Mixing
Algorithm to define min-Max ranges with some defined bound
$begingroup$
Having to populate the following table of MIN-MAX cells, starting with only the knowledge of the IC value
I was thinking about a formula to get the values of A, B, C, D, E, F, G
which works also for the values of IC and 2xIC
I'm able to get the values from 0 to IC using the following formula:
$$K = 3$$
$$LEVEL.MIN = frac{IC}{K} times (LEVEL-1)$$
$$LEVEL.MAX = frac{IC}{K} times (LEVEL)$$
I need another similar formula for the values of E, F, G, 2xIC.
Maybe, since $E=IC$, the formula should have $+IC$ as a fxed part.
algorithms
asked Jan 30 at 10:38
1Z101Z10
1105
$endgroup$
add a comment |
$begingroup$
Having to populate the following table of MIN-MAX cells, starting with only the knowledge of the IC value
I was thinking about a formula to get the values of A, B, C, D, E, F, G
which works also for the values of IC and 2xIC
I'm able to get the values from 0 to IC using the following formula:
$$K = 3$$
$$LEVEL.MIN = frac{IC}{K} times (LEVEL-1)$$
$$LEVEL.MAX = frac{IC}{K} times (LEVEL)$$
I need another similar formula for the values of E, F, G, 2xIC.
Maybe, since $E=IC$, the formula should have $+IC$ as a fxed part.
algorithms
asked Jan 30 at 10:38
1Z101Z10
1105
$endgroup$
$begingroup$
What do the different levels mean? What is IC? So I understand that "MIN" is the minimum value of some set, and "MAX" is the maximum value of some set, but what are these sets? Could you give more context to your problem? And how did you obtain the formulae that you wrote?
$endgroup$
– Matti P.
Jan 30 at 10:41
$begingroup$
Each level is a rang of economic values, and I have the IC value as input. They are needed to know in which level to put an item based on its value.
$endgroup$
– 1Z10
Jan 30 at 10:44
$begingroup$
Are there some conditions for the values of A, B, C, D, E, F, G .... ?
$endgroup$
– Matti P.
Jan 30 at 10:45
$begingroup$
Each level from 1 to 3 needs to have the same width = max - min Each level from 4 to 5 needs to have the same width = max - min and Level[N].min = Level[N-1].max
$endgroup$
– 1Z10
Jan 30 at 10:49
add a comment |
$begingroup$
Having to populate the following table of MIN-MAX cells, starting with only the knowledge of the IC value
I was thinking about a formula to get the values of A, B, C, D, E, F, G
which works also for the values of IC and 2xIC
I'm able to get the values from 0 to IC using the following formula:
$$K = 3$$
$$LEVEL.MIN = frac{IC}{K} times (LEVEL-1)$$
$$LEVEL.MAX = frac{IC}{K} times (LEVEL)$$
I need another similar formula for the values of E, F, G, 2xIC.
Maybe, since $E=IC$, the formula should have $+IC$ as a fxed part.
algorithms
asked Jan 30 at 10:38
1Z101Z10
1105
$endgroup$
Having to populate the following table of MIN-MAX cells, starting with only the knowledge of the IC value
I was thinking about a formula to get the values of A, B, C, D, E, F, G
which works also for the values of IC and 2xIC
I'm able to get the values from 0 to IC using the following formula:
$$K = 3$$
$$LEVEL.MIN = frac{IC}{K} times (LEVEL-1)$$
$$LEVEL.MAX = frac{IC}{K} times (LEVEL)$$
I need another similar formula for the values of E, F, G, 2xIC.
Maybe, since $E=IC$, the formula should have $+IC$ as a fxed part.
algorithms
algorithms
asked Jan 30 at 10:38
1Z101Z10
1105
asked Jan 30 at 10:38
1Z101Z10
1105
edited Jan 30 at 11:30
1Z10
asked Jan 30 at 10:38
1Z101Z10
1105
asked Jan 30 at 10:38
1Z101Z10
1105
asked Jan 30 at 10:38
1Z101Z10
1105
1105
$begingroup$
What do the different levels mean? What is IC? So I understand that "MIN" is the minimum value of some set, and "MAX" is the maximum value of some set, but what are these sets? Could you give more context to your problem? And how did you obtain the formulae that you wrote?
