Extend the flow properties and definitions to the multiple-source, multiple- sink problem. show that any flow in a multiple-source, multiple-sink flow network corresponds to a flow of identical value in the single-source, single- sink network obtained by adding a supersource and a supersink, and vice versa.

We add a super source s and add a directed edge (s, si) with capacity c(s, si) = ∞ for each i = 1, 2, . . . , m. We also create a new super sink t and add a directed edge (ti, t) with capacity c(ti, t) = ∞ for each i = 1, 2, . . . , n. The single source s simply provides as much flow as desired for the multiple sources si, and the single sink t likewise consumes as much flow as desired for the multiple sinks ti.

Because the virtual edges of s and t can consume as much flows as they want, they don't influence the actual edges.

Explanation:

okay, so i know we just goofed around in that chat, but ive been like genuinly depressed, like medically depressed for almost 4 years now. i had my first panic attack when i was 8. i woke my mum up and told her i felt like i was in a dream. like i was a goldfish in a bowl, looking at all these things going on around me and feeling . tiny. wort hless. and i now am now 17 y/o. i still feel those emotions daily. life used to go by so quick.like every day i would wake up and just like want to go back to bed cause i always felt like i was in the wrong place. i guess looking back, i was in the wrong state of mind. i took a expensive like nice trip to whyoming with my grandfather and ha ted it. like idk why. i would have loved it now, but i found myself writing in a journal everyday because i would forget what happened the day before, couldnt remember what i ate for like the previous meal. just my memory left me for the week i was there. worst feeling ive ever experienced.

best bet is to just buy a vpn