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I have an unsorted array, what is the best method to remove all the duplicates of an element if present?
e.g:
a[1,5,2,6,8,9,1,1,10,3,2,4,1,3,11,3]
so after that operation the array should look like
a[1,5,2,6,8,9,10,3,4,11]
Check every element against every other element
The naive solution is to check every element against every other element. This is wasteful and yields an O(n2) solution, even if you only go "forward".
Sort then remove duplicates
A better solution is sort the array and then check each element to the one next to it to find duplicates. Choose an efficient sort and this is O(n log n).
The disadvantage with the sort-based solution is order is not maintained. An extra step can take care of this however. Put all entries (in the unique sorted array) into a hashtable, which has O(1) access. Then iterate over the original array. For each element, check if it is in the hash table. If it is, add it to the result and delete it from the hash table. You will end up with a resultant array that has the order of the original with each element being in the same position as its first occurrence.
Linear sorts of integers
If you're dealing with integers of some fixed range you can do even better by using a radix sort. If you assume the numbers are all in the range of 0 to 1,000,000 for example, you can allocate a bit vector of some 1,000,001. For each element in the original array, you set the corresponding bit based on its value (eg a value of 13 results in setting the 14th bit). Then traverse the original array, check if it is in the bit vector. If it is, add it to the result array and clear that bit from the bit vector. This is O(n) and trades space for time.
Hash table solution
Which leads us to the best solution of all: the sort is actually a distraction, though useful. Create a hashtable with O(1) access. Traverse the original list. If it is not in the hashtable already, add it to the result array and add it to the hash table. If it is in the hash table, ignore it.
This is by far the best solution. So why the rest? Because problems like this are about adapting knowledge you have (or should have) to problems and refining them based on the assumptions you make into a solution. Evolving a solution and understanding the thinking behind it is far more useful than regurgitating a solution.
Also, hash tables are not always available. Take an embedded system or something where space is VERY limited. You can implement an quick sort in a handful of opcodes, far fewer than any hash table could be.
This can be done in amortized O(n) using a hashtable-based set.
Psuedo-code:
s := new HashSet
c := 0
for each el in a
Add el to s.
If el was not already in s, move (copy) el c positions left.
If it was in s, increment c.
If you don't need to keep the original object you can loop it and create a new array of unique values. In C# use a List to get access to the required functionality. It's not the most attractive or intelligent solution, but it works.
int[] numbers = new int[] {1,2,3,4,5,1,2,2,2,3,4,5,5,5,5,4,3,2,3,4,5};
List<int> unique = new List<int>();
foreach (int i in numbers)
if (!unique.Contains(i))
unique.Add(i);
unique.Sort();
numbers = unique.ToArray();
Treat numbers as keys. for each elem in array:
if hash(elem) == 1 //duplicate
ignore it
next
else
hash(elem) = 1
add this to resulting array
end
If you know about the data like the range of numbers and if it is finite, then you can initialize that big array with ZERO's.array flag[N] //N is the max number in the array
for each elem in input array:
if flag[elem - 1] == 0
flag[elem - 1] = 1
add it to resulatant array
else
discard it //duplicate
end
indexOutput = 1;
outputArray[0] = arrayInt[0];
int j;
for (int i = 1; i < arrayInt.length; i++) {
j = 0;
while ((outputArray[j] != arrayInt[i]) && j < indexOutput) {
j++;
}
if(j == indexOutput){
outputArray[indexOutput] = arrayInt[i];
indexOutput++;
}
}
Use a Set implementation.
HashSet,TreeSet or LinkedHashSet if its Java.
