Here is the pseudocode for Selection Sort with time values given. You can assume that lines

without time values take no time at all.

# Selection Sort

# A is a list of length $n.$

for $i=0$ to $n-2$

minindex $=i,c_1$

for $j=i+1$ to $n-1$

if $=j,c_2{c}_{3}0p1T(n)p,c_1,c_2{c}_{3}T(n)=,n^2+|,n+A[j]$

minindex $=j,c_2$

end

end

swap $A[i]$ with $A[minindex]c_3$

end

Suppose the inputs $to$ this implementation are such that $on$ average the $if$ statement $is$ true

with constant probability $0p1.$

$(a)$ Write down a nested sum which represents the time $T(n)$ taken $by$ this algorithm.

$(b)$ Evaluate this sum and simplify $to$ a polynomial. The coefficients could include $p,c_1,c_2,[10pts]$

$an\frac{d}{o}r{c}_3.$

$T(n)=,n^2+|,n+$