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 <[email protected]> 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 <[email protected]> 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 <[email protected]> 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
> > > <[email protected]> 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 <[email protected]>
> > > 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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> > --
> > *
> >
> > Regards*
> > *"The Coder"*
> >
> > *"Life is a Game. The more u play, the more u win, the more u win , the
> > more successfully u play"*
>
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