  The multi-beam measurement system plays a crucial role in ocean mapping and
underwater terrain detection. By simultaneously transmitting multiple beams,
the system can accurately receive sound waves reflected from the seabed,
providing more precise and comprehensive water depth information while
effectively revealing the complexity and characteristics of underwater terrain.
Building upon the background and application provided by Question B of the 2023
National Mathematical Contest in Modeling for College Students, this paper
investigates the relationship between ocean floor width measurement and factors
such as beam position, angle, and slope. Utilizing geometric relations,
trigonometric similarity, and sine theorem, a mathematical model is established
to determine adjacent strip coverage width and overlap ratio. Furthermore, an
optimal strategy is determined using a greedy algorithm, while binary search
backtracking is employed to derive the interval of the next adjacent survey
line with the required overlap ratio in order to obtain an optimal terrain
detection strategy.