This is a code segment i created in C++, Try out it
#include <iostream>
using namespace std;
int main()
{
cout << " Delete the duplicate" << endl;
int numberOfLoop = 10;
int loopCount =0;
int indexOfLargeNumber = 0;
int largeValue = 0;
int indexOutput = 1;
//Array to hold the numbers
int arrayInt[10] = {};
int outputArray [10] = {};
// Loop for reading the numbers from the user input
while(loopCount < numberOfLoop){
cout << "Please enter one Integer number" << endl;
cin >> arrayInt[loopCount];
loopCount = loopCount + 1;
}
outputArray[0] = arrayInt[0];
int j;
for (int i = 1; i < numberOfLoop; i++) {
j = 0;
while ((outputArray[j] != arrayInt[i]) && j < indexOutput) {
j++;
}
if(j == indexOutput){
outputArray[indexOutput] = arrayInt[i];
indexOutput++;
}
}
cout << "Printing the Non duplicate array"<< endl;
//Reset the loop count
loopCount =0;
while(loopCount < numberOfLoop){
if(outputArray[loopCount] != 0){
cout << outputArray[loopCount] << endl;
}
loopCount = loopCount + 1;
}
return 0;
}
My solution(O(N)) does not use additional memory, but array must been sorted(my class using insertion sort algorithm, but it doesn't matter.):
public class MyArray
{
//data arr
private int[] _arr;
//field length of my arr
private int _leght;
//counter of duplicate
private int countOfDup = 0;
//property length of my arr
public int Length
{
get
{
return _leght;
}
}
//constructor
public MyArray(int n)
{
_arr = new int[n];
_leght = 0;
}
// put element into array
public void Insert(int value)
{
_arr[_leght] = value;
_leght++;
}
//Display array
public void Display()
{
for (int i = 0; i < _leght; i++) Console.Out.Write(_arr[i] + " ");
}
//Insertion sort for sorting array
public void InsertSort()
{
int t, j;
for (int i = 1; i < _leght; i++)
{
t = _arr[i];
for (j = i; j > 0; )
{
if (_arr[j - 1] >= t)
{
_arr[j] = _arr[j - 1];
j--;
}
else break;
}
_arr[j] = t;
}
}
private void _markDuplicate()
{
//mark duplicate Int32.MinValue
for (int i = 0; i < _leght - 1; i++)
{
if (_arr[i] == _arr[i + 1])
{
countOfDup++;
_arr[i] = Int32.MinValue;
}
}
}
//remove duplicates O(N) ~ O(2N) ~ O(N + N)
public void RemoveDups()
{
_markDuplicate();
if (countOfDup == 0) return; //no duplicate
int temp = 0;
for (int i = 0; i < _leght; i++)
{
// if duplicate remember and continue
if (_arr[i] == Int32.MinValue) continue;
else //else need move
{
if (temp != i) _arr[temp] = _arr[i];
temp++;
}
}
_leght -= countOfDup;
}
}
And Main
static void Main(string[] args)
{
Random r = new Random(DateTime.Now.Millisecond);
int i = 11;
MyArray a = new MyArray(i);
for (int j = 0; j < i; j++)
{
a.Insert(r.Next(i - 1));
}
a.Display();
Console.Out.WriteLine();
a.InsertSort();
a.Display();
Console.Out.WriteLine();
a.RemoveDups();
a.Display();
Console.ReadKey();
}
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Set;
public class testing {
public static void main(String[] args) {
EligibleOffer efg = new EligibleOffer();
efg.setCode("1234");
efg.setName("hey");
EligibleOffer efg1 = new EligibleOffer();
efg1.setCode("1234");
efg1.setName("hey1");
EligibleOffer efg2 = new EligibleOffer();
efg2.setCode("1235");
efg2.setName("hey");
EligibleOffer efg3 = new EligibleOffer();
efg3.setCode("1235");
efg3.setName("hey");
EligibleOffer[] eligibleOffer = { efg, efg1,efg2 ,efg3};
removeDupliacte(eligibleOffer);
}
public static EligibleOffer[] removeDupliacte(EligibleOffer[] array) {
List list = Arrays.asList(array);
List list1 = new ArrayList();
int len = list.size();
for (int i = 0; i <= len-1; i++) {
boolean isDupliacte = false;
EligibleOffer eOfr = (EligibleOffer) list.get(i);
String value = eOfr.getCode().concat(eOfr.getName());
if (list1.isEmpty()) {
list1.add(list.get(i));
continue;
}
int len1 = list1.size();
for (int j = 0; j <= len1-1; j++) {
EligibleOffer eOfr1 = (EligibleOffer) list1.get(j);
String value1 = eOfr1.getCode().concat(eOfr1.getName());
if (value.equals(value1)) {
isDupliacte = true;
break;
}
System.out.println(value+"\t"+value1);
}
if (!isDupliacte) {
list1.add(eOfr);
}
}
System.out.println(list1);
EligibleOffer[] eligibleOffer = new EligibleOffer[list1.size()];
list1.toArray(eligibleOffer);
return eligibleOffer;
}
}
Time O(n) space O(n)
#include <iostream>
#include<limits.h>
using namespace std;
void fun(int arr[],int size){
int count=0;
int has[100]={0};
for(int i=0;i<size;i++){
if(!has[arr[i]]){
arr[count++]=arr[i];
has[arr[i]]=1;
}
}
for(int i=0;i<count;i++)
cout<<arr[i]<<" ";
}
int main()
{
//cout << "Hello World!" << endl;
int arr[]={4, 8, 4, 1, 1, 2, 9};
int size=sizeof(arr)/sizeof(arr[0]);
fun(arr,size);
return 0;
}
public class RemoveDuplicateArray {
public static void main(String[] args) {
int arr[] = new int[] { 1, 2, 3, 4, 5, 6, 7, 2, 3, 4, 9 };
int size = arr.length;
for (int i = 0; i < size; i++) {
for (int j = i+1; j < size; j++) {
if (arr[i] == arr[j]) {
while (j < (size) - 1) {
arr[j] = arr[j + 1];
j++;
}
size--;
}
}
}
for (int i = 0; i < size; i++) {
System.out.print(arr[i] + " ");
}
}
}
output - 1 2 3 4 5 6 7 9
You can use the "in" and "not in" syntax in python which makes it pretty straight forward.
