I am just trying to understand the number of ways we can form this number,
lets say d is the absolute difference between the numbers and the length of
the numbers is n. Lets say we are considering base 10 numbers, so lets say
radix r = 10.
if you try to see all the comparisons, here is what holds:
for d = 0, possible 2 digit numbers are ( r - d ) x 2 .
For example if n = 2 the possible 2 digit numbers are (10 -2) x 2 = 16
the only place we have to be careful is when d = 0, because then both the
digits will be same and we will have to divide it by the number of digits
because 11 and 11 are both same if we flip the digits. So according to the
logic, if lets say we have the below difference between numbers:
3 2 5 1 so the total number of numbers possible are (10-3) x 2 x (10- 2) x
2 x (10 -5 ) x 2 x (10 - 1 ) x 2
In case when you have 0 0 0 as the difference, possible combinations are
(10 - 0) x 2 / 2 x 1 way x 1 way = 10 ways
Gaurav
On Tue, Dec 13, 2011 at 10:55 AM, Gaurav Kumar <gkuma...@gmail.com> wrote:
> When the difference is 0, the numbers will be repeated:
> 000, 111, 222, 333, 444, 555, 666, 777, 888, 999 but only these are
> possible.
>
> Gaurav
>
>
> On Tue, Dec 13, 2011 at 10:47 AM, Don <dondod...@gmail.com> wrote:
>
>> Moheed,
>> If n=3 and absdiff = {0,0}, your program says that there are 100
>> possible numbers. Can you show me at least 10 of them?
>> Don
>>
>> On Dec 13, 12:24 pm, Moheed Moheed Ahmad <mohe...@gmail.com> wrote:
>> > To get a abs difference of 0 there are 10 ways
>> > similarly getting abs difference of 1 there are 9x2 ways(w1)
>> > for 2 its 8x2 (say w(2)
>> > for 3 its 7x2
>> > .....
>> > for 9 its 1x2(w9)
>> > let w(i) represents the number of ways to get abs diff of i.
>> > So total numbers that are possible from the given abs diff i j k l m
>> ...
>> > (w(i) x w(j) x w(k) x w(l) x.....)
>> >
>> > Now algo will be to scan the given abs diff and multiply the w(i) for
>> each
>> > absdiff .
>> >
>> > int calculate_possible_nums(int absdiff[], int len){
>> > int ways[]={10, 18, 16, 14, 12, 10, 8, 6, 4, 2, 1};
>> > int numways=1;
>> > for ( i=0; i < len; i++){
>> > numways = numways * ways[absdiff[i]];
>> > }
>> > return numways;}
>> >
>> > -Moheed
>> > 'If a man neglects education, he walks lame to the end of his life.'
>> >
>> > On Tue, Dec 13, 2011 at 11:20 PM, Don <dondod...@gmail.com> wrote:
>> > > There should be 39 combinations with that input. You are missing
>> > > numbers which include the digit zero, such as 14610, 30278, and 52056.
>> >
>> > > Don
>> >
>> > > On Dec 13, 11:37 am, tech coder <techcoderonw...@gmail.com> wrote:
>> > > > I tried the problem and written the code for it . it is in java. it
>> is
>> > > > printing all the possible numbers
>> > > > I am treating the differences ans an array of integers.
>> >
>> > > > here is the code
>> >
>> > > > public class Main {
>> >
>> > > > public static void main(String[] args)
>> > > > {
>> > > > int digit[]={3,2,5,1};// array of absolute differences
>> >
>> > > > int digit[]={3,2,5,1};
>> > > > for(int num=1;num<=9;num++) // call with all possible
>> initial
>> > > > numbers
>> > > > findNumber(digit,4,num,0,num);
>> > > > }
>> >
>> > > > public static void findNumber(int digit[],int n,int num,int
>> i,int
>> > > > oldDigit)
>> > > > {
>> > > > if(i==n)
>> > > > {
>> > > > System.out.print(num+" ");
>> > > > return;
>> > > > }
>> >
>> > > > {
>> > > > int o=digit[i]+oldDigit;
>> > > > if(o<10)
>> > > > findNumber(digit,n,10*num+o,i+1,o);
>> > > > o=oldDigit-digit[i];
>> > > > if(o>0)
>> > > > findNumber(digit,n,10*num+o,i+1,o);
>> >
>> > > > }
>> > > > }
>> >
>> > > > }
>> >
>> > > > and here is the output
>> >
>> > > > 14612 14278 14276 25723 25721 25389 25387 36834 36832 36498
>> > > 47945
>> > > > 47943 41389 41387 58612 52498 69723 69721 63167 63165
>> 74612
>> > > > 74278 74276 85723 85721 85389 85387 96834 96832 96498
>> > > > BUILD SUCCESSFUL (total time: 0 seconds)
>> >
>> > > > On Tue, Dec 13, 2011 at 11:11 PM, Dave <dave_and_da...@juno.com>
>> wrote:
>> > > > > @Amir: Presumably, since these are digits in a number, they are
>> > > > > bounded on the bottom by 0 and on the top by radix-1. So in
>> decimal,
>> > > > > if a digit is 7 and the absolute difference between it and the
>> next
>> > > > > digit is 3, there is only one possibility for the next digit, 7-3
>> = 4,
>> > > > > since 7+3 is too large. So only some subset of the 2^(n-1)
>> > > > > combinations of addition and subtraction may be possible.
>> >
>> > > > > Dave
>> >
>> > > > > On Dec 13, 4:15 am, Amir hossein Shahriari
>> > > > > <amir.hossein.shahri...@gmail.com> wrote:
>> > > > > > actually there are infinite number of sequences that match it
>> > > > > > for example if the absolute differences are 3 2 5 1
>> > > > > > one possible sequence is 6 3 5 0 1 one other is 7 4 6 1 2 or 8
>> 5 7 2
>> > > 3
>> > > > > > and you can add any integer value to all elements and the
>> result will
>> > > > > still
>> > > > > > be valid
>> > > > > > actually you can start with any number and and then the second
>> number
>> > > > > will
>> > > > > > be equal to the first number that you chose plus/minus the first
>> > > absolute
>> > > > > > difference and so on
>> >
>> > > > > > so if we are given the first element of the sequence there are
>> > > 2^(n-1)
>> > > > > ways
>> > > > > > to find a valid sequence because for each absolute difference
>> we can
>> > > > > either
>> > > > > > add the absolute difference to the last sequence element or
>> subtract
>> > > the
>> > > > > > absolute difference from it
>> >
>> > > > > > On Mon, Dec 12, 2011 at 9:01 PM, KAY <
>> amulya.manches...@gmail.com>
>> > > > > wrote:
>> > > > > > > If for a number n digits long, the absolute difference between
>> > > > > > > adjacent digits is given, how to find out the number of
>> different
>> > > > > > > numbers with these absolute differences ?
>> >
>> > > > > > > for eg,
>> > > > > > > if n=5
>> > > > > > > and the absolute differences are
>> > > > > > > 3 2 5 1
>> > > > > > > then 1 possible number is
>> > > > > > > 6 3 5 0 1 (because |6-3|=3,|3-5|=2 and so on...)
>> >
>> > > > > > > How many such numbers will be there?
>> >
>> > > > > > > --
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>> >
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>> >
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>> the
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