Re: Strange problem with "for" and "while"

*To*: mathgroup at smc.vnet.net*Subject*: [mg68379] Re: Strange problem with "for" and "while"*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Thu, 3 Aug 2006 06:06:50 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <eapru8$s5i$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

LordBeotian wrote: > When I try to compute this: > > For[k = 1, k < 10, k++, > i := 0; > While [k > 1, i++; k--]; > Print[i, k]] > > Mathematica outputs a neverending sequence of "1,1" (and it is impossible to > abort the computation!) > > When instead I try to manually do the "for" and compute > > k := ...; > i = 0; > While [k > 1, i++; k--]; > Print[i, k] > > giving to k all the values 1,2,...,9 the computation are all correct (the > outputs are "01", "11", "21", ..., "81". > > I cannot understand what is the problem. > Mathematica is right, since it follows and does exactly what you coded although possibly not what you intended! Think carefully about the real value of k; in other word try to think as if you were the processor. During the *first* iteration, the While statement is *not* executed since k is equal to 1; therefore, Mathematica prints 01 -- you can verify that by adding an unconditional Break[] expression after the Print statement [1]. Then, the increment expression of the For loop is executed and the value of k reaches 2. From the second iteration onwards, the While loop is going to be executed every time since k will always be equal to two when reaching the While statement. Let's see what happens here. k is equal to two. i is set to to zero. Is k greater than one? Yes, thus the While loop is executed: i is incremented by one from zero to one, and k is decremented by one from two to one. Then, the condition to the While loop is tested again and failed to be met since k is now equal to one. Mathematica ends the While loop and print 11. We are back to the For loop now, and k is incremented from one, its current value, to two. Then, i is set to zero and the answer to the question "Is k greater than one?" is positive since the current value of k is two. Then... but I imagine you have seen the pattern by now, pattern of a never ending loop indeed. One way of solving this issue is using an additional variable in place of k within the While loop. In the following example, you can see that j is always displayed with the value one. However, k is correctly incremented and the iterations end. For[k = 1, k < 10, k++, i = 0; j = k; While[j > 1, i++; j--]; Print[i, " ", j, " ", k] ] yields 0" "1" "1 1" "1" "2 2" "1" "3 3" "1" "4 4" "1" "5 5" "1" "6 6" "1" "7 7" "1" "8 8" "1" "9 HTH, Jean-Marc [1] The following loop ends after the first iteration: For[k = 1, k < 10, k++, i := 0; While[k > 1, i++; k--]; Print[i, k]; Break[]]