2. (25 points) consider the following procedure acting on an array a[1: : n]. insertion sort(a[1: : n]) cost times 1. for j 2 to n c1 2. key a[ j] c2 3. i c3 4. while i > 0 and a[i] > key c4 5. a[i+1] a[i] c5 6. i c6 7. a[i+1] key c7 (a) let t j denote the number of times the while loop test in line 4 is executed for that value of j. fill in for each line of instruction, the number of times the instruction is executed. (b) derive the expression for the running time of insertion sort in terms of n, ci, and t j. (c) what is t j for the best-case scenario, i. e., when the running time of the algorithm is the smallest. use that to derive the expression for the best-case running time of insertion sort in terms of n and ci. what is the best-case time complexity of insertion sort using the big-o notation? (d) what is t j for the worst-case scenario, i. e., when the running time of the algorithm is the largest. use that to derive the expression for the worst-case running time of insertion sort in terms of n and ci. what is the worst-case time complexity of insertion sort using the big-o notation?

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.

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