Re: [algogeeks] Re: adobe problem---array
i like the idea whereby when you xor again with all xored, essentially, we are removing one xor and the result would be the left number(which were repeated odd number of times) however, this will simply not work when a] there are multiple single numbers like 1,2,1,3,1,4,5 b] this would need two occurrence of three time repeated numbers to be adjacent eg : for {5,3,3,1,5,7,7,5,8,8} this won't work but what i think is that a bit modification of this approach can be used to identify the numbers which occur odd times so the new set would be {5,1,5,5} now can we proceed from here, still thinking... Best Regards Ashish Goel Think positive and find fuel in failure +919985813081 +919966006652 On Fri, Jul 9, 2010 at 1:10 AM, Anand anandut2...@gmail.com wrote: One more approach using XOR to find the element repeated thrice. Complexity: O(n). Space :0 http://codepad.org/p82TGhjR main() { int arr[]= {5,3,3,1,5,5,7,7,8,8}; int len, set_bit_no, x,y,i; int xor, prev; len = sizeof(arr)/sizeof(arr[0]); xor = arr[0]; x = y=0; for(i=1;ilen;i++) { xor ^= arr[i]; } printf(xor:%d\n,xor); for(i=0;ilen;i++) { xor ^= arr[i]; if(xor == 0 prev == arr[i]) { printf(Found:%d\n, arr[i]); break; } prev = arr[i]; } } On Thu, Jul 8, 2010 at 6:46 AM, jalaj jaiswal jalaj.jaiswa...@gmail.comwrote: @ any solution less then nlogn would do + O(1) space On Thu, Jul 8, 2010 at 12:38 AM, souravsain souravs...@gmail.com wrote: @jalaj Are we looking for a better than )(nlogn) time and O(1) space solution? What if our target? If a solution is required simple, then as mentioned by Satya, sort the numbers in O(nlogn) time and scan once in O(n) time. So we get the number repeated 3 times in O(nlogn) time and O(1) space. Sourav On Jul 7, 7:36 pm, Priyanka Chatterjee dona.1...@gmail.com wrote: I am sceptical whether any XOR solution exits for your question. But if the question is modified as : *Only one number repeats once,* some no.s repeat twice and only one number repeat thrice, here is the XOR solution for that. suppose the sample array is A[]={1, 3,3,5,5,5, 7,7,8,8} in the example 1 repeats once and 5 repeats thrice. 1let T= XOR( all elements)= 1^5. (all elements occurring even no of times nullify) -O(N) ( let x=1, y=5 As we know the no. repeating once and the no. repeating thrice are unequal, there must exist some bit 'k' such that x[k]!=y[k]. There may be more than such bits in x and y. But one such bit certainly yields T[k]=1 after x^y) 2 Now traverse along each bit of T( in binary) from left or right and consider T[i] =1 which is encountered first. store it . let b=i; (O(M) time and O(M) space to store binary if M is the bit length of T.) 3 T1= XOR(all elements in given array having bit b as 1). (O(N) time and O(M) space) ( time is O(MN) but as M=32 , complexity remain O(N)) 4 T0= XOR( all elements in given array having bit b as 0) (O(N) time and O(M) space) One of (T1,T0) gives the no. that repeats once and the other gives the no that repeats thrice. 6 Now traverse the along array A and compute count for T1 and T0. The count that equals 3 gives the corresponding no. repeating thrice. -O(N) Time complexity is O(N+M) . Linear space complexity is O(M) to store binary form. But this algo certainly fails if more than one no. repeats once. -- Thanks Regards, Priyanka Chatterjee Final Year Undergraduate Student, Computer Science Engineering, National Institute Of Technology,Durgapur Indiahttp://priyanka-nit.blogspot.com/- 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 algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.comalgogeeks%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en. -- With Regards, Jalaj Jaiswal +919026283397 B.TECH IT IIIT ALLAHABAD -- You received this message because you are subscribed to the Google Groups Algorithm Geeks group. To post to this group, send email to algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.comalgogeeks%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en. -- You received this message because you are subscribed to the Google Groups Algorithm Geeks group. To post to this group, send email to algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.comalgogeeks%2bunsubscr...@googlegroups.com . For more options, visit this group at
Re: [algogeeks] Re: adobe problem---array