The complexity is higher than the hashing approach though since a "not in" is equivalent to a linear traversal to find out whether that entry exists or not.
li = map(int, raw_input().split(","))
a = []
for i in li:
if i not in a:
a.append(i)
print a
I am doing it in Python.
array1 = [1,2,2,3,3,3,4,5,6,4,4,5,5,5,5,10,10,8,7,7,9,10]
array1.sort() # sorting is must
print(array1)
current = NONE
count = 0
# overwriting the numbers at the frontal part of the array
for item in array1:
if item != current:
array1[count] = item
count +=1
current=item
print(array1)#[1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 5, 5, 5, 5, 6, 7, 7, 8, 9, 10, 10, 10]
print(array1[:count])#[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
The most Efficient method is :
array1 = [1,2,2,3,3,3,4,5,6,4,4,5,5,5,5,10,10,8,7,7,9,10]
array1.sort()
print(array1)
print([*dict.fromkeys(array1)])#[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
#OR#
aa = list(dict.fromkeys(array1))
print( aa)#[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
use an dictionary array and add each items as key
if an item was duplicated , dictionary avoid to add it!
it's the best solution
int[] numbers = new int[] {1,2,3,4,5,1,2,2,2,3,4,5,5,5,5,4,3,2,3,4,5};
IDictionary<int, string> newArray = new Dictionary<int, string>();
for (int i = 0; i < numbers.count() ; i++)
{
newArray .Add(numbers[i] , "");
}
I have an array that I would like to iterate in random order. That is, I would like my iteration to visit each element only once in a seemingly random order.
Would it be possible to implement an iterator that would iterate elements like this without storing the order or other data in a lookup table first?
Would it be possible to do it for N-dimensional arrays where N>1?
UPDATE: Some of the answers mention how to do this by storing indices. A major point of this question is how to do it without storing indices or other data.
I decided to solve this, because it annoyed me to death not remembering the name of solution that I had heard before. I did however remember in the end, more on that in the bottom of this post.
My solution depends on the mathematical properties of some cleverly calculated numbers
range = array size
prime = closestPrimeAfter(range)
root = closestPrimitiveRootTo(range/2)
state = root
With this setup we can calculate the following repeatedly and it will iterate all elements of the array exactly once in a seemingly random order, after which it will loop to traverse the array in the same exact order again.
state = (state * root) % prime
I implemented and tested this in Java, so I decided to paste my code here for future reference.
