Find the number of multiplications x ones1 n t linspace0 1

Find the number of multiplications x = ones(1, n); t = linspace(0, 1, 100); y = ones(size(t)); for k = 1:n x(k:n) = k* x(k:n); end for k=n-1:-1:1 y = y .* t + x(k); end

Solution

x = ones(1, n) %x is an array of n 1\'s.

t = linspace(0, 1, 100); %100 values between 0, and 1 inclusively.

y = ones(size(t)); %y is an array of 100 1\'s.

%No multiplications till now.

for k = 1 : n

x(k:n) = k * x(k:n) %Multiplications are happening here.

%When k = 1, n multiplications.

%When k = 2, n-1 multiplications.

%.....

%When k = n, 1 multiplication.

end

%So, as of now, the number of multiplications is: 1 + 2 + ... + n =

%n*(n+1)/2.

for k = n-1 : -1 : 1

y = y .* t + x(k) %More multiplications here.

%When k = n-1, 100 multiplications.

%When k = n-2, 100 multiplications.

%.....

%When k = 1, 100 multiplications.

end

%So, for this loop, the number of multiplications is: (n-1) * 100.

%Therefore, total number of multiplications is: 100(n-1) + n(n+1)/2