Who to talk to about non recursive Ackermann function? - function

I have written a non recursive solution to the Ackermann function, it seems to work perfectly and work faster than the common recursive solution. So I am confused as to why it is a non primitive recursive function if it can be solved iteratively? Could anyone tell me if I have misunderstood something about what primitive recursive functions are or who should I talk to about this to get an answer?
Below is the Java code:
import java.util.Scanner;
import java.util.ArrayList;
public class ackermann {
public static void main(String[] args){
Scanner in = new Scanner(System.in);
System.out.println("Enter m:");
int m = in.nextInt();
System.out.println("Enter n:");
int n = in.nextInt();
ack(m, n);
}
public static void ack(int inM, int inN){
if(inM < 0 || inN < 0) return;
ArrayList<ArrayList<Integer>> arr = new ArrayList<ArrayList<Integer>>();
for(int m = 0; m <= inM; m++){
arr.add(new ArrayList<Integer>());
}
Boolean done = false;
while(done == false){
for(int m = 0; m <= inM; m++){
int n = arr.get(m).size();
int a = 0;
if(m == 0) a = n + 1;
else if(n == 0){
if(arr.get(m - 1).size() <= 1) break;
a = arr.get(m - 1).get(1);
} else {
int k = arr.get(m).get(n - 1);
if(arr.get(m - 1).size() <= k) break;
a = arr.get(m - 1).get(k);
}
arr.get(m).add(a);
if(m == inM && n == inN){
System.out.println("Ack(" + inM + ", " + inN + ") = " + a);
done = true;
break;
}
}
}
}
}

Primitive recursive functions can be implemented using only assignment, +, and definite loops. By this I mean loops of the form:
for(int i = 0; i < n; i++) { ... }
Where n is a variable that isn't changed in the loop body. To get Ackermann's function, which majorizes all primitive recursive functions, one needs to add either a goto command or indefinite loops like your while loop.

Related

Server Implementation in C

I'm currently working on a server which is part of my course requirement. The specs require me to parse a request line and store the appropriate data as absolute path (abs_path) and query.
Here is my code:
bool parse(const char* line, char* abs_path, char* query)
{
int space = 0;
if (strchr(line, '"') != NULL)
{
error(400);
return false;
}
for (int i = 0; line[i] != '\0'; i++)
{
if (line[i] == ' ')
{
space++;
}
}
if (space != 2)
{
error(400);
return false;
}
if (strncmp("GET ", line, 4) != 0)
{
error(405);
return false;
}
line = strchr(line, ' ');
line++;
if (strncmp("/", line, 1) != 0)
{
error(501);
return false;
}
int j = 0;
int k = 4;
while (line[k] != ' ')
{
int m = k;
abs_path[j] = line[k];
j++;
if (line[k+1] == '?')
{
abs_path[j] = '\0';
int l = 0;
m = k+2;
while (line[m] != ' ')
{
query[l] = line[m];
l++;
m++;
}
if (line[m] == ' ' && l == 0)
{
query[0] = '\0';
}
}
k = m;
k++;
if (line[k] == ' ')
{
abs_path[j] = '\0';
break;
}
}
char* last = strrchr(line, ' ');
last++;
if (strcmp("HTTP/1.1", last) != 0)
{
error(505);
return false;
}
free(abs_path);
return true;
}
I keep getting a segmentation fault with this. After some debugging, I've found the segmentation fault to be eliminated if I declare, on line 20, abs_path as an array instead of a pointer. However, it is necessary for me to declare abs_path as a pointer, so I need another solution to this. Can someone explain to me what exactly I am doing wrong with regards to strings and their handling?
I have been quite rusty with this due to personal reasons so pardon me if I misunderstand something basic.
Thank you in advance!
You need to allocate memory for the char*. An array does this automatically during compile time. Try malloc.
char* abs_path = 0;
abs_path = (char*)malloc(256);
Essentially, malloc performs an operating system call to reserve sequential memory from the heap. The argument of malloc is how many bytes to reserve. Therefore, you should be aware that the example above enables the abs_path char* to point to a string that is at max 255 characters (leaving 1 byte for the null character '\0'). Don't let your code write more than 255 characters or you will overwrite other data in memory, which is why you received a seg-fault before.
As someone else noted, you should DEFINITELY free up memory reserved dynamically with malloc.
free(abs_path);

