# 代做CIS 413/513编程、Python，Java编程

 代做CIS 413/513作业、Python，Java编程语言作业调试、C++实验作业代做、代写Data Structures作业 CIS 413/513 Advanced Data Structures Winter 2020 Assignment 3 due Wednesday, February 12, 2020 1. (question 4 from chap 10 of Er) Let G be a flow network that contains an opposing pair of edges u → v and v → u, both with positive capacity. Let G0 be the flow network obtained from G by decreasing the capacities of both these edges by min{c(u → v), c(v → u)}. In other words: • if c(u → v) > c(v → u), change the capacity of u → v to c(u → v)−c(v → u) and delete v → u. • if c(u → v) < c(v → u), change the capacity of v → u to c(v → u)−c(u → v) and delete u → v. • if c(u → v) = c(v → u), delete both u → v and v → u. (a) Prove that every maximum (s, t)-flow in G0 is also a maximum (s, t)-flow in G. (Thus, by simplifying every opposing pair of edges in G, we obtain a new reduced flow network with the same maximum flow value as G.) (b) Prove that every minimum (s, t)-cut in G is also a minimum (s, t)-cut in G0 and vice versa. (c) (for 513) Prove that there is at least one maximum (s, t)-flow in G that is not a maximum (s, t)-flow in G0 . 1 如有需要，请加QQ：99515681 或邮箱：99515681@qq.com 微信：codehelp
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