As i understand FCFS does not need any sorting but there are no examples covered in the internet what happens if waiting time goes negative?
So i understand that algorithm for waiting time is: WT = CT (Completion Time) - AT (Arrival Time) - BT (Burst Time).
But what happens if i have:
AT: 0 / BT: 2
AT: 0 / BT: 4
AT: 15 / BT: 5
AT: 21 / BT: 10
My calculations would be:
WT = 2 - 0 - 2 = 0
WT = 6 - 0 - 4 = 2
WT = 11 - 15 -5 = -9
WT = 21 - 21 - 10 = -10
Avg: (0+2-10-9)/4 = -17/4 = -4,25 (seems unreal)
Is the correct answer negative or should i modify the algorithm somehow?
Related
I have a vector
A = [ 1 1 1 2 2 3 6 8 9 9 ]
I would like to write a loop that counts the frequencies of values in my vector within a range I choose, this would include values that have 0 frequencies
For example, if I chose the range of 1:9 my results would be
3 2 1 0 0 1 0 1 2
If I picked 1:11 the result would be
3 2 1 0 0 1 0 1 2 0 0
Is this possible? Also ideally I would have to do this for giant matrices and vectors, so the fasted way to calculate this would be appreciated.
Here's an alternative suggestion to histcounts, which appears to be ~8x faster on Matlab 2015b:
A = [ 1 1 1 2 2 3 6 8 9 9 ];
maxRange = 11;
N = accumarray(A(:), 1, [maxRange,1])';
N =
3 2 1 0 0 1 0 1 2 0 0
Comparing the speed:
K>> tic; for i = 1:100000, N1 = accumarray(A(:), 1, [maxRange,1])'; end; toc;
Elapsed time is 0.537597 seconds.
K>> tic; for i = 1:100000, N2 = histcounts(A,1:maxRange+1); end; toc;
Elapsed time is 4.333394 seconds.
K>> isequal(N1, N2)
ans =
1
As per the loop request, here's a looped version, which should not be too slow since the latest engine overhaul:
A = [ 1 1 1 2 2 3 6 8 9 9 ];
maxRange = 11; %// your range
output = zeros(1,maxRange); %// initialise output
for ii = 1:maxRange
tmp = A==ii; %// temporary storage
output(ii) = sum(tmp(:)); %// find the number of occurences
end
which would result in
output =
3 2 1 0 0 1 0 1 2 0 0
Faster and not-looping would be #beaker's suggestion to use histcounts:
[N,edges] = histcounts(A,1:maxRange+1);
N =
3 2 1 0 0 1 0 1 2 0
where the +1 makes sure the last entry is included as well.
Assuming the input A to be a sorted array and the range starts from 1 and goes until some value greater than or equal to the largest element in A, here's an approach using diff and find -
%// Inputs
A = [2 4 4 4 8 9 11 11 11 12]; %// Modified for variety
maxN = 13;
idx = [0 find(diff(A)>0) numel(A)]+1;
out = zeros(1,maxN); %// OR for better performance : out(maxN) = 0;
out(A(idx(1:end-1))) = diff(idx);
Output -
out =
0 1 0 3 0 0 0 1 1 0 3 1 0
This can be done very easily with bsxfun.
Let the data be
A = [ 1 1 1 2 2 3 6 8 9 9 ]; %// data
B = 1:9; %// possible values
Then
result = sum(bsxfun(#eq, A(:), B(:).'), 1);
gives
result =
3 2 1 0 0 1 0 1 2
Consider we have N points on a circle. To each point an index is assigned i = (1,2,...,N). Now, for a randomly selected point, I want to have a vector including the indices of 5 points, [two left neighbors, the point itself, two right neighbors].
See the figure below.
Some sxamples are as follows:
N = 18;
selectedPointIdx = 4;
sequence = [2 3 4 5 6];
selectedPointIdx = 1
sequence = [17 18 1 2 3]
selectedPointIdx = 17
sequence = [15 16 17 18 1];
The conventional way to code this is considering the exceptions as if-else statements, as I did:
if ii == 1
lseq = [N-1 N ii ii+1 ii+2];
elseif ii == 2
lseq = [N ii-1 ii ii+1 ii+2];
elseif ii == N-1
lseq=[ii-2 ii-1 ii N 1];
elseif ii == N
lseq=[ii-2 ii-1 ii 1 2];
else
lseq=[ii-2 ii-1 ii ii+1 ii+2];
end
where ii is selectedPointIdx.
It is not efficient if I consider for instance 7 points instead of 5. What is a more efficient way?
How about this -
off = -2:2
out = mod((off + selectedPointIdx) + 17,18) + 1
For a window size of 7, edit off to -3:3.
It uses the strategy of subtracting 1 + modding + adding back 1 as also discussed here.
Sample run -
>> off = -2:2;
for selectedPointIdx = 1:18
disp(['For selectedPointIdx =',num2str(selectedPointIdx),' :'])
disp(mod((off + selectedPointIdx) + 17,18) + 1)
end
For selectedPointIdx =1 :
17 18 1 2 3
For selectedPointIdx =2 :
18 1 2 3 4
For selectedPointIdx =3 :
1 2 3 4 5
For selectedPointIdx =4 :
2 3 4 5 6
For selectedPointIdx =5 :
3 4 5 6 7
For selectedPointIdx =6 :
4 5 6 7 8
....
For selectedPointIdx =11 :
9 10 11 12 13
For selectedPointIdx =12 :
10 11 12 13 14
For selectedPointIdx =13 :
11 12 13 14 15
For selectedPointIdx =14 :
12 13 14 15 16
For selectedPointIdx =15 :
13 14 15 16 17
For selectedPointIdx =16 :
14 15 16 17 18
For selectedPointIdx =17 :
15 16 17 18 1
For selectedPointIdx =18 :
16 17 18 1 2
You can use modular arithmetic instead: Let p be the point among N points numbered 1 to N. Say you want m neighbors on each side, you can get them as follows:
(p - m - 1) mod N + 1
...
(p - 4) mod N + 1
(p - 3) mod N + 1
(p - 2) mod N + 1
p
(p + 1) mod N + 1
(p + 2) mod N + 1
(p + 3) mod N + 1
...
(p + m - 1) mod N + 1
Code:
N = 18;
p = 2;
m = 3;
for i = p - m : p + m
nb = mod((i - 1) , N) + 1;
disp(nb);
end
Run code here
I would like you to note that you might not necessarily improve performance by avoiding a if statement. A benchmark might be necessary to figure this out. However, this will only be significant if you are treating tens of thousands of numbers.
Given an image I and two matrices m_1 ;m_2 (same size with I). The function f is defined as:
Because my goal design wants to get the sign of f . Hence, the function f can rewritten as following:
I think that second formula is faster than first formula because: It
can ignore the square term
It can compute the sign directly, instead of two steps in first equation: compute the f and check sign.
Do you agree with me? Do you have another faster formula for f
I =[16 23 11 42 10
11 21 22 24 30
16 22 154 155 156
25 28 145 151 156
11 38 147 144 153];
m1 =[0 0 0 0 0
0 0 22 11 0
0 23 34 56 0
0 56 0 0 0
0 11 0 0 0];
m2 =[0 0 0 0 0
0 0 12 11 0
0 22 111 156 0
0 32 0 0 0
0 12 0 0 0];
The ouput f is
f =[1 1 1 1 1
1 1 -1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1]
I implemented the first way, but I did not finish the second way by matlab. Could you check help me the second way and compare it
UPDATE: I would like to add code of chepyle and Divakar to make clearly question. Note that both of them give the same result as above f
function compare()
I =[16 23 11 42 10
11 21 22 24 30
16 22 154 155 156
25 28 145 151 156
11 38 147 144 153];
m1 =[0 0 0 0 0
0 0 22 11 0
0 23 34 56 0
0 56 0 0 0
0 11 0 0 0];
m2 =[0 0 0 0 0
0 0 12 11 0
0 22 111 156 0
0 32 0 0 0
0 12 0 0 0];
function f=first_way()
f=sign((I-m1).^2-(I-m2).^2);
f(f==0)=1;
end
function f= second_way()
f = double(abs(I-m1) >= abs(I-m2));
f(f==0) = -1;
end
function f= third_way()
v1=abs(I-m1);
v2=abs(I-m2);
f= int8(v1>v2) + -1*int8(v1<v2); % need to convert to int from logical
f(f==0) = 1;
end
disp(['First way : ' num2str(timeit(#first_way))])
disp(['Second way: ' num2str(timeit(#second_way))])
disp(['Third way : ' num2str(timeit(#third_way))])
end
First way : 1.2897e-05
Second way: 1.9381e-05
Third way : 2.0077e-05
This seems to be comparable and might be a wee bit faster at times than the original approach -
f = sign(abs(I-m1) - abs(I-m2)) + sign(abs(m1-m2)) + ...
sign(abs(2*I-m1-m2)) - 1 -sign(abs(2*I-m1-m2) + abs(m1-m2))
Benchmarking Code
%// Create random inputs
N = 5000;
I = randi(1000,N,N);
m1 = randi(1000,N,N);
m2 = randi(1000,N,N);
num_iter = 20; %// Number of iterations for all approaches
%// Warm up tic/toc.
for k = 1:100000
tic(); elapsed = toc();
end
disp('------------------------- With Original Approach')
tic
for iter = 1:num_iter
out1 = sign((I-m1).^2-(I-m2).^2);
out1(out1==0)=-1;
end
toc, clear out1
disp('------------------------- With Proposed Approach')
tic
for iter = 1:num_iter
out2 = sign(abs(I-m1) - abs(I-m2)) + sign(abs(m1-m2)) + ...
sign(abs(2*I-m1-m2)) - 1 -sign(abs(2*I-m1-m2) + abs(m1-m2));
end
toc
Results
------------------------- With Original Approach
Elapsed time is 1.751966 seconds.
------------------------- With Proposed Approach
Elapsed time is 1.681263 seconds.
There is a problem with the accuracy of second formula, but for the sake of comparison, here's how I would implement it in matlab, along with a third approach to avoid squaring and the sign() function, inline with your intent. Note that the matlab's matrix and sign functions are pretty well optimized, the second and third approaches are both slower.
function compare()
I =[16 23 11 42 10
11 21 22 24 30
16 22 154 155 156
25 28 145 151 156
11 38 147 144 153];
m1 =[0 0 0 0 0
0 0 22 11 0
0 23 34 56 0
0 56 0 0 0
0 11 0 0 0];
m2 =[0 0 0 0 0
0 0 12 11 0
0 22 111 156 0
0 32 0 0 0
0 12 0 0 0];
function f=first_way()
f=sign((I-m1).^2-(I-m2).^2);
end
function f= second_way()
v1=(I-m1);
v2=(I-m2);
f= int8(v1<=0 & v2>0) + -1* int8(v1>0 & v2<=0);
end
function f= third_way()
v1=abs(I-m1);
v2=abs(I-m2);
f= int8(v1>v2) + -1*int8(v1<v2); % need to convert to int from logical
end
disp(['First way : ' num2str(timeit(#first_way))])
disp(['Second way: ' num2str(timeit(#second_way))])
disp(['Third way : ' num2str(timeit(#third_way))])
end
The output:
First way : 9.4226e-06
Second way: 1.2247e-05
Third way : 1.1546e-05
I have just learnt that to get the formula to find the 1st Complement is
-x = 2^n - x - 1
I have managed to apply it on a binary case:
-00001100 (base 2) = 2^8 - 12 - 1
= 243
= 11110011 (1s)
However, when I try to apply the same formula to a base 5 number,
-1042 (base 4) = 5^4 - 1042 - 1
= 625 - 1042 - 1
= - 400 (which is not the answer)
Can some one help me out here? Thanks
you cannot calculate any formula with numbers in 2 different bases, you have to use their decimal representation (or an other representation you can handle)
I'll give it a try in dec:
1042 (base 5) = 1* 5^3 + 4* 5^1 + 2 = 125 + 20 + 2 = 147 dec
5^4 - 147 - 1 = 477 dec
477 = 3* 5^3 + 4* 5^2 + 2 = 3402 (base 5)
in base 5:
5^4 - 1042 - 1 = 10000 - 1043 = 3402
Let A be an matrix of size [n,n]. If I want to extract its diagonal, I do diag(A).
Actually, I want the opposite diagonal, which would be [A(n,1),A(n-1,2),A(n-2,3),...].
One way to do this is via diag(flipud(A)). However, flipud(A) is quite wasteful and multiplies the time it takes by a factor of 10 compared to finding the usual diagonal.
I'm looking for a fast way of obtaining the opposite diagonal. Naturally, for loops seem abysmally slow. Suggestions would be greatly appreciated.
Here is my matrix, produced by A = magic(5)
A =
17 24 1 8 15
23 5 7 14 16
4 6 13 20 22
10 12 19 21 3
11 18 25 2 9
s = size(A,1)
A(s:s-1:end-1)
ans =
11 12 13 14 15
Below is a comparison of all the methods mentioned so far, plus a few other variations I could think of. This was tested on 64-bit R2013a using TIMEIT function.
function [t,v] = testAntiDiag()
% data and functions
A = magic(5000);
f = {
#() func0(A) ;
#() func1(A) ;
#() func2(A) ;
#() func3(A) ;
#() func4(A) ;
#() func5(A) ;
#() func6(A) ;
#() func7(A) ;
};
% timeit and check results
t = cellfun(#timeit, f, 'UniformOutput',true);
v = cellfun(#feval, f, 'UniformOutput',false);
assert( isequal(v{:}) )
end
function d = func0(A)
d = diag(A(end:-1:1,:));
end
function d = func1(A)
d = diag(flipud(A));
end
function d = func2(A)
d = flipud(diag(fliplr(A)));
end
function d = func3(A)
d = diag(rot90(A,3));
end
function d = func4(A)
n = size(A,1);
d = A(n:n-1:end-1).';
end
function d = func5(A)
n = size(A,1);
d = A(cumsum(n + [0,repmat(-1,1,n-1)])).';
end
function d = func6(A)
n = size(A,1);
d = A(sub2ind([n n], n:-1:1, 1:n)).';
end
function d = func7(A)
n = size(A,1);
d = zeros(n,1);
for i=1:n
d(i) = A(n-i+1,i);
end
end
The timings (in the same order they are defined above):
>> testAntiDiag
ans =
0.078635867152801
0.077895631970976 % #AlexR.
0.080368641824528
0.195832501156751
0.000074983294297 % #thefourtheye
0.000143019460665 % #woodchips
0.000174679680437
0.000152488508547 % for-loop
The most suprising result to me is the last one. Apparently JIT compilation is very effective on such simple for-loops.
The elements you want are easily obtained by indexing. For example, this should do the trick.
n = 4;
A = magic(n)
A =
16 2 3 13
5 11 10 8
9 7 6 12
4 14 15 1
A(cumsum(n + [0,repmat(-1,1,n-1)]))
ans =
4 7 10 13
I could also have used sub2ind to get those element indexes, but this does it a bit more cleanly, though less obvious in how it works.
A = magic(6)
A =
35 1 6 26 19 24
3 32 7 21 23 25
31 9 2 22 27 20
8 28 33 17 10 15
30 5 34 12 14 16
4 36 29 13 18 11
b = diag(A(1:length(A),length(A):-1:1))
b =
24
23
22
33
5
4