@all: First of all apologize for posting the wrong solution. The whole idea behind it was first find the xor of all array elements and this will have xor of only those value which got repeated once and thrice b'cos element which got repeated twice gets nullified. Now intention behind xoring it again was to remove the element which got repeated once. and checking the previous value would catch the element which got repeated thrice which allows us to break through the loop. But for some corner cases it fails. Thanks all of you to bring it to notice. Will work on it to find something better which covers all cases. On Fri, Jul 9, 2010 at 6:39 AM, Ashish Goel ashg...@gmail.com wrote: i like the idea whereby when you xor again with all xored, essentially, we are removing one xor and the result would be the left number(which were repeated odd number of times) however, this will simply not work when a] there are multiple single numbers like 1,2,1,3,1,4,5 b] this would need two occurrence of three time repeated numbers to be adjacent eg : for {5,3,3,1,5,7,7,5,8,8} this won't work but what i think is that a bit modification of this approach can be used to identify the numbers which occur odd times so the new set would be {5,1,5,5} now can we proceed from here, still thinking... Best Regards Ashish Goel Think positive and find fuel in failure +919985813081 +919966006652 On Fri, Jul 9, 2010 at 1:10 AM, Anand anandut2...@gmail.com wrote: One more approach using XOR to find the element repeated thrice. Complexity: O(n). Space :0 http://codepad.org/p82TGhjR main() { int arr[]= {5,3,3,1,5,5,7,7,8,8}; int len, set_bit_no, x,y,i; int xor, prev; len = sizeof(arr)/sizeof(arr[0]); xor = arr[0]; x = y=0; for(i=1;ilen;i++) { xor ^= arr[i]; } printf(xor:%d\n,xor); for(i=0;ilen;i++) { xor ^= arr[i]; if(xor == 0 prev == arr[i]) { printf(Found:%d\n, arr[i]); break; } prev = arr[i]; } } On Thu, Jul 8, 2010 at 6:46 AM, jalaj jaiswal jalaj.jaiswa...@gmail.comwrote: @ any solution less then nlogn would do + O(1) space On Thu, Jul 8, 2010 at 12:38 AM, souravsain souravs...@gmail.comwrote: @jalaj Are we looking for a better than )(nlogn) time and O(1) space solution? What if our target? If a solution is required simple, then as mentioned by Satya, sort the numbers in O(nlogn) time and scan once in O(n) time. So we get the number repeated 3 times in O(nlogn) time and O(1) space. Sourav On Jul 7, 7:36 pm, Priyanka Chatterjee dona.1...@gmail.com wrote: I am sceptical whether any XOR solution exits for your question. But if the question is modified as : *Only one number repeats once,* some no.s repeat twice and only one number repeat thrice, here is the XOR solution for that. suppose the sample array is A[]={1, 3,3,5,5,5, 7,7,8,8} in the example 1 repeats once and 5 repeats thrice. 1let T= XOR( all elements)= 1^5. (all elements occurring even no of times nullify) -O(N) ( let x=1, y=5 As we know the no. repeating once and the no. repeating thrice are unequal, there must exist some bit 'k' such that x[k]!=y[k]. There may be more than such bits in x and y. But one such bit certainly yields T[k]=1 after x^y) 2 Now traverse along each bit of T( in binary) from left or right and consider T[i] =1 which is encountered first. store it . let b=i; (O(M) time and O(M) space to store binary if M is the bit length of T.) 3 T1= XOR(all elements in given array having bit b as 1). (O(N) time and O(M) space) ( time is O(MN) but as M=32 , complexity remain O(N)) 4 T0= XOR( all elements in given array having bit b as 0) (O(N) time and O(M) space) One of (T1,T0) gives the no. that repeats once and the other gives the no that repeats thrice. 6 Now traverse the along array A and compute count for T1 and T0. The count that equals 3 gives the corresponding no. repeating thrice. -O(N) Time complexity is O(N+M) . Linear space complexity is O(M) to store binary form. But this algo certainly fails if more than one no. repeats once. -- Thanks Regards, Priyanka Chatterjee Final Year Undergraduate Student, Computer Science Engineering, National Institute Of Technology,Durgapur Indiahttp://priyanka-nit.blogspot.com/- 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 algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.comalgogeeks%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en. -- With Regards, Jalaj Jaiswal +919026283397 B.TECH IT IIIT ALLAHABAD -- You received this message
Re: [algogeeks] Re: adobe problem---array
