@dave or anyone: can u pls explain the logic of n&3 in dave's solution? why is it subtracted from n(which is divided by 4 using >>2) and what does n& 3 indicate?
On Sat, May 7, 2011 at 9:38 AM, Dave <[email protected]> wrote: > @Umer: Do you suppose that you can convert an int into a string > without using division or mod, either directly or indirectly? > > Dave > > On May 4, 1:12 am, Umer Farooq <[email protected]> wrote: > > I'm surprised to see that why are you guys making this problem so > complex. > > This problem can be solved in two steps only. > > > > 1- Convert the given int into string > > 2- Check if the last character is 0 or 5. // it yes, then return true > else > > return false > > > > for e.g. > > > > 125 (last character is 5 ... therefore it is divisible by 5) > > 120 (last character is 0 ... therefore it is divisible by 5) > > 111 (last character is 1 ... therefore it is not divisible by 5) > > > > The pseudo-code has been written in my above email. > > > > > > > > > > > > On Wed, May 4, 2011 at 1:49 AM, Dave <[email protected]> wrote: > > > @anshu: Spoiler alert... I was thinking of something more along the > > > line > > > > > int DivisibleBy5 (int n) > > > { > > > n = n > 0 ? n : -n; > > > while( n > 0 ) > > > n = (n >> 2) - (n & 3); > > > return (n == 0); > > > } > > > > > To see that it works, write n as n = 4*a + b, where 0 <= b <= 3. Then > > > the iteration replaces n by a - b. Consider (4*a + b) + (a - b), the > > > sum of two consecutive values of n. This simplifies to 5*a, which is a > > > multiple of 5. Thus, n is a multiple of 5 before an iteration if and > > > only if it also is a multiple of 5 afterwards, > > > > > It is clearly log n because n is replaced by a number no greater than > > > n/4 on each iteration. > > > > > Examples: > > > n = 125. The sequence of iterates is 30, 5, 0. Ergo, 125 is a multiple > > > of 5. > > > n = 84. The sequence of iterates is 21, 4, -1. Ergo, 84 is not a > > > multiple of 5. > > > > > Dave > > > > > On May 3, 3:13 am, anshu <[email protected]> wrote: > > > > algorithm: > > > > > > if any number(a) is divisible by 5 it can be wriiten as 4*b + b --> > > > > this cleary shows the last two bit of a & b will be same. > > > > > > lets understand by an example (35)10 = (100011)2 > > > > > > xx1100 > > > > + xx11 > > > > --------- > > > > 100011 > > > > > > now this clearly shows we can calculate the unknowns(x) by traversing > > > > right to left > > > > > > code: > > > > > > int main() > > > > { > > > > int n, m; > > > > cin >> n; > > > > m = n; > > > > > > int a, b; > > > > int i=2; > > > > > > a = (m&3)<<2; > > > > b = (m&3); > > > > m >>= 2; > > > > > > bool rem = 0,s,r; > > > > > > while (m>3) > > > > { > > > > r = a&(1<<i); > > > > s = r^(m&1)^rem; > > > > b = b|(s<<i); > > > > a = a|(s<<(i+2)); > > > > rem = (r&s)|(s&rem)|(r&rem) ; > > > > i++; > > > > m >>= 1; > > > > } > > > > > > if (a+b == n) cout << "yes\n"; > > > > else cout << "no\n"; > > > > > > return 0; > > > > > > }- Hide quoted text - > > > > > > - Show quoted text - > > > > > -- > > > You received this message because you are subscribed to the Google > Groups > > > "Algorithm Geeks" group. > > > To post to this group, send email to [email protected]. > > > To unsubscribe from this group, send email to > > > [email protected]. > > > For more options, visit this group at > > >http://groups.google.com/group/algogeeks?hl=en. > > > > -- > > Umer- Hide quoted text - > > > > - Show quoted text - > > -- > You received this message because you are subscribed to the Google Groups > "Algorithm Geeks" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/algogeeks?hl=en. > > -- "People often say that motivation doesn't last. Well, neither does bathing - that's why we recommend it daily." -- You received this message because you are subscribed to the Google Groups "Algorithm Geeks" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
