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--- haas:spring2015:cprog:projects:mbe1 [2015/02/06 19:10] – [Multiplying any double digit number by 11] wedge
+++ haas:spring2015:cprog:projects:mbe1 [2015/02/07 13:31] (current) – wedge
@@ Line 6: / Line 6: @@
 ~~TOC~~
-======Project: MENTAL MATH - MULTIPLY BY 11 (mbe0)======
+======Project: MENTAL MATH - MULTIPLY BY 11 (mbe1)======
 =====Objective=====
@@ Line 274: / Line 274: @@
-====Multiplying any three-digit number by 11====
+====Multiplying a number (of varying digits) by 11====
-In this case we merely extend the pattern from double digits, rippling through a series of comparing each set of two consecutive digits.
+In **mbe0**, we specifically looked at 3 usage cases for our mental math problem: 1-, 2-, and 3-digit number. I limited it to those because, lacking arrays and loops for that project, the code would have gotten impossibly long and complex, plus: I wanted you to focus on the basics of variable usage and if-statements.
-Let's look at 123 x 11:
+Now that we have those down, we can now apply arrays and loops to optimize and enhance a solution, and to allow it to scale to a wider range of possibilities (why limit ourselves to just 1-, 2-, and 3-digit values? Once we see the pattern, we can apply this to 4-, 5-, 6-digit numbers and beyond).
+===3-digits (review)===
+Again, to review, let's look at a 3-digit example. 123 x 11:
 <code>
-x 11 = 1 (1 + 2) (2 + 3) 3
+x 11 = 1       (1 + 2) (2 + 3) 3
-         = 1 3       5       3
+         = (1 + 0) (3 + 0) 5       3  (what are those + 0's? Carry values.)
+         = 1       3       5       3
          = 1353
 </code>
@@ Line 291: / Line 295: @@
 <code>
 x 11 = 5       (5 + 6) (6 + 7) 7
-         = (5 + 1) (1 + 1) 3       7
+         = (5)+1   (11)+1  (13)+0  7  the outside numbers are the carry values
          = 6       2       3       7
          = 6237
@@ Line 305: / Line 309: @@
 A dual benefit of this project is that in addition to extending your programming experience / understanding of C, you could develop this as a mental ability (that is where it originated), and you could then use it as a means of checking your work.
+===4-digits===
+Now let us process a 4-digit example (look for similarities to the 3-digit process, specifically how this is merely an expansion, or an additional step-- due to the additional digit):
+x 11:
+<code>
+x 11 = 4       (4 + 5) (5  + 6) (6 + 7) 7
+          = (4)+1   (9)+1   (11)+1   (13)+0  7   the numbers outside are the carry
+          = 5       0       2        3       7
+          = 50237
+</code>
+Remember, we are processing this from right to left (so that the carry values can properly propagate). While there is no initial carry coming in, we'll add one anyway (0), so we see 13+0 (which is simply 13)... but because we're interested in place values, this is actually a sum of 3, carry of 1... and that one gets sent over to the next place (which has an 11)... so 11+1 will be 12, or sum of 2, carry 1... that carry will propagate to the next position to the left (the 9)... so there's a rippling effect taking place (math in action).
+Can you see how "the same" this process for 4-digit numbers is when comparing to the process for 3-digit numbers? And how the same comparison can be made for 2-digit, and 5-digit, 6-digit, etc.? Please take some time, working through some examples (by hand) to identify and notice the pattern, or essence, of this process. You need to see how it doesn't matter in the long run how many digits- because you're doing the same thing (just a different number of times).
+That "different number of times" will be based on the length of the number... could that be used to help us?
+(Also, the potential exception here would possibly be 1-digit values... if you cannot easily find a way to make 1-digit numbers work with greater-than-1-digit numbers, that's where an if-statement would come into play-- if 1-digit, do this specific process, else do the regular process). I'm not saying one universal solution isn't possible, but at this stage of your structured programming development, such solutions may take a bit more work (and that's okay).
 =====Program=====
-It is your task to write the program that will use the above method to compute the requested one-, two-, or three-digit value against a multiplicand of 11 (without using any multiplication to obtain your result).
+It is your task to write an optimized version of your multiply by eleven program that will use arrays and loops to enable you to enhance and expand the functional capabilities of your program. No longer will you be limited by 1-, 2-, or 3-digit numbers, but you will be able to input up to 8-digit numbers and have your program successfully determine the result (and 8 is merely an arbitrary value I picked, you should easily be able to up it to the tens of thousands and experience no change in functionality) -- actually, our 8-digit limit is considering a data type limitation... the maximum size of an int: **signed int**s can have a maximum value of 2.4 billion, so unless we change to a different data type (or different method of inputting the source number), this will be our limitation.
 Your program should:
   * obtain its input from STDIN.