@ any solution less then nlogn would do + O(1) space On Thu, Jul 8, 2010 at 12:38 AM, souravsain souravs...@gmail.com wrote: @jalaj Are we looking for a better than )(nlogn) time and O(1) space solution? What if our target? If a solution is required simple, then as mentioned by Satya, sort the numbers in O(nlogn) time and scan once in O(n) time. So we get the number repeated 3 times in O(nlogn) time and O(1) space. Sourav On Jul 7, 7:36 pm, Priyanka Chatterjee dona.1...@gmail.com wrote: I am sceptical whether any XOR solution exits for your question. But if the question is modified as : *Only one number repeats once,* some no.s repeat twice and only one number repeat thrice, here is the XOR solution for that. suppose the sample array is A[]={1, 3,3,5,5,5, 7,7,8,8} in the example 1 repeats once and 5 repeats thrice. 1let T= XOR( all elements)= 1^5. (all elements occurring even no of times nullify) -O(N) ( let x=1, y=5 As we know the no. repeating once and the no. repeating thrice are unequal, there must exist some bit 'k' such that x[k]!=y[k]. There may be more than such bits in x and y. But one such bit certainly yields T[k]=1 after x^y) 2 Now traverse along each bit of T( in binary) from left or right and consider T[i] =1 which is encountered first. store it . let b=i; (O(M) time and O(M) space to store binary if M is the bit length of T.) 3 T1= XOR(all elements in given array having bit b as 1). (O(N) time and O(M) space) ( time is O(MN) but as M=32 , complexity remain O(N)) 4 T0= XOR( all elements in given array having bit b as 0) (O(N) time and O(M) space) One of (T1,T0) gives the no. that repeats once and the other gives the no that repeats thrice. 6 Now traverse the along array A and compute count for T1 and T0. The count that equals 3 gives the corresponding no. repeating thrice. -O(N) Time complexity is O(N+M) . Linear space complexity is O(M) to store binary form. But this algo certainly fails if more than one no. repeats once. -- Thanks Regards, Priyanka Chatterjee Final Year Undergraduate Student, Computer Science Engineering, National Institute Of Technology,Durgapur Indiahttp://priyanka-nit.blogspot.com/- 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 algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.comalgogeeks%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en. -- With Regards, Jalaj Jaiswal +919026283397 B.TECH IT IIIT ALLAHABAD -- You received this message because you are subscribed to the Google Groups Algorithm Geeks group. To post to this group, send email to algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
Re: [algogeeks] Re: adobe problem---array
One more approach using XOR to find the element repeated thrice. Complexity: O(n). Space :0 http://codepad.org/p82TGhjR main() { int arr[]= {5,3,3,1,5,5,7,7,8,8}; int len, set_bit_no, x,y,i; int xor, prev; len = sizeof(arr)/sizeof(arr[0]); xor = arr[0]; x = y=0; for(i=1;ilen;i++) { xor ^= arr[i]; } printf(xor:%d\n,xor); for(i=0;ilen;i++) { xor ^= arr[i]; if(xor == 0 prev == arr[i]) { printf(Found:%d\n, arr[i]); break; } prev = arr[i]; } } On Thu, Jul 8, 2010 at 6:46 AM, jalaj jaiswal jalaj.jaiswa...@gmail.comwrote: @ any solution less then nlogn would do + O(1) space On Thu, Jul 8, 2010 at 12:38 AM, souravsain souravs...@gmail.com wrote: @jalaj Are we looking for a better than )(nlogn) time and O(1) space solution? What if our target? If a solution is required simple, then as mentioned by Satya, sort the numbers in O(nlogn) time and scan once in O(n) time. So we get the number repeated 3 times in O(nlogn) time and O(1) space. Sourav On Jul 7, 7:36 pm, Priyanka Chatterjee dona.1...@gmail.com wrote: I am sceptical whether any XOR solution exits for your question. But if the question is modified as : *Only one number repeats once,* some no.s repeat twice and only one number repeat thrice, here is the XOR solution for that. suppose the sample array is A[]={1, 3,3,5,5,5, 7,7,8,8} in the example 1 repeats once and 5 repeats thrice. 1let T= XOR( all elements)= 1^5. (all elements occurring even no of times nullify) -O(N) ( let x=1, y=5 As we know the no. repeating once and the no. repeating thrice are unequal, there must exist some bit 'k' such that x[k]!=y[k]. There may be more than such bits in x and y. But one such bit certainly yields T[k]=1 after x^y) 2 Now traverse along each bit of T( in binary) from left or right and consider T[i] =1 which is encountered first. store it . let b=i; (O(M) time and O(M) space to store binary if M is the bit length of T.) 3 T1= XOR(all elements in given array having bit b as 1). (O(N) time and O(M) space) ( time is O(MN) but as M=32 , complexity remain O(N)) 4 T0= XOR( all elements in given array having bit b as 0) (O(N) time and O(M) space) One of (T1,T0) gives the no. that repeats once and the other gives the no that repeats thrice. 