Doubt in computing complexity

#1

sir, in the last exercise we have multiplied the complexities of both inner and outer loop but in exercise 1 and 2 we have added them why is it so?

#2

hello @we_kaash
in excercise 1 ->
outer loop was going from i=0…n-1
and inner loo from j=i to k
so in 1st iteration of outer loop -> the inner loop will execute k times
so in 2nd iteration of outer loop -> the inner loop will execute k-2 times
so in 3rd iteration of outer loop -> the inner loop will execute k-3 times
…
…
so on

so in kth iteration of outer loop -> the inner loop will execute 1 times
after that k+1…n-1 inner loop will never execute that why
time complexity =k*(k+1)/2 + n-k+1

in last exercise for every iteration of outer loop inner loop is executing exeactly k times.
thats why n * k is the time complexity in last case

#3

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