I have a project I need to do for my online class and I can not figure out how to do this. So it is suppose to be a program where you put a base and an exponent.
Let's say your base was 4 and exponent was 3 it should give an answer that looks like this. 4 exponent 0 = 1 4 exponent 1 = 4 4 exponent 2 = 16 4 exponent 3 = 64.
Related
Table 1:
Position
Team
1
MCI
2
LIV
3
MAN
4
CHE
5
LEI
6
AST
7
BOU
8
BRI
9
NEW
10
TOT
Table 2
Position
Team
1
LIV
2
MAN
3
MCI
4
CHE
5
AST
6
LEI
7
BOU
8
TOT
9
BRI
10
NEW
Output I'm looking for is
Position difference = 10 as that is the total of the positional difference. How can I do this in excel/google sheets? So the positional difference is always a positive even if it goes up or down. Think of it as a league table.
Table 2 New (using formula to find positional difference):
Position
Team
Positional Difference
1
LIV
1
2
MAN
1
3
MCI
2
4
CHE
0
5
AST
1
6
LEI
1
7
BOU
0
8
TOT
2
9
BRI
1
10
NEW
1
Try this:
=IFNA(ABS(INDEX(A:B,MATCH(E2,B:B,0),1)-D2),"-")
Assuming that table 1 is at columns A:B:
Minimum number states in the DFA accepting strings (base 3 i.e,, ternary form) congruent to 5 modulo 6?
I have tried but couldn't do it.
At first sight, It seems to have 6 states but then it can be minimised further.
Let's first see the state transition table:
Here, the states q0, q1, q2,...., q5 corresponds to the states with modulo 0,1,2,..., 5 respectively when divided by 6. q0 is our initial state and since we need modulo 5 therefore our final state will be q5
Few observations drawn from above state transition table:
states q0, q2 and q4 are exactly same
states q1, q3 and q5 are exactly same
The states which make transitions to the same states on the same inputs can be merged into a single state.
Note: Final and Non-final states can never be merged.
Therefore, we can merge q0, q2, q4 together and q1, q3 together leaving the state q5 aloof from collation.
The final Minimal DFA has 3 states as shown below:
Let's look at a few strings in the language:
12 = 1*3 + 2 = 5 ~ 5 (mod 6)
102 = 1*9 + 0*3 + 2 = 11 ~ 5 (mod 6)
122 = 1*9 + 2*3 + 2 = 17 ~ 5 (mod 6)
212 = 2*9 + 1*3 + 2 = 23 ~ 5 (mod 6)
1002 = 1*18 + 0*9 + 0*9 + 2 = 29 ~ 5 (mod 6)
We notice that all the strings end in 2. This makes sense since 6 is a multiple of 3 and the only way to get 5 from a multiple of 3 is to add 2. Based on this, we can try to solve the problem of strings congruent to 3 modulo 6:
10 = 3
100 = 9
120 = 15
210 = 21
1000 = 27
There's not a real pattern emerging, but consider this: every base-3 number ending in 0 is definitely divisible by 3. The ones that are even are also divisible by 6; so the odd numbers whose base-3 representation ends in 0 must be congruent to 3 mod 6. Because all the powers of 3 are odd, we know we have an odd number if the number of 1s in the string is odd.
So, our conditions are:
the string begins with a 1;
the string has an odd number of 1s;
the string ends with 2;
the string can contain any number of 2s and 0s.
To get the minimum number of states in such a DFA, we can use the Myhill-Nerode theorem beginning with the empty string:
the empty string can be followed by any string in the language. Call its equivalence class [e]
the string 0 cannot be followed by anything since valid base-3 representations don't have leading 0s. Call its equivalence class [0].
the string 1 must be followed with stuff that has an even number of 1s in it ending with a 2. Call its equivalence class [1].
the string 2 can be followed by anything in the language. Indeed, you can verify that putting a 2 at the front of any string in the language gives another string in the language. However, it can also be followed by strings beginning with 0. Therefore, its class is new: [2].
the string 00 can't be followed by anything to fix it; its class is the same as its prefix 0, [0]. same for the string 01.
the string 10 can be followed by any string with an even number of 1s that ends in a 2; it is therefore equivalent to the class [1].
the string 11 can be followed by any string in the language whatever; indeed, you can verify prepending 11 in front of any string in the language gives another solution. However, it can also be followed by strings beginning with 0. Therefore, its class is the same as [2].
12 can be followed by a string with an even number of 1s ending in 2, as well as by the empty string (since 12 is in fact in the language). This is a new class, [12].
