a step size of 3, visualised by CMG Lee. Time progresses inwards along the spiral, green dots denoting live soldiers, grey dead soldiers, and crosses killings.
Although Josephus says that he describes the events contained in Antiquities "in the order of time that belongs to them," [63] Feldman argues that Josephus "aimed to organize [his] material systematically rather than chronologically" and had a scope that "ranged far beyond mere political history to political institutions, religious and private ...