6 Now traverse the along array A and compute count for T1 and T0. The count that equals 3 gives the corresponding no. repeating thrice. -O(N) Time complexity is O(N+M) . Linear space complexity is O(M) to store binary form. But this algo certainly fails if more than one no. repeats once. -- Thanks Regards, Priyanka Chatterjee Final Year Undergraduate Student, Computer Science Engineering, National Institute Of Technology,Durgapur Indiahttp://priyanka-nit.blogspot.com/- 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 algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.comalgogeeks%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en. -- With Regards, Jalaj Jaiswal +919026283397 B.TECH IT IIIT ALLAHABAD -- You received this message because you are subscribed to the Google Groups Algorithm Geeks group. To post to this group, send email to algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.comalgogeeks%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en. -- You received this message because you are subscribed to the Google Groups Algorithm Geeks group. To post to this group, send email to algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
Re: [algogeeks] Re: adobe problem---array
Then do a inplace merge sort / a quick sort and then get a number which repeats 3 times On Thu, Jul 8, 2010 at 7:16 PM, jalaj jaiswal jalaj.jaiswa...@gmail.comwrote: @ any solution less then nlogn would do + O(1) space On Thu, Jul 8, 2010 at 12:38 AM, souravsain souravs...@gmail.com wrote: @jalaj Are we looking for a better than )(nlogn) time and O(1) space solution? What if our target? If a solution is required simple, then as mentioned by Satya, sort the numbers in O(nlogn) time and scan once in O(n) time. So we get the number repeated 3 times in O(nlogn) time and O(1) space. Sourav On Jul 7, 7:36 pm, Priyanka Chatterjee dona.1...@gmail.com wrote: I am sceptical whether any XOR solution exits for your question. But if the question is modified as : *Only one number repeats once,* some no.s repeat twice and only one number repeat thrice, here is the XOR solution for that. suppose the sample array is A[]={1, 3,3,5,5,5, 7,7,8,8} in the example 1 repeats once and 5 repeats thrice. 1let T= XOR( all elements)= 1^5. (all elements occurring even no of times nullify) -O(N) ( let x=1, y=5 As we know the no. repeating once and the no. repeating thrice are unequal, there must exist some bit 'k' such that x[k]!=y[k]. There may be more than such bits in x and y. But one such bit certainly yields T[k]=1 after x^y) 2 Now traverse along each bit of T( in binary) from left or right and consider T[i] =1 which is encountered first. store it . let b=i; (O(M) time and O(M) space to store binary if M is the bit length of T.) 3 T1= XOR(all elements in given array having bit b as 1). (O(N) time and O(M) space) ( time is O(MN) but as M=32 , complexity remain O(N)) 4 T0= XOR( all elements in given array having bit b as 0) (O(N) time and O(M) space) One of (T1,T0) gives the no. that repeats once and the other gives the no that repeats thrice. 6 Now traverse the along array A and compute count for T1 and T0. The count that equals 3 gives the corresponding no. repeating thrice. -O(N) Time complexity is O(N+M) . Linear space complexity is O(M) to store binary form. But this algo certainly fails if more than one no. repeats once. -- Thanks Regards, Priyanka Chatterjee Final Year Undergraduate Student, Computer Science Engineering, National Institute Of Technology,Durgapur Indiahttp://priyanka-nit.blogspot.com/- 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 algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.comalgogeeks%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en. -- With Regards, Jalaj Jaiswal +919026283397 B.TECH IT IIIT ALLAHABAD -- You received this message because you are subscribed to the Google Groups Algorithm Geeks group. To post to this group, send email to algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.comalgogeeks%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en. -- You received this message because you are subscribed to the Google Groups Algorithm Geeks group. To post to this group, send email to algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
Re: [algogeeks] Re: adobe problem---array
@anand Your code wont work for many of the cases int arr[]= {5,3,1,11,5,7,11,5,8}; please check the correctness before posting any solution -- Regards Jitendra Kushwaha MNNIT, Allahabad -- You received this message because you are subscribed to the Google Groups Algorithm Geeks group. To post to this group, send email to algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.
Re: [algogeeks] Re: adobe problem---array
@Anand: Awesome solution ,it works even if more than 1 number repeats once... On 9 July 2010 01:10, Anand anandut2...@gmail.com wrote: One more approach using XOR to find the element repeated thrice. Complexity: O(n). Space :0 http://codepad.org/p82TGhjR main() { int arr[]= {5,3,3,1,5,5,7,7,8,8}; int len, set_bit_no, x,y,i; int xor, prev; len = sizeof(arr)/sizeof(arr[0]); xor = arr[0]; x = y=0; for(i=1;ilen;i++) { xor ^= arr[i]; } printf(xor:%d\n,xor); for(i=0;ilen;i++) { xor ^= arr[i]; if(xor == 0 prev == arr[i]) { printf(Found:%d\n, arr[i]); break; } prev = arr[i]; } } On Thu, Jul 8, 2010 at 6:46 AM, jalaj jaiswal jalaj.jaiswa...@gmail.comwrote: @ any solution less then nlogn would do + O(1) space On Thu, Jul 8, 2010 at 12:38 AM, souravsain souravs...@gmail.com wrote: @jalaj Are we looking for a better than )(nlogn) time and O(1) space solution? What if our target? If a solution is required simple, then as mentioned by Satya, sort the numbers in O(nlogn) time and scan once in O(n) time. So we get the number repeated 3 times in O(nlogn) time and O(1) space. Sourav On Jul 7, 7:36 pm, Priyanka Chatterjee dona.1...@gmail.com wrote: I am sceptical whether any XOR solution exits for your question. But if the question is modified as : *Only one number repeats once,* some no.s repeat twice and only one number repeat thrice, here is the XOR solution for that. suppose the sample array is A[]={1, 3,3,5,5,5, 7,7,8,8} in the example 1 repeats once and 5 repeats thrice. 1let T= XOR( all elements)= 1^5. (all elements occurring even no of times nullify) -O(N) ( let x=1, y=5 As we know the no. repeating once and the no. repeating thrice are unequal, there must exist some bit 'k' such that x[k]!=y[k]. There may be more than such bits in x and y. But one such bit certainly yields T[k]=1 after x^y) 2 Now traverse along each bit of T( in binary) from left or right and consider T[i] =1 which is encountered first. store it . let b=i; (O(M) time and O(M) space to store binary if M is the bit length of T.) 3 T1= XOR(all elements in given array having bit b as 1). (O(N) time and O(M) space) ( time is O(MN) but as M=32 , complexity remain O(N)) 4 T0= XOR( all elements in given array having bit b as 0) (O(N) time and O(M) space) One of (T1,T0) gives the no. that repeats once and the other gives the no that repeats thrice. 6 Now traverse the along array A and compute count for T1 and T0. The count that equals 3 gives the corresponding no. repeating thrice. -O(N) Time complexity is O(N+M) . Linear space complexity is O(M) to store binary form. But this algo certainly fails if more than one no. repeats once. -- Thanks Regards, Priyanka Chatterjee Final Year Undergraduate Student, Computer Science Engineering, National Institute Of Technology,Durgapur Indiahttp://priyanka-nit.blogspot.com/- 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 algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.comalgogeeks%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en. -- With Regards, Jalaj Jaiswal +919026283397 B.TECH IT IIIT ALLAHABAD -- You received this message because you are subscribed to the Google Groups Algorithm Geeks group. To post to this group, send email to algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.comalgogeeks%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en. -- You received this message because you are subscribed to the Google Groups Algorithm Geeks group. To post to this group, send email to algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.comalgogeeks%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en. -- Thanks Regards, Priyanka Chatterjee Final Year Undergraduate Student, Computer Science Engineering, National Institute Of Technology,Durgapur India http://priyanka-nit.blogspot.com/ -- You received this message because you are subscribed to the Google Groups Algorithm Geeks group. To post to this group, send email to algoge...@googlegroups.com. To unsubscribe from this group, send email to algogeeks+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/algogeeks?hl=en.