This paper delves into the specific application of dynamic programming algorithms in solving the shortest path problem in multi-stage graphs. Faced with a given multi-stage graph structure, we are committed to finding an optimal path from vertex 0 to vertex 9, with the aim of minimizing the total length of the pipeline laid, which represents a classic optimization problem. To efficiently and accurately address this challenge, we have chosen dynamic programming as our core tool. This algorithm constructs solutions step-by-step and leverages the results of already solved sub problems to avoid redundant calculations, thereby significantly enhancing computational efficiency. The paper not only elaborates on the fundamental principles of dynamic programming and its application in the shortest path problem within multi-stage graphs, but also provides specific algorithm implementation code in C++ programming language. Our goal is to offer readers a comprehensive and in-depth guide, enabling them to understand and apply dynamic programming algorithms to successfully solve similar optimization problems related to the shortest path in multi-stage graphs.

Weiqing Wan, Yuanci Wan. Application of Dynamic Programming Algorithm in the Shortest Path Problem. Academic Journal of Computing & Information Science (2024), Vol. 7, Issue 12: 79-84. https://doi.org/10.25236/AJCIS.2024.071211.

[1] Sedgewick R, Wayne K. Algorithms [M]. Translated by Xie Luyun. 4th Edition. Beijing: People's Posts and Telecommunications Press, 2012

[2] Cormen T H, et al. Introduction to Algorithms [M]. Translated by Pan Jingui, et al. Beijing: China Machine Press, 2009

[3] Levitin A. Fundamentals of Algorithm Design and Analysis [M]. Translated by Pan Yan. Beijing: Tsinghua University Press, 2015

[4] Goodrich M T, et al. Algorithm Design and Applications [M]. Translated by Qiao Haiyan, et al. 3rd Edition. Beijing: China Machine Press, 2018

[5] Alsuwaiyel M H. Algorithmic Design Techniques and Analysis [M]. Translated by Wu Weichang, et al. Beijing: Publishing House of Electronics Industry, 2004

[6] Zhang Defu. Algorithm Design and Analysis [M]. Beijing: National Defense Industry Press, 2009

[7] Qu Wanling, Liu Tian, Zhang Liang, et al. Algorithm Design and Analysis [M]. 2nd Edition. Beijing: Tsinghua University Press, 2016

[8] Qu Wanling, Liu Tian, Zhang Liang, et al. Solutions and Learning Guidance for Algorithms Design and Analysis Exercises [M]. 2nd Edition. Beijing: Tsinghua University Press, 2016

[9] Wang Xiaodong. Computer Algorithm Design and Analysis [M]. 4th Edition. Beijing: Tsinghua University Press, 2018

[10] Li Chunbao. Algorithm Design and Analysis [M]. 2nd Edition. Beijing: Tsinghua University Press, 2018

[11] Li Chunbao, Li Xiaochi. In-depth Analysis of Algorithm Design for Programmer Interviews and Written Tests [M]. Beijing: Tsinghua University Press, 2018

[12] Li Chunbao, Data Structure Tutorial [M]. 5th Edition. Beijing: Tsinghua University Press, 2018