Post by thread:[OT]: C Question. Please help!

Hi, as there are more variables than equations, there is no solution at all (theoretically), or better, there are infinite number of values. However, as there are all three variables integers and they are constrained (8-bit vars), it is an integer programming problem I think with the goal to minimize the difference between lhs and rhs. I am not sure it is a problem to be solved with a PIC. A brute force approach may be used, though: as Num is also constrained (I think so from the example), at least x variable should be equal to 1. However, it would be easy to calculate the upper bound for every variable, then use a brute force approach. Let us see your example: 122 = x * ( y * (3*z + 4) + 4) + 18 104 = x * ( y * (3*z + 4) + 4) | | +------- a -------+ So, at first, determine the minimum of a! It is 4, if both y and z are zero. So the upper bound for x is 104 / 4 = 26. The lower bound for x is 1. The upper bound for a is 104 (when x = 1). Let introduce b = y * (3 * z + 4). The upper bound for b is 100. Obviously, y is at least 0 (for b = 0), and y is at most 25 (if z is 0). Then, max of 3 * z is 96 if y = 1, so z should lie between 0 and 32. Now, the number of trials for the brute force method is 26 * 26 * 32 = 21632. It is nonetheless O((Num/4)³), but for a fast processor it may be satisfying. I hope this helps. Regards, Imre PS: this is a q&d approach only, maybe there is a more exact solution. On Mon, 8 Jul 2002, Thomas N wrote: {Quote hidden}> Hello everyone, > > How to I search for x, y, and z variables in the equation below to get the > answer that's closest to Num variable using C language? > > Num = x * ( y * (3*z + 4) + 4) + 18 > > For example, if num = 122. The answer for x is 2, y is 3, z is 4. > > Best regards, > Thomas > > -- > http://www.piclist.com hint: The PICList is archived three different > ways. See http://www.piclist.com/#archives for details. > > > -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

On Mon, 8 Jul 2002, Thomas N wrote: > Hello everyone, > > How to I search for x, y, and z variables in the equation below to get the > answer that's closest to Num variable using C language? > > Num = x * ( y * (3*z + 4) + 4) + 18 > > For example, if num = 122. The answer for x is 2, y is 3, z is 4. This wouldn't have anything to do with loop delay calculation by any chance? :) You've stumbled onto a Diophantine equation. In your subsequent email you stated that x,y, and z are constrained to 8-bit unsigned integers. This limits the number of solutions. However, just because you have three parameters, it doesn't gurantee that you can find an (x,y,z) triplet that will map to all integers in some range Nmin to Nmax. Solving these types of equations in general is much more difficult than solving algebraic equations. Maybe after reading TAOCP: http://www-cs-faculty.stanford.edu/~knuth/taocp.html you'll be able to solve it no time! Now, if this is a loop calculation, I'd suggest rearranging the loop so that the loop delay is a function of one parameter. There are several that exist. For example, the code generated by Nicolai's delay generator produces something like: delay: movlw X1 movwf x movlw Y1 movwf y movlw Z1 movwf z loop decfsz z,f goto $+2 decfsz y,f goto $+2 decfsz x,f goto loop return The time for this loop to execute is: for x,y,z all greater than zero: Delay = (7*z' - 1) + (256*7)*y' + (256*256*7)*x' + 6 + 4 = 7* N + 9 Where, x' = x-1, y' = y-1, and z' = z-1, and N = x':y':z' is a 24-bit integer. (There maybe an error in the above equation that I'm sure someone will point out). From this, it's much easier to calculate the integers x,y,z given a desired delay. Please note that the minimum time doesn't occur for x,y, and z all zero. Instead it occurs for x,y, and z equal to 1. If x,y, or z are 0, then replace them with 256 in the Delay equation. Scott PS. I hope this code isn't being used a timer for bomb. -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.

Note ************ I do not know how others will react to this kind of topic, but I expect to find out. I realize that it would be bad if the list filled up with non pic programming questions from students. **************** Looks to me like it is a class assignment in a c programming class. And yes, some students get on the net and expect to find someone to write and debug their assignments for them by two o'clock the same day. And then others do want to learn and are willing to put effort into the assignment. I think people here would help, I know I would. But you will need to show some effort. The first thing is to reduce that formula so you can understand it better. I would assume that you are studying loops and/or nested loops. That is a big hint as to the program. What is the range the variables can take? I assume that none can be zero, so 1 is the minimum value for all, and none can be greater than 255. But surly a better maximum than 255 can be found for each variable. A lot of programming is just looking at the problem and thinking about it. When you get the concept down to the point where you can explain it and they say "What's so complicated about that?", then you are ready to put "keys to the screen". So reduce the formula and attempt to find some better max values that 255. Then come back with that information. Programming can be fun. Enjoy it. Bill > On Mon, 8 Jul 2002, Thomas N wrote: > > > Hello everyone, > > > > How to I search for x, y, and z variables in the equation below to get the > > answer that's closest to Num variable using C language? > > > > Num = x * ( y * (3*z + 4) + 4) + 18 > > > > For example, if num = 122. The answer for x is 2, y is 3, z is 4. -- http://www.piclist.com hint: The PICList is archived three different ways. See http://www.piclist.com/#archives for details.