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Random;
public class PseudoRandomSequence {
private long state;
private final long range;
private final long root;
private final long prime;
//Debugging counter
private int dropped = 0;
public PseudoRandomSequence(int r) {
range = r;
prime = closestPrimeAfter(range);
root = modPow(generator(prime), closestPrimeTo(prime / 2), prime);
reset();
System.out.println("-- r:" + range);
System.out.println(" p:" + prime);
System.out.println(" k:" + root);
System.out.println(" s:" + state);
}
// https://en.wikipedia.org/wiki/Primitive_root_modulo_n
private static long modPow(long base, long exp, long mod) {
return BigInteger.valueOf(base).modPow(BigInteger.valueOf(exp), BigInteger.valueOf(mod)).intValue();
}
//http://e-maxx-eng.github.io/algebra/primitive-root.html
private static long generator(long p) {
ArrayList<Long> fact = new ArrayList<Long>();
long phi = p - 1, n = phi;
for (long i = 2; i * i <= n; ++i) {
if (n % i == 0) {
fact.add(i);
while (n % i == 0) {
n /= i;
}
}
}
if (n > 1) fact.add(n);
for (long res = 2; res <= p; ++res) {
boolean ok = true;
for (long i = 0; i < fact.size() && ok; ++i) {
ok &= modPow(res, phi / fact.get((int) i), p) != 1;
}
if (ok) {
return res;
}
}
return -1;
}
public long get() {
return state - 1;
}
public void advance() {
//This loop simply skips all results that overshoot the range, which should never happen if range is a prime number.
dropped--;
do {
state = (state * root) % prime;
dropped++;
} while (state > range);
}
public void reset() {
state = root;
dropped = 0;
}
private static boolean isPrime(long num) {
if (num == 2) return true;
if (num % 2 == 0) return false;
for (int i = 3; i * i <= num; i += 2) {
if (num % i == 0) return false;
}
return true;
}
private static long closestPrimeAfter(long n) {
long up;
for (up = n + 1; !isPrime(up); ++up)
;
return up;
}
private static long closestPrimeBefore(long n) {
long dn;
for (dn = n - 1; !isPrime(dn); --dn)
;
return dn;
}
private static long closestPrimeTo(long n) {
final long dn = closestPrimeBefore(n);
final long up = closestPrimeAfter(n);
return (n - dn) > (up - n) ? up : dn;
}
private static boolean test(int r, int loops) {
final int array[] = new int[r];
Arrays.fill(array, 0);
System.out.println("TESTING: array size: " + r + ", loops: " + loops + "\n");
PseudoRandomSequence prs = new PseudoRandomSequence(r);
final long ct = loops * r;
//Iterate the array 'loops' times, incrementing the value for each cell for every visit.
for (int i = 0; i < ct; ++i) {
prs.advance();
final long index = prs.get();
array[(int) index]++;
}
//Verify that each cell was visited exactly 'loops' times, confirming the validity of the sequence
for (int i = 0; i < r; ++i) {
final int c = array[i];
if (loops != c) {
System.err.println("ERROR: array element #" + i + " was " + c + " instead of " + loops + " as expected\n");
return false;
}
}
//TODO: Verify the "randomness" of the sequence
System.out.println("OK: Sequence checked out with " + prs.dropped + " drops (" + prs.dropped / loops + " per loop vs. diff " + (prs.prime - r) + ") \n");
return true;
}
//Run lots of random tests
public static void main(String[] args) {
Random r = new Random();
r.setSeed(1337);
for (int i = 0; i < 100; ++i) {
PseudoRandomSequence.test(r.nextInt(1000000) + 1, r.nextInt(9) + 1);
}
}
}
As stated in the top, about 10 minutes after spending a good part of my night actually getting a result, I DID remember where I had read about the original way of doing this. It was in a small C implementation of a 2D graphics "dissolve" effect as described in Graphics Gems vol. 1 which in turn is an adaption to 2D with some optimizations of a mechanism called "LFSR" (wikipedia article here, original dissolve.c source code here).
You could collect all possible indices in a list and then remove a random indece to visit. I know this is sort of like a lookup table, but i don't see any other option than this.
Here is an example for a one-dimensional array (adaption to multiple dimensions should be trivial):
class RandomIterator<T> {
T[] array;
List<Integer> remainingIndeces;
public RandomIterator(T[] array) {
this.array = array;
this.remainingIndeces = new ArrayList<>();
for(int i = 0;i<array.length;++i)
remainingIndeces.add(i);
}
public T next() {
return array[remainingIndeces.remove((int)(Math.random()*remainingIndeces.size()))];
}
public boolean hasNext() {
return !remainingIndeces.isEmpty();
}
}
On a side note: If this code is performance relevant, this method would perform worse by far, as the random removing from the list triggers copies if you use a list backed by an array (a linked-list won't help either, as indexed access is O(n)). I would suggest a lookup-structure (e.g. HashSet in Java) that stores all visited indices to circumvent this problem (though that's exactly what you did not want to use)
EDIT: Another approach is to copy said array and use a library function to shuffle it and then traverse it in linear order. If your array isn't that big, this seems like the most readable and performant option.