21 is equivalent to 1; class [1]
22 is equivalent to 2; class [2]
20 is equivalent to 2; class [2]
120 is indistinguishable from 1; its class is [1].
121 is indistinguishable from [2].
122 is indistinguishable from [12].
We have seen no new equivalence classes on new strings of length 3; so, we know we have seen all the equivalence classes. They are the following:
[e]: any string in the language can follow this
[0]: no string can follow this
[1]: a string with an even number of 1s ending in 2 can follow this
[2]: same as [e] but also strings beginning with 0
[12]: same as [1] but also the empty string
This means that a minimal DFA for our language has five states. Here is the DFA:
[0]
^
|
0
|
----->[e]--2-->[2]<-\
| ^ |
| | |
1 __1__/ /
| / /
| | 1
V V |
[1]--2-->[12]
^ |
| |
\___0___/
(transitions not pictured are self-loops on the respective states).
Note: I expected this DFA to have 6 states, as Welbog pointed out in the other answer, so I might have missed an equivalence class. However, the DFA seems right after checking a few examples and thinking about what it's doing: you can only get to accepting state [12] by seeing a 2 as the last symbol (definitely necessary) and you can only get to state [12] from state [1] and you must have seen an odd number of 1s to get to [1]…
The minimum number of states for almost all modulus problems is the base of the modulus. The general strategy is one state for every modulus, as transitions between moduli are independent of what the previous numbers were. For example, if you're in state r4 (representing x = 4 (mod 6)), and you encounter a 1 as your next input, your new modulus is 4x6+1 = 25 = 1 (mod 6), so the transition from r4 on input 1 is to r1. You'll find that the start state and r0 can be merged, for a total of 6 states.
I was wondering how modulo works. I know how it works when the bigger number comes first, but not the opposite. I know that 7 % 3 = 1 as 3 goes up to 7 2 times and the remaining is 1. However, when it's 3 % 7. I have used the calculator it shows 3. Is this because 7 goes up to 3 zero times and the remaining is 3? Is that how it works?
Your reasoning is correct. Any time the divisor is larger than the dividend, the result of the modulo operation equals the dividend.
7*x + y = 3, x and y are int, and x >= 0,
what y = ?
yes, y = 3.
3 MOD 7 = 0R3
This is so because 3/7 is >0 but <1
Mod just means you take the remainder after performing the division. When you divide 3 by 7 you get 3= 0*7 + 3 which means that the remainder is 3.
7/3 -> 3 goes into 7 2 times, and 7 - (3x2) = 1, so your modulus is 1
3/7 -> 7 goes into 3 zero times, and 3 - 0 = 3, so here your modulus is 3
I know that tensors have an apply method, but this only applies a function to each element. Is there an elegant way to do row-wise operations? For example, can I multiply each row by a different value?
Say
A =
1 2 3
4 5 6
7 8 9
and
B =
1
2
3
and I want to multiply each element in the ith row of A by the ith element of B to get
1 2 3
8 10 12
21 24 27
how would I do that?
See this link: Torch - Apply function over dimension
(Thanks to Alexander Lutsenko for providing it. I just moved it to the answer.)
One possibility is to expand B as follow:
1 1 1
2 2 2
3 3 3
[torch.DoubleTensor of size 3x3]
Then you can use element-wise multiplication directly:
local A = torch.Tensor{{1,2,3},{4,5,6},{7,8,9}}
local B = torch.Tensor{1,2,3}
local C = A:cmul(B:view(3,1):expand(3,3))
We have a legacy COBOL program that formats the iso 8583 0100 authorization request. Recently we were told the track II data was invalid due to the separator. The track II data is in a PIC X() field and we simply replace the = with the character D before running the data through a binary intrinsic 2 bytes at a time.
We are told that the character is converting to 4 on their side. My question is: What character should we use to replace the = character? Or do we leave the = character alone?
Thanks for any guidance.
Track 2 data is stored on a Credit card as Binary Coded Decimal with parity and the other possible binary values are used for controls.
Hex ASCII Meaning
0 0 0
1 1 1
2 2 2
3 3 3
4 4 4
5 5 5
6 6 6
7 7 7
8 8 8
9 9 9
A : (not used)
B ; Start Sentinel
C < (not used)
D = Field Separator
E > (not used)
F ? End Sentinel
I have a feeling that the "binary intrinsic" is simply converting ASCII to BCD, which if you used the standard ASCII characters you would get what you want, as the = is a 0x3D in ASCII and if you strip off the first nibble you are left with a 0xD.