chap analysis techniques setmark(vcomp)for (int first( ) () next(vw)if ( getmark( = dfs component(gwcomp)use the concept of potential from amortized analysis to explain why the total cost of this algorithm is th(| | |(note that this will not be true amortized analysis because this algorithm does not allow an arbitrary series of dfs operations but rather is fixed to do single call to dfs from each vertex give proof similar to that used for theorem to show that the total number of comparisons required by any series of or more searches on self-organizing list of length using the count heuristic is never more than twice the total number of comparisons required when series is applied to the list stored in its optimal static order use mathematical induction to prove that ib(if ib( for > = use mathematical induction to prove that fib(iis even if and only if is divisible by use mathematical induction to prove that for > ib( ( / ) - find closed forms for each of the following recurrences (af (nf ( ( (bf ( ( ) ( (cf ( ( ( (df ( nf ( ) ( (ef ( ( ) ( (ff ( - = ( ) ( find th for each of the following recurrence relations (at ( ( / (bt ( ( / (ct ( ( / (dt ( ( / (et ( ( / (ft ( ( / (gt ( ( / (ht ( ( / log (it ( ( / log