You would need to create a pseudo random number generator that generates values from 0 to X-1 and takes X iterations before repeating the cycle, where X is the product of all the dimension sizes. I don't know if there is a generic solution to doing this. Wiki article for one type of random number generator:
http://en.wikipedia.org/wiki/Linear_congruential_generator
Yes, it is possible. Imagine 3D array (you not likely use anything more than that). This is like a cube and where all 3 lines connect is a cell. You can enumerate your cells 1 to N using a dictionary, you can do this initialization in loops, and create a list of cells to use for random draw
Initialization
totalCells = ... (xMax * yMax * zMax)
index = 0
For (x = 0; x < xMax ; x++)
{
For (y = 0; y < yMax ; y++)
{
For (z = 0; z < zMax ; z++)
{
dict.Add(i, new Cell(x, y, z))
lst.Add(i)
i++
}
}
}
Now, all you have to do is iterate randomly
Do While (lst.Count > 0)
{
indexToVisit = rand.Next(0, lst.Count - 1)
currentCell = dict[lst[indexToVisit]]
lst.Remove(indexToVisit)
// Do something with current cell here
. . . . . .
}
This is pseudo code, since you didn't mention language you work in
Another way is to randomize 3 (or whatever number of dimensions you have) lists and then just nested loop through them - this will be random in the end.
I think it is basically an easy problem, but I'm stuck. My brain is blocked by this problem, so I hope you can help me.
I have 2 to N arrays of integers, like
{1,2,3,4,5}
{1,2,3,4,5,6}
{1,3,5}
.....
Now i want to have a list containing arrays of int[N] with every posibillity like
{1,1,1}
{1,1,3}
{1,1,5}
{1,2,1}
....
{1,3,1}
....
{2,1,1}
{2,1,3}
....
{5,6,5}
so there are 6*5*3 (90) elements in it.
Is there a simple algorithm to do it? I think the language didn't matter but I prefer Java.
Thx for the help!
I add a valid answer with the implementation in java for the next guy, who has the same problem. I also do it generic so u can have any CartesianProduct on any Object, not just ints:
public class Product {
#SuppressWarnings("unchecked")
public static <T> List<T[]> getCartesianProduct(T[]... objects){
List<T[]> ret = null;
if (objects != null){
//saves length from first dimension. its the size of T[] of the returned list
int len = objects.length;
//saves all lengthes from second dimension
int[] lenghtes = new int[len];
// arrayIndex
int array = 0;
// saves the sum of returned T[]'s
int lenSum = 1;
for (T[] t: objects){
lenSum *= t.length;
lenghtes[array++] = t.length;
}
//initalize the List with the correct lenght to avoid internal array-copies
ret = new ArrayList<T[]>(lenSum);
//reusable class for instatiation of T[]
Class<T> clazz = (Class<T>) objects[0][0].getClass();
T[] tArray;
//values stores arrayIndexes to get correct values from objects
int[] values = new int[len];
for (int i = 0; i < lenSum; i++){
tArray = (T[])Array.newInstance(clazz, len);
for (int j = 0; j < len; j++){
tArray[j] = objects[j][values[j]];
}
ret.add(tArray);
//value counting:
//increment first value
values[0]++;
for (int v = 0; v < len; v++){
//check if values[v] doesn't exceed array length
if (values[v] == lenghtes[v]){
//set it to null and increment the next one, if not the last
values[v] = 0;
if (v+1 < len){
values[v+1]++;
}
}
}
}
}
return ret;
}
}
As i understand what you want, you need to get all permutations.
Use recursive algorithm, detailed here.
As I see this should work fine:
concatMap (λa -> concatMap (λb -> concatMap (λc -> (a,b,c)) L3) L2) L1
where concatMap(called SelectMany in C#) is defined as
concatMap f l = concat (map f l).
and map maps a function over a list
and concat(sometimes called flatten) takes a List of List and turns it into a flat List
I'm not sure how to ask my question in a succinct way, so I'll start with examples and expand from there. I am working with VBA, but I think this problem is non language specific and would only require a bright mind that can provide a pseudo code framework. Thanks in advance for the help!