Extra 0 in starting of the output of decimal to binary code conversion

I seem to have a problem in the output of my code (A decimal to binary conversion code). If I enter a number, for example 12, it'll output 01100. I just want it to output 1100 (without the 0 in the very first). Is there something that I may have missed?
Thank you in advance! Here is my code below :
import java.util.*;
public class DtoB{
public static void main(String[] args){
Scanner in = new Scanner(System.in);
System.out.print("Enter a positive integer: ");
int number = in.nextInt();
int i;
int j;
int[] binary = new int[10];
if ( number > 0 ){
for (i = 0; number != 0; i++){
binary[i] = number % 2;
number /= 2;
}
for ( j = i; j >= 0; j-- ){
System.out.print(binary[j]);
}
System.out.print(" is the binary conversion of your integer.");
} else {
System.out.print("Error: You have not entered a positive integer.");
}
}
}
Initialize j with i-1
for ( j = i-1; j >= 0; j-- ){
System.out.print(binary[j]);
}

Returns and/or breaks in the middle of a loop. Is it ever acceptable?

Suppose we have an array of integers. We've written a function to fetch the index of the first specified value in the array, or -1 if the array does not contain the value..
So for example, if the array = { 4, 5, 4, 4, 7 }, then getFirstIndexOf(4) would return 0, getFirstIndexOf(7) would return 4, and getFirstIndexOf(8) would return -1.
Below, I have presented three different ways to write this function. It is a widely accepted coding standard that returns in the middle of functions, and breaks in the middle of loops are poor practice. It seems to me that this might be an acceptable use for them.
public int getFirstIndexOf(int specifiedNumber) {
for (int i = 0; i < array.length; i++) {
if (array[i] == specifiedNumber) {
return i;
}
}
return -1;
}
VS.
public int getFirstIndexOf(int specifiedNumber) {
int result = -1;
for (int i = 0; i < array.length; i++) {
if (array[i] == specifiedNumber) {
result = i;
break;
}
}
return result;
}
VS.
public int getFirstIndexOf(int specifiedNumber) {
int result = -1;
for (int i = 0; i < array.length; i++) {
if (array[i] == specifiedNumber && result == -1) {
result = i;
}
}
return result;
}
What do you think? Which is best? Why? Is there perhaps another way to do this?
I think it's poor practice to run a full loop when you have already found your result...
If you really want to avoid using return from the middle of the loop, I would sugest to use a "sentinel" to stop your loop.
public int getFirstIndexOf(int specifiedNumber, int[] array) {
boolean found = false;
boolean exit = false;
int i = 0;
int arraySize = array.length();
while(!found && !exit) {
if(array[i] == specifiedNumber) {
found = true;
} else {
if(i++ > arraySize) {
exit = true;
}
}
if(found ==true) {
return i;
} else {
return 99999;
}
}
edit: I hate to indent code using spaces in StackOverflow...
That's why do...while & while loop was invented.
As requested:
public int getFirstIndexOf(int specifiedNumber) {
int i = array.Length;
while(--i > -1 && array[i] != specifiedNumber);
return i;
}

How would you calculate all possible permutations of 0 through N iteratively?

I need to calculate permutations iteratively. The method signature looks like:
int[][] permute(int n)
For n = 3 for example, the return value would be:
[[0,1,2],
[0,2,1],
[1,0,2],
[1,2,0],
[2,0,1],
[2,1,0]]
How would you go about doing this iteratively in the most efficient way possible? I can do this recursively, but I'm interested in seeing lots of alternate ways to doing it iteratively.
see QuickPerm algorithm, it's iterative : http://www.quickperm.org/
Edit:
Rewritten in Ruby for clarity:
def permute_map(n)
results = []
a, p = (0...n).to_a, [0] * n
i, j = 0, 0
i = 1
results << yield(a)
while i < n
if p[i] < i
j = i % 2 * p[i] # If i is odd, then j = p[i], else j = 0
a[j], a[i] = a[i], a[j] # Swap
results << yield(a)
p[i] += 1
i = 1
else
p[i] = 0
i += 1
end
end
return results
end
The algorithm for stepping from one permutation to the next is very similar to elementary school addition - when an overflow occurs, "carry the one".
Here's an implementation I wrote in C:
#include <stdio.h>
//Convenience macro. Its function should be obvious.
#define swap(a,b) do { \
typeof(a) __tmp = (a); \
(a) = (b); \
(b) = __tmp; \
} while(0)
void perm_start(unsigned int n[], unsigned int count) {
unsigned int i;
for (i=0; i<count; i++)
n[i] = i;
}
//Returns 0 on wraparound
int perm_next(unsigned int n[], unsigned int count) {
unsigned int tail, i, j;
if (count <= 1)
return 0;
/* Find all terms at the end that are in reverse order.
Example: 0 3 (5 4 2 1) (i becomes 2) */
for (i=count-1; i>0 && n[i-1] >= n[i]; i--);
tail = i;
if (tail > 0) {
/* Find the last item from the tail set greater than
the last item from the head set, and swap them.
Example: 0 3* (5 4* 2 1)
Becomes: 0 4* (5 3* 2 1) */
for (j=count-1; j>tail && n[j] <= n[tail-1]; j--);
swap(n[tail-1], n[j]);
}
/* Reverse the tail set's order */
for (i=tail, j=count-1; i<j; i++, j--)
swap(n[i], n[j]);
/* If the entire list was in reverse order, tail will be zero. */
return (tail != 0);
}
int main(void)
{
#define N 3
unsigned int perm[N];
perm_start(perm, N);
do {
int i;
for (i = 0; i < N; i++)
printf("%d ", perm[i]);
printf("\n");
} while (perm_next(perm, N));
return 0;
}
Is using 1.9's Array#permutation an option?
>> a = [0,1,2].permutation(3).to_a
=> [[0, 1, 2], [0, 2, 1], [1, 0, 2], [1, 2, 0], [2, 0, 1], [2, 1, 0]]
Below is my generics version of the next permutation algorithm in C# closely resembling the STL's next_permutation function (but it doesn't reverse the collection if it is the max possible permutation already, like the C++ version does)
In theory it should work with any IList<> of IComparables.
static bool NextPermutation<T>(IList<T> a) where T: IComparable
{
if (a.Count < 2) return false;
var k = a.Count-2;
while (k >= 0 && a[k].CompareTo( a[k+1]) >=0) k--;
if(k<0)return false;
var l = a.Count - 1;
while (l > k && a[l].CompareTo(a[k]) <= 0) l--;
var tmp = a[k];
a[k] = a[l];
a[l] = tmp;
var i = k + 1;
var j = a.Count - 1;
while(i<j)
{
tmp = a[i];
a[i] = a[j];
a[j] = tmp;
i++;
j--;
}
return true;
}
And the demo/test code:
var src = "1234".ToCharArray();
do
{
Console.WriteLine(src);
}
while (NextPermutation(src));
I also came across the QuickPerm algorithm referenced in another answer. I wanted to share this answer in addition, because I saw some immediate changes one can make to write it shorter. For example, if the index array "p" is initialized slightly differently, it saves having to return the first permutation before the loop. Also, all those while-loops and if's took up a lot more room.
void permute(char* s, size_t l) {
int* p = new int[l];
for (int i = 0; i < l; i++) p[i] = i;
for (size_t i = 0; i < l; printf("%s\n", s)) {
std::swap(s[i], s[i % 2 * --p[i]]);
for (i = 1; p[i] == 0; i++) p[i] = i;
}
}
I found Joey Adams' version to be the most readable, but I couldn't port it directly to C# because of how C# handles the scoping of for-loop variables. Hence, this is a slightly tweaked version of his code:
/// <summary>
/// Performs an in-place permutation of <paramref name="values"/>, and returns if there
/// are any more permutations remaining.
/// </summary>
private static bool NextPermutation(int[] values)
{
if (values.Length == 0)
throw new ArgumentException("Cannot permutate an empty collection.");
//Find all terms at the end that are in reverse order.
// Example: 0 3 (5 4 2 1) (i becomes 2)
int tail = values.Length - 1;
while(tail > 0 && values[tail - 1] >= values[tail])
tail--;
if (tail > 0)
{
//Find the last item from the tail set greater than the last item from the head
//set, and swap them.
// Example: 0 3* (5 4* 2 1)
// Becomes: 0 4* (5 3* 2 1)
int index = values.Length - 1;
while (index > tail && values[index] <= values[tail - 1])
index--;
Swap(ref values[tail - 1], ref values[index]);
}
//Reverse the tail set's order.
int limit = (values.Length - tail) / 2;
for (int index = 0; index < limit; index++)
Swap(ref values[tail + index], ref values[values.Length - 1 - index]);
//If the entire list was in reverse order, tail will be zero.
return (tail != 0);
}
private static void Swap<T>(ref T left, ref T right)
{
T temp = left;
left = right;
right = temp;
}
Here's an implementation in C#, as an extension method:
public static IEnumerable<List<T>> Permute<T>(this IList<T> items)
{
var indexes = Enumerable.Range(0, items.Count).ToArray();
yield return indexes.Select(idx => items[idx]).ToList();
var weights = new int[items.Count];
var idxUpper = 1;
while (idxUpper < items.Count)
{
if (weights[idxUpper] < idxUpper)
{
var idxLower = idxUpper % 2 * weights[idxUpper];
var tmp = indexes[idxLower];
indexes[idxLower] = indexes[idxUpper];
indexes[idxUpper] = tmp;
yield return indexes.Select(idx => items[idx]).ToList();
weights[idxUpper]++;
idxUpper = 1;
}
else
{
weights[idxUpper] = 0;
idxUpper++;
}
}
}
And a unit test:
[TestMethod]
public void Permute()
{
var ints = new[] { 1, 2, 3 };
var orderings = ints.Permute().ToList();
Assert.AreEqual(6, orderings.Count);
AssertUtil.SequencesAreEqual(new[] { 1, 2, 3 }, orderings[0]);
AssertUtil.SequencesAreEqual(new[] { 2, 1, 3 }, orderings[1]);
AssertUtil.SequencesAreEqual(new[] { 3, 1, 2 }, orderings[2]);
AssertUtil.SequencesAreEqual(new[] { 1, 3, 2 }, orderings[3]);
AssertUtil.SequencesAreEqual(new[] { 2, 3, 1 }, orderings[4]);
AssertUtil.SequencesAreEqual(new[] { 3, 2, 1 }, orderings[5]);
}
The method AssertUtil.SequencesAreEqual is a custom test helper which can be recreated easily enough.
How about a recursive algorithm you can call iteratively? If you'd actually need that stuff as a list like that (you should clearly inline that rather than allocate a bunch of pointless memory). You could simply calculate the permutation on the fly, by its index.
Much like the permutation is carry-the-one addition re-reversing the tail (rather than reverting to 0), indexing the specific permutation value is finding the digits of a number in base n then n-1 then n-2... through each iteration.
public static <T> boolean permutation(List<T> values, int index) {
return permutation(values, values.size() - 1, index);
}
private static <T> boolean permutation(List<T> values, int n, int index) {
if ((index == 0) || (n == 0)) return (index == 0);
Collections.swap(values, n, n-(index % n));
return permutation(values,n-1,index/n);
}
The boolean returns whether your index value was out of bounds. Namely that it ran out of n values but still had remaining index left over.
And it can't get all the permutations for more than 12 objects.
12! < Integer.MAX_VALUE < 13!
-- But, it's so very very pretty. And if you do a lot of things wrong might be useful.
I have implemented the algorithm in Javascript.
var all = ["a", "b", "c"];
console.log(permute(all));
function permute(a){
var i=1,j, temp = "";
var p = [];
var n = a.length;
var output = [];
output.push(a.slice());
for(var b=0; b <= n; b++){
p[b] = b;
}
while (i < n){
p[i]--;
if(i%2 == 1){
j = p[i];
}
else{
j = 0;
}
temp = a[j];
a[j] = a[i];
a[i] = temp;
i=1;
while (p[i] === 0){
p[i] = i;
i++;
}
output.push(a.slice());
}
return output;
}
I've used the algorithms from here. The page contains a lot of useful information.
Edit: Sorry, those were recursive. uray posted the link to the iterative algorithm in his answer.
I've created a PHP example. Unless you really need to return all of the results, I would only create an iterative class like the following:
<?php
class Permutator implements Iterator
{
private $a, $n, $p, $i, $j, $k;
private $stop;
public function __construct(array $a)
{
$this->a = array_values($a);
$this->n = count($this->a);
}
public function current()
{
return $this->a;
}
public function next()
{
++$this->k;
while ($this->i < $this->n)
{
if ($this->p[$this->i] < $this->i)
{
$this->j = ($this->i % 2) * $this->p[$this->i];
$tmp = $this->a[$this->j];
$this->a[$this->j] = $this->a[$this->i];
$this->a[$this->i] = $tmp;
$this->p[$this->i]++;
$this->i = 1;
return;
}
$this->p[$this->i++] = 0;
}
$this->stop = true;
}
public function key()
{
return $this->k;
}
public function valid()
{
return !$this->stop;
}
public function rewind()
{
if ($this->n) $this->p = array_fill(0, $this->n, 0);
$this->stop = $this->n == 0;
$this->i = 1;
$this->j = 0;
$this->k = 0;
}
}
foreach (new Permutator(array(1,2,3,4,5)) as $permutation)
{
var_dump($permutation);
}
?>
Note that it treats every PHP array as an indexed array.

How to decode HTML Entities in C?

I'm interested in unescaping text for example: \ maps to \ in C. Does anyone know of a good library?
As reference the Wikipedia List of XML and HTML Character Entity References.
For another open source reference in C to decoding these HTML entities you can check out the command line utility uni2ascii/ascii2uni. The relevant files are enttbl.{c,h} for entity lookup and putu8.c which down converts from UTF32 to UTF8.
uni2ascii
I wrote my own unescape code; very simplified, but does the job: pn_util.c
Function Description: Convert special HTML entities back to characters.
Need to do some modifications to fit your requirement.
char* HtmlSpecialChars_Decode(char* encodedHtmlSpecialEntities)
{
int encodedLen = 0;
int escapeArrayLen = 0;
static char decodedHtmlSpecialChars[TITLE_SIZE];
char innerHtmlSpecialEntities[MAX_CONFIG_ITEM_SIZE];
/* This mapping table can be extended if necessary. */
static const struct {
const char* encodedEntity;
const char decodedChar;
} entityToChars[] = {
{"<", '<'},
{">", '>'},
{"&", '&'},
{""", '"'},
{"'", '\''},
};
if(strchr(encodedHtmlSpecialEntities, '&') == NULL)
return encodedHtmlSpecialEntities;
memset(decodedHtmlSpecialChars, '\0', TITLE_SIZE);
memset(innerHtmlSpecialEntities, '\0', MAX_CONFIG_ITEM_SIZE);
escapeArrayLen = sizeof(entityToChars) / sizeof(entityToChars[0]);
strcpy(innerHtmlSpecialEntities, encodedHtmlSpecialEntities);
encodedLen = strlen(innerHtmlSpecialEntities);
for(int i = 0; i < encodedLen; i++)
{
if(innerHtmlSpecialEntities[i] == '&')
{
/* Potential encode char. */
char * tempEntities = innerHtmlSpecialEntities + i;
for(int j = 0; j < escapeArrayLen; j++)
{
if(strncmp(tempEntities, entityToChars[j].encodedEntity, strlen(entityToChars[j].encodedEntity)) == 0)
{
int index = 0;
strncat(decodedHtmlSpecialChars, innerHtmlSpecialEntities, i);
index = strlen(decodedHtmlSpecialChars);
decodedHtmlSpecialChars[index] = entityToChars[j].decodedChar;
if(strlen(tempEntities) > strlen(entityToChars[j].encodedEntity))
{
/* Not to the end, continue */
char temp[MAX_CONFIG_ITEM_SIZE] = {'\0'};
strcpy(temp, tempEntities + strlen(entityToChars[j].encodedEntity));
memset(innerHtmlSpecialEntities, '\0', MAX_CONFIG_ITEM_SIZE);
strcpy(innerHtmlSpecialEntities, temp);
encodedLen = strlen(innerHtmlSpecialEntities);
i = -1;
}
else
encodedLen = 0;
break;
}
}
}
}
if(encodedLen != 0)
strcat(decodedHtmlSpecialChars, innerHtmlSpecialEntities);
return decodedHtmlSpecialChars;
}
QString UNESC(const QString &txt) {
QStringList bld;
static QChar AMP = '&', SCL = ';';
static QMap<QString, QString> dec = {
{"<", "<"}, {">", ">"}
, {"&", "&"}, {""", R"(")"}, {"'", "'"} };
if(!txt.contains(AMP)) { return txt; }
int bgn = 0, pos = 0;
while((pos = txt.indexOf(AMP, pos)) != -1) {
int end = txt.indexOf(SCL, pos)+1;
QString val = dec[txt.mid(pos, end - pos)];
bld << txt.mid(bgn, pos - bgn);
if(val.isEmpty()) {
end = txt.indexOf(AMP, pos+1);
bld << txt.mid(pos, end - pos);
} else {
bld << val;
}// else // if(val.isEmpty())
bgn = end; pos = end;
}// while((pos = txt.indexOf(AMP, pos)) != -1)
return bld.join(QString());
}// UNESC