$endgroup$
– Matti P.
Jan 30 at 10:41
$begingroup$
Each level is a rang of economic values, and I have the IC value as input. They are needed to know in which level to put an item based on its value.
$endgroup$
– 1Z10
Jan 30 at 10:44
$begingroup$
Are there some conditions for the values of A, B, C, D, E, F, G .... ?
$endgroup$
– Matti P.
Jan 30 at 10:45
$begingroup$
Each level from 1 to 3 needs to have the same width = max - min Each level from 4 to 5 needs to have the same width = max - min and Level[N].min = Level[N-1].max
$endgroup$
– 1Z10
Jan 30 at 10:49
add a comment |
$begingroup$
What do the different levels mean? What is IC? So I understand that "MIN" is the minimum value of some set, and "MAX" is the maximum value of some set, but what are these sets? Could you give more context to your problem? And how did you obtain the formulae that you wrote?
$endgroup$
– Matti P.
Jan 30 at 10:41
$begingroup$
Each level is a rang of economic values, and I have the IC value as input. They are needed to know in which level to put an item based on its value.
$endgroup$
– 1Z10
Jan 30 at 10:44
$begingroup$
Are there some conditions for the values of A, B, C, D, E, F, G .... ?
$endgroup$
– Matti P.
Jan 30 at 10:45
$begingroup$
Each level from 1 to 3 needs to have the same width = max - min Each level from 4 to 5 needs to have the same width = max - min and Level[N].min = Level[N-1].max
$endgroup$
– 1Z10
Jan 30 at 10:49
$begingroup$
What do the different levels mean? What is IC? So I understand that "MIN" is the minimum value of some set, and "MAX" is the maximum value of some set, but what are these sets? Could you give more context to your problem? And how did you obtain the formulae that you wrote?
$endgroup$
– Matti P.
Jan 30 at 10:41
$begingroup$
What do the different levels mean? What is IC? So I understand that "MIN" is the minimum value of some set, and "MAX" is the maximum value of some set, but what are these sets? Could you give more context to your problem? And how did you obtain the formulae that you wrote?
$endgroup$
– Matti P.
Jan 30 at 10:41
$begingroup$
Each level is a rang of economic values, and I have the IC value as input. They are needed to know in which level to put an item based on its value.
$endgroup$
– 1Z10
Jan 30 at 10:44
$begingroup$
Each level is a rang of economic values, and I have the IC value as input. They are needed to know in which level to put an item based on its value.
$endgroup$
– 1Z10
Jan 30 at 10:44
$begingroup$
Are there some conditions for the values of A, B, C, D, E, F, G .... ?
$endgroup$
– Matti P.
Jan 30 at 10:45
$begingroup$
Are there some conditions for the values of A, B, C, D, E, F, G .... ?
$endgroup$
– Matti P.
Jan 30 at 10:45
$begingroup$
Each level from 1 to 3 needs to have the same width = max - min Each level from 4 to 5 needs to have the same width = max - min and Level[N].min = Level[N-1].max
$endgroup$
– 1Z10
Jan 30 at 10:49
$begingroup$
Each level from 1 to 3 needs to have the same width = max - min Each level from 4 to 5 needs to have the same width = max - min and Level[N].min = Level[N-1].max
$endgroup$
– 1Z10
Jan 30 at 10:49
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Let's look at the conditions that you gave. You say that the MIN of level $n$ should be equal to the MAX of level $n-1$. Using this condition, we should rename the variables like so:
- Level 1: MIN = 0, MAX = A
- Level 2: MIN = A, MAX = D
- Level 3: MIN = D, MAX = E= IC
- Level 4: MIN = E, MAX = G
- Level 5: MIN = G, MAX = 2IC = 2E
The next condition is that each level from 1 to 3 needs to have the same difference between MAX and MIN. In other words,
$$
A = D-A = IC-D
$$
From this condition we see that $D = 2A$ and of course $$A=IC-D qquad Rightarrow qquad D = 2IC - 2D qquad Rightarrow qquad 3D=2IC$$
The next condition is that levels 4 and 5 need to have the same difference between MAX and MIN. In other words,
$$
G-E = 2E - G
$$
Adding $E+G$ to boths sides, this is the same as $2G = 3E$. Now we can plug in these results to get the new level hierarchy:
- Level 1: MIN = $0$, MAX = $A$
- Level 2: MIN = $A$, MAX = $2A$
- Level 3: MIN = $2A$, MAX = $IC$
- Level 4: MIN = $IC$, MAX = $frac{3}{2} IC$
- Level 5: MIN = $frac{3}{2} IC$, MAX = $2IC$
With these conditions, the hierarchy is left with two free variables, IC and A. But otherwise, the hierarchy now follows the conditions that you gave.
answered Jan 30 at 11:09
Matti P.Matti P.
2,2811514
$endgroup$
$begingroup$
$$A=frac{IC}{K}=frac{IC}{3}$$ I think I found the equivalent formula for the other values.
$endgroup$
– 1Z10
Jan 30 at 11:25
add a comment |
$begingroup$
Ok, I finally got it.
The values from E to 2xIC can be calculated using the following formula:
$$W=2$$
$$LEVEL.MIN = frac{LEVEL-1-1}{W} times IC$$
$$LEVEL.MAX = frac{LEVEL-1}{W} times IC$$
answered Jan 30 at 11:22
1Z101Z10
1105
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
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votes
active
oldest
votes
$begingroup$
Let's look at the conditions that you gave. You say that the MIN of level $n$ should be equal to the MAX of level $n-1$. Using this condition, we should rename the variables like so:
- Level 1: MIN = 0, MAX = A
- Level 2: MIN = A, MAX = D
- Level 3: MIN = D, MAX = E= IC
- Level 4: MIN = E, MAX = G
- Level 5: MIN = G, MAX = 2IC = 2E
The next condition is that each level from 1 to 3 needs to have the same difference between MAX and MIN. In other words,
$$
A = D-A = IC-D
$$
From this condition we see that $D = 2A$ and of course $$A=IC-D qquad Rightarrow qquad D = 2IC - 2D qquad Rightarrow qquad 3D=2IC$$
The next condition is that levels 4 and 5 need to have the same difference between MAX and MIN. In other words,
$$
G-E = 2E - G
$$
Adding $E+G$ to boths sides, this is the same as $2G = 3E$. Now we can plug in these results to get the new level hierarchy:
- Level 1: MIN = $0$, MAX = $A$
- Level 2: MIN = $A$, MAX = $2A$
- Level 3: MIN = $2A$, MAX = $IC$
- Level 4: MIN = $IC$, MAX = $frac{3}{2} IC$
- Level 5: MIN = $frac{3}{2} IC$, MAX = $2IC$
With these conditions, the hierarchy is left with two free variables, IC and A. But otherwise, the hierarchy now follows the conditions that you gave.
answered Jan 30 at 11:09
Matti P.Matti P.
2,2811514
$endgroup$
$begingroup$
$$A=frac{IC}{K}=frac{IC}{3}$$ I think I found the equivalent formula for the other values.
$endgroup$
– 1Z10
Jan 30 at 11:25
add a comment |
$begingroup$
Let's look at the conditions that you gave. You say that the MIN of level $n$ should be equal to the MAX of level $n-1$. Using this condition, we should rename the variables like so:
- Level 1: MIN = 0, MAX = A
- Level 2: MIN = A, MAX = D
- Level 3: MIN = D, MAX = E= IC
- Level 4: MIN = E, MAX = G
- Level 5: MIN = G, MAX = 2IC = 2E
The next condition is that each level from 1 to 3 needs to have the same difference between MAX and MIN. In other words,
$$
A = D-A = IC-D
$$
From this condition we see that $D = 2A$ and of course $$A=IC-D qquad Rightarrow qquad D = 2IC - 2D qquad Rightarrow qquad 3D=2IC$$
The next condition is that levels 4 and 5 need to have the same difference between MAX and MIN. In other words,
$$
G-E = 2E - G
$$
Adding $E+G$ to boths sides, this is the same as $2G = 3E$. Now we can plug in these results to get the new level hierarchy:
- Level 1: MIN = $0$, MAX = $A$
- Level 2: MIN = $A$, MAX = $2A$
- Level 3: MIN = $2A$, MAX = $IC$
- Level 4: MIN = $IC$, MAX = $frac{3}{2} IC$
- Level 5: MIN = $frac{3}{2} IC$, MAX = $2IC$
With these conditions, the hierarchy is left with two free variables, IC and A. But otherwise, the hierarchy now follows the conditions that you gave.
answered Jan 30 at 11:09
Matti P.Matti P.
2,2811514
$endgroup$
$begingroup$
$$A=frac{IC}{K}=frac{IC}{3}$$ I think I found the equivalent formula for the other values.
$endgroup$
– 1Z10
Jan 30 at 11:25
add a comment |
$begingroup$
Let's look at the conditions that you gave. You say that the MIN of level $n$ should be equal to the MAX of level $n-1$. Using this condition, we should rename the variables like so:
- Level 1: MIN = 0, MAX = A
- Level 2: MIN = A, MAX = D
- Level 3: MIN = D, MAX = E= IC
- Level 4: MIN = E, MAX = G
- Level 5: MIN = G, MAX = 2IC = 2E
The next condition is that each level from 1 to 3 needs to have the same difference between MAX and MIN. In other words,
$$
A = D-A = IC-D
$$
From this condition we see that $D = 2A$ and of course $$A=IC-D qquad Rightarrow qquad D = 2IC - 2D qquad Rightarrow qquad 3D=2IC$$
The next condition is that levels 4 and 5 need to have the same difference between MAX and MIN. In other words,
$$
G-E = 2E - G
$$
Adding $E+G$ to boths sides, this is the same as $2G = 3E$. Now we can plug in these results to get the new level hierarchy:
- Level 1: MIN = $0$, MAX = $A$
- Level 2: MIN = $A$, MAX = $2A$
- Level 3: MIN = $2A$, MAX = $IC$
- Level 4: MIN = $IC$, MAX = $frac{3}{2} IC$
- Level 5: MIN = $frac{3}{2} IC$, MAX = $2IC$
With these conditions, the hierarchy is left with two free variables, IC and A. But otherwise, the hierarchy now follows the conditions that you gave.
answered Jan 30 at 11:09
Matti P.Matti P.
2,2811514
$endgroup$
Let's look at the conditions that you gave. You say that the MIN of level $n$ should be equal to the MAX of level $n-1$. Using this condition, we should rename the variables like so:
- Level 1: MIN = 0, MAX = A
- Level 2: MIN = A, MAX = D
- Level 3: MIN = D, MAX = E= IC
- Level 4: MIN = E, MAX = G
- Level 5: MIN = G, MAX = 2IC = 2E
The next condition is that each level from 1 to 3 needs to have the same difference between MAX and MIN. In other words,
$$
A = D-A = IC-D
$$
From this condition we see that $D = 2A$ and of course $$A=IC-D qquad Rightarrow qquad D = 2IC - 2D qquad Rightarrow qquad 3D=2IC$$
The next condition is that levels 4 and 5 need to have the same difference between MAX and MIN. In other words,
$$
G-E = 2E - G
$$
Adding $E+G$ to boths sides, this is the same as $2G = 3E$. Now we can plug in these results to get the new level hierarchy:
- Level 1: MIN = $0$, MAX = $A$
- Level 2: MIN = $A$, MAX = $2A$
- Level 3: MIN = $2A$, MAX = $IC$
- Level 4: MIN = $IC$, MAX = $frac{3}{2} IC$
- Level 5: MIN = $frac{3}{2} IC$, MAX = $2IC$
With these conditions, the hierarchy is left with two free variables, IC and A. But otherwise, the hierarchy now follows the conditions that you gave.
answered Jan 30 at 11:09
Matti P.Matti P.
2,2811514
answered Jan 30 at 11:09
Matti P.Matti P.
2,2811514
answered Jan 30 at 11:09
Matti P.Matti P.
2,2811514
answered Jan 30 at 11:09
Matti P.Matti P.
2,2811514
2,2811514
$begingroup$
$$A=frac{IC}{K}=frac{IC}{3}$$ I think I found the equivalent formula for the other values.
$endgroup$
– 1Z10
Jan 30 at 11:25
add a comment |
$begingroup$
$$A=frac{IC}{K}=frac{IC}{3}$$ I think I found the equivalent formula for the other values.
$endgroup$
– 1Z10
Jan 30 at 11:25
$begingroup$
$$A=frac{IC}{K}=frac{IC}{3}$$ I think I found the equivalent formula for the other values.
$endgroup$
– 1Z10
Jan 30 at 11:25
$begingroup$
$$A=frac{IC}{K}=frac{IC}{3}$$ I think I found the equivalent formula for the other values.
$endgroup$
– 1Z10
Jan 30 at 11:25
add a comment |
$begingroup$
Ok, I finally got it.
The values from E to 2xIC can be calculated using the following formula:
$$W=2$$
$$LEVEL.MIN = frac{LEVEL-1-1}{W} times IC$$
$$LEVEL.MAX = frac{LEVEL-1}{W} times IC$$
answered Jan 30 at 11:22
1Z101Z10
1105
$endgroup$
add a comment |
$begingroup$
Ok, I finally got it.
The values from E to 2xIC can be calculated using the following formula:
$$W=2$$
$$LEVEL.MIN = frac{LEVEL-1-1}{W} times IC$$
$$LEVEL.MAX = frac{LEVEL-1}{W} times IC$$
answered Jan 30 at 11:22
1Z101Z10
1105
$endgroup$
add a comment |
$begingroup$
Ok, I finally got it.
The values from E to 2xIC can be calculated using the following formula:
$$W=2$$
$$LEVEL.MIN = frac{LEVEL-1-1}{W} times IC$$
$$LEVEL.MAX = frac{LEVEL-1}{W} times IC$$
answered Jan 30 at 11:22
1Z101Z10
1105
$endgroup$
Ok, I finally got it.
The values from E to 2xIC can be calculated using the following formula:
$$W=2$$
$$LEVEL.MIN = frac{LEVEL-1-1}{W} times IC$$
$$LEVEL.MAX = frac{LEVEL-1}{W} times IC$$
answered Jan 30 at 11:22
1Z101Z10
1105
answered Jan 30 at 11:22
1Z101Z10
1105
answered Jan 30 at 11:22
1Z101Z10
1105
answered Jan 30 at 11:22
1Z101Z10
1105
1105
add a comment |
add a comment |
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$begingroup$
What do the different levels mean? What is IC? So I understand that "MIN" is the minimum value of some set, and "MAX" is the maximum value of some set, but what are these sets? Could you give more context to your problem? And how did you obtain the formulae that you wrote?
$endgroup$
– Matti P.
Jan 30 at 10:41
$begingroup$
Each level is a rang of economic values, and I have the IC value as input. They are needed to know in which level to put an item based on its value.
$endgroup$
– 1Z10
Jan 30 at 10:44
$begingroup$
Are there some conditions for the values of A, B, C, D, E, F, G .... ?
$endgroup$
– Matti P.
Jan 30 at 10:45
$begingroup$
Each level from 1 to 3 needs to have the same width = max - min Each level from 4 to 5 needs to have the same width = max - min and Level[N].min = Level[N-1].max
$endgroup$
– 1Z10
Jan 30 at 10:49