Example:
I have 3 Character Arrays Like So:
Arr_1 = [X,Y,Z]
Arr_2 = [A,B]
Arr_3 = [1,2,3,4]
I would like to generate ALL possible permutations of the character arrays like so:
XA1
XA2
XA3
XA4
XB1
XB2
XB3
XB4
YA1
YA2
.
.
.
ZB3
ZB4
This can be easily solved using 3 while loops or for loops. My question is how do I solve for this if the # of arrays is unknown and the length of each array is unknown?
So as an example with 4 character arrays:
Arr_1 = [X,Y,Z]
Arr_2 = [A,B]
Arr_3 = [1,2,3,4]
Arr_4 = [a,b]
I would need to generate:
XA1a
XA1b
XA2a
XA2b
XA3a
XA3b
XA4a
XA4b
.
.
.
ZB4a
ZB4b
So the Generalized Example would be:
Arr_1 = [...]
Arr_2 = [...]
Arr_3 = [...]
.
.
.
Arr_x = [...]
Is there a way to structure a function that will generate an unknown number of loops and loop through the length of each array to generate the permutations? Or maybe there's a better way to think about the problem?
Thanks Everyone!
Recursive solution
This is actually the easiest, most straightforward solution. The following is in Java, but it should be instructive:
public class Main {
public static void main(String[] args) {
Object[][] arrs = {
{ "X", "Y", "Z" },
{ "A", "B" },
{ "1", "2" },
};
recurse("", arrs, 0);
}
static void recurse (String s, Object[][] arrs, int k) {
if (k == arrs.length) {
System.out.println(s);
} else {
for (Object o : arrs[k]) {
recurse(s + o, arrs, k + 1);
}
}
}
}
(see full output)
Note: Java arrays are 0-based, so k goes from 0..arrs.length-1 during the recursion, until k == arrs.length when it's the end of recursion.
Non-recursive solution
It's also possible to write a non-recursive solution, but frankly this is less intuitive. This is actually very similar to base conversion, e.g. from decimal to hexadecimal; it's a generalized form where each position have their own set of values.
public class Main {
public static void main(String[] args) {
Object[][] arrs = {
{ "X", "Y", "Z" },
{ "A", "B" },
{ "1", "2" },
};
int N = 1;
for (Object[] arr : arrs) {
N = N * arr.length;
}
for (int v = 0; v < N; v++) {
System.out.println(decode(arrs, v));
}
}
static String decode(Object[][] arrs, int v) {
String s = "";
for (Object[] arr : arrs) {
int M = arr.length;
s = s + arr[v % M];
v = v / M;
}
return s;
}
}
(see full output)
This produces the tuplets in a different order. If you want to generate them in the same order as the recursive solution, then you iterate through arrs "backward" during decode as follows:
static String decode(Object[][] arrs, int v) {
String s = "";
for (int i = arrs.length - 1; i >= 0; i--) {
int Ni = arrs[i].length;
s = arrs[i][v % Ni] + s;
v = v / Ni;
}
return s;
}
(see full output)
Thanks to #polygenelubricants for the excellent solution.
Here is the Javascript equivalent:
var a=['0'];
var b=['Auto', 'Home'];
var c=['Good'];
var d=['Tommy', 'Hilfiger', '*'];
var attrs = [a, b, c, d];
function recurse (s, attrs, k) {
if(k==attrs.length) {
console.log(s);
} else {
for(var i=0; i<attrs[k].length;i++) {
recurse(s+attrs[k][i], attrs, k+1);
}
}
}
recurse('', attrs, 0);
EDIT: Here's a ruby solution. Its pretty much the same as my other solution below, but assumes your input character arrays are words: So you can type:
% perm.rb ruby is cool
~/bin/perm.rb
#!/usr/bin/env ruby
def perm(args)
peg = Hash[args.collect {|v| [v,0]}]
nperms= 1
args.each { |a| nperms *= a.length }
perms = Array.new(nperms, "")
nperms.times do |p|
args.each { |a| perms[p] += a[peg[a]] }
args.each do |a|
peg[a] += 1
break if peg[a] < a.length
peg[a] = 0
end
end
perms
end
puts perm ARGV
OLD - I have a script to do this in MEL, (Maya's Embedded Language) - I'll try to translate to something C like, but don't expect it to run without a bit of fixing;) It works in Maya though.
First - throw all the arrays together in one long array with delimiters. (I'll leave that to you - