Number of solutions to a Linear equation $a_1(x-1) + a_2(x-2) + a_3(x-3) + . . . +a_{x-1} = x$
0
$begingroup$
$$a_1(x-1) + a_2(x-2) + a_3(x-3) + . . . +a_{x-1} = x$$
Where $a_i = (1 quad or quad 0)$
I was thinking if there exists some solution that takes only O($N$) linear time computation.
linear-algebra
asked Dec 15 '18 at 8:04
Dragon SurferDragon Surfer
7416
$endgroup$
add a comment |
0
$begingroup$
$$a_1(x-1) + a_2(x-2) + a_3(x-3) + . . . +a_{x-1} = x$$
Where $a_i = (1 quad or quad 0)$
I was thinking if there exists some solution that takes only O($N$) linear time computation.
linear-algebra
asked Dec 15 '18 at 8:04
Dragon SurferDragon Surfer
7416
$endgroup$
1
$begingroup$
Can you look at your sum again i don't think the last term is $a_{x-1}$. If it is i don't understand what terms are in the "+...+". Also, what is the relation between the number of solutions (question in title) and computation time?
$endgroup$
– TheD0ubleT
Dec 15 '18 at 9:00
$begingroup$
I missed that $a_i$ is either 0 or 1. So what I want to count the number of ways a number X can be represented as sum of values lesser than X, without repetition.
$endgroup$
– Dragon Surfer
Dec 15 '18 at 14:40
add a comment |
0
0
0
$begingroup$
$$a_1(x-1) + a_2(x-2) + a_3(x-3) + . . . +a_{x-1} = x$$
Where $a_i = (1 quad or quad 0)$
I was thinking if there exists some solution that takes only O($N$) linear time computation.
linear-algebra
asked Dec 15 '18 at 8:04
Dragon SurferDragon Surfer
7416
$endgroup$
$$a_1(x-1) + a_2(x-2) + a_3(x-3) + . . . +a_{x-1} = x$$
Where $a_i = (1 quad or quad 0)$
I was thinking if there exists some solution that takes only O($N$) linear time computation.
linear-algebra
linear-algebra
asked Dec 15 '18 at 8:04
Dragon SurferDragon Surfer
7416
asked Dec 15 '18 at 8:04
Dragon SurferDragon Surfer
7416
edited Dec 15 '18 at 14:38
Dragon Surfer
asked Dec 15 '18 at 8:04
Dragon SurferDragon Surfer
7416
asked Dec 15 '18 at 8:04
Dragon SurferDragon Surfer
7416
asked Dec 15 '18 at 8:04
Dragon SurferDragon Surfer
7416
7416
1
$begingroup$
Can you look at your sum again i don't think the last term is $a_{x-1}$. If it is i don't understand what terms are in the "+...+". Also, what is the relation between the number of solutions (question in title) and computation time?
$endgroup$
– TheD0ubleT
Dec 15 '18 at 9:00
$begingroup$
I missed that $a_i$ is either 0 or 1. So what I want to count the number of ways a number X can be represented as sum of values lesser than X, without repetition.
$endgroup$
– Dragon Surfer
Dec 15 '18 at 14:40
add a comment |
1
$begingroup$
Can you look at your sum again i don't think the last term is $a_{x-1}$. If it is i don't understand what terms are in the "+...+". Also, what is the relation between the number of solutions (question in title) and computation time?
$endgroup$
– TheD0ubleT
Dec 15 '18 at 9:00
$begingroup$
I missed that $a_i$ is either 0 or 1. So what I want to count the number of ways a number X can be represented as sum of values lesser than X, without repetition.
$endgroup$
– Dragon Surfer
Dec 15 '18 at 14:40
1
1
$begingroup$
Can you look at your sum again i don't think the last term is $a_{x-1}$. If it is i don't understand what terms are in the "+...+". Also, what is the relation between the number of solutions (question in title) and computation time?
$endgroup$
– TheD0ubleT
Dec 15 '18 at 9:00
$begingroup$
Can you look at your sum again i don't think the last term is $a_{x-1}$. If it is i don't understand what terms are in the "+...+". Also, what is the relation between the number of solutions (question in title) and computation time?
$endgroup$
– TheD0ubleT
Dec 15 '18 at 9:00
$begingroup$
I missed that $a_i$ is either 0 or 1. So what I want to count the number of ways a number X can be represented as sum of values lesser than X, without repetition.
$endgroup$
– Dragon Surfer
Dec 15 '18 at 14:40
$begingroup$
I missed that $a_i$ is either 0 or 1. So what I want to count the number of ways a number X can be represented as sum of values lesser than X, without repetition.
$endgroup$
– Dragon Surfer
Dec 15 '18 at 14:40
add a comment |
0
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1
$begingroup$
Can you look at your sum again i don't think the last term is $a_{x-1}$. If it is i don't understand what terms are in the "+...+". Also, what is the relation between the number of solutions (question in title) and computation time?
$endgroup$
– TheD0ubleT
Dec 15 '18 at 9:00
$begingroup$
I missed that $a_i$ is either 0 or 1. So what I want to count the number of ways a number X can be represented as sum of values lesser than X, without repetition.
$endgroup$
– Dragon Surfer
Dec 15 '18 at 14:40