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When timetables are constructed by hand, the process is often 10% mathematics and 90% politics, [2] leading to errors, inefficiencies, and resentment among teachers and students." [1] For the simplest school timetable, such as an elementary school, these conditions must be satisfied: [3] a teacher cannot teach two courses in the same time slot
For example, to solve a system of n equations for n unknowns by performing row operations on the matrix until it is in echelon form, and then solving for each unknown in reverse order, requires n(n + 1)/2 divisions, (2n 3 + 3n 2 − 5n)/6 multiplications, and (2n 3 + 3n 2 − 5n)/6 subtractions, [10] for a total of approximately 2n 3 /3 operations.
[1] [2] The project attracts graduates and students interested in mathematics and computer programming. Since its creation in 2001 by Colin Hughes, Project Euler has gained notability and popularity worldwide. [3] It includes 923 problems as of December 22 2024, [4] with a new one added approximately every week. [5]
LeetCode LLC, doing business as LeetCode, is an online platform for coding interview preparation. The platform provides coding and algorithmic problems intended for users to practice coding . [ 1 ] LeetCode has gained popularity among job seekers in the software industry and coding enthusiasts as a resource for technical interviews and coding ...
Claude Gaspar Bachet de Méziriac's interpretation of the Josephus problem with 41 soldiers and a step size of 3, showing that places 16 and 31 are last to be killed – time progresses inwards along the spiral, green dots denoting live soldiers, grey dead soldiers, and crosses killings
Another example is attempting to make 40 US cents without nickels (denomination 25, 10, 1) with similar result — the greedy chooses seven coins (25, 10, and 5 × 1), but the optimal is four (4 × 10). A coin system is called "canonical" if the greedy algorithm always solves its change-making problem optimally.
If x 1 is the remaining fraction after the first step of the greedy expansion, it satisfies the equation P 0 (x 1 + 1) = 0, which can be expanded as P 1 (x 1) = x 2 1 + x 1 − 1 = 0 . Since P 1 ( x ) < 0 for x = 1 / 2 , and P 1 ( x ) > 0 for all x > 1 , the root of P 1 lies between 1 / 2 and 1, and the first term in its greedy ...
The individual competition consisted of seven questions of varying value, worth a total of 14 points, that students had 40 minutes to answer. The team competition was a proof-based competition, where many questions were asked about a particular situation, and a team of four students was given 60 minutes to answer. [4]