I was recently solving 1316E - Team Building problem but I couldn't understand why we sorted the audience array. Can anyone help?
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I think it's because that the total number of people is not $$$n$$$.
So choosing audience is done greedily.. just pick the ones with highest $$$a_i$$$.
This way you don't have to add another dimension $$$(the \space number \space of \space audience)$$$ to your $$$dp$$$ state.
Or as the Tutorial says:
If we don't choose $$$i$$$ as a player, then we can take him as an audience member or not take him at all. I claim that if the number of audience members chosen till now $$$ \lt$$$ $$$k$$$ , then we must select $$$i$$$ as an audience member , We can prove this. If we don't select $$$i$$$ as audience, we will need to select some $$$j$$$ ($$$j \gt i$$$ ), strength in that case will include $$$a_j$$$ but not $$$a_i$$$ , but as $$$a_i \ge a_j$$$ , it is always better to select $$$i$$$ .