     * input should be in the form of a single integer value
-  * determine from the input if it is a one-, two-, or three-digit number
+  * determine the number of digits of the inputted value (store this in a variable)
   * perform the correct algorithm against the input
   * propagate any carries
-  * output the final value
+  * use an array (**digit**) to store individual digits from the number input
-    * you can display each digit individually, or combine them into one variable and display that (whichever you prefer)
+  * use another array (**result**) to store the digits of the result number, following manipulations
+    * hint: you will want to make the **result** array one element larger. Why is this?
+  * Display output showing aspects of the process (see example execution below)
+  * output the final value (by iterating through the array, displaying one value at a time)
 =====Execution=====
@@ Line 326: / Line 352: @@
 Enter value: 31415926
 Digits detected: 8
-result[0] = 6
-result[1] =
+Obtaining unique digits, storing in array...
+digit[0] = 6
+digit[1] = 2
+digit[2] = 9
+digit[3] = 5
+digit[4] = 1
+digit[5] = 4
+digit[6] = 1
+digit[7] = 3
+Applying process...
+result[0] = 6 + 0 + 0 (sum of 6, carry out of 0)
+result[1] = 2 + 6 + 0 (sum of 8, carry out of 0)
+result[2] = 9 + 2 + 0 (sum of 1, carry out of 1)
+result[3] = 5 + 9 + 1 (sum of 5, carry out of 1)
+result[4] = 1 + 5 + 1 (sum of 7, carry out of 0)
+result[5] = 4 + 1 + 0 (sum of 5, carry out of 0)
+result[6] = 1 + 4 + 0 (sum of 5, carry out of 0)
+result[7] = 3 + 1 + 0 (sum of 4, carry out of 0)
+result[8] = 3 + 0 + 0 (sum of 3, carry out of 0)
+Displaying result...
 31415926 x 11 = 345575186
 lab46:~/src/cprog/mbe1$
@@ Line 337: / Line 384: @@
 lab46:~/src/cprog/mbe1$ ./mbe1
 Enter value: 7104
+Digits detected: 4
+Obtaining unique digits, storing in array...
+digit[0] = 4
+digit[1] = 0
+digit[2] = 1
+digit[3] = 7
+Applying process...
+result[0] = 4 + 0 + 0 (sum of 4, carry out of 0)
+result[1] = 0 + 4 + 0 (sum of 4, carry out of 0)
+result[2] = 1 + 0 + 0 (sum of 1, carry out of 0)
+result[3] = 7 + 1 + 0 (sum of 8, carry out of 0)
+result[4] = 7 + 0 + 0 (sum of 7, carry out of 0)
+Displaying result...
 x 11 = 78144
 lab46:~/src/cprog/mbe1$
@@ Line 346: / Line 409: @@
 lab46:~/src/cprog/mbe1$ ./mbe1
 Enter value: 56789
+Digits detected: 5
+Obtaining unique digits, storing in array...
+digit[0] = 9
+digit[1] = 8
+digit[2] = 7
+digit[3] = 6
+digit[4] = 5
+Applying process...
+result[0] = 9 + 0 + 0 (sum of 9, carry out of 0)
+result[1] = 8 + 9 + 0 (sum of 7, carry out of 1)
+result[2] = 7 + 8 + 1 (sum of 6, carry out of 1)
+result[3] = 6 + 7 + 1 (sum of 4, carry out of 1)
+result[4] = 5 + 6 + 1 (sum of 2, carry out of 1)
+result[5] = 5 + 1 + 0 (sum of 6, carry out of 0)
+Displaying result...
 x 11 = 624679
 lab46:~/src/cprog/mbe1$
@@ Line 351: / Line 432: @@
 The execution of the program is short and simple- obtain the input, do the processing, produce the output, and then terminate.
-=====Reflection=====
-Be sure to provide any commentary on your opus regarding realizations had and discoveries made during your pursuit of this project.
-  * Does this process work for four digit numbers?
-  * How about five digit numbers?
-  * Do you see a pattern for now this trick could be extended?
 =====Submission=====
@@ Line 362: / Line 437: @@
   * Code must compile cleanly (no warnings or errors)
-  * Output must be correct, and match the form given in the sample output above.
+  * Output must be correct, and resemble the form given in the sample output above.
   * Code must be nicely and consistently indented (you may use the **indent** tool)
   * Code must utilize the algorithm presented above
@@ Line 368: / Line 443: @@
     * have a properly filled-out comment banner at the top
     * have at least 20% of your program consist of **<nowiki>//</nowiki>**-style descriptive comments
-  * Output Formatting (including spacing) of program must conform to the provided output (see above).
   * Track/version the source code in a repository
   * Submit a copy of your source code to me using the **submit** tool.
@@ Line 375: / Line 449: @@
 <cli>
-$ submit cprog mbe1 multby11v2.c mbe1.c
+$ submit cprog mbe1 mbe1.c
 Submitting cprog project "mbe1":
-    -> multby11v2.c(OK)
     -> mbe1.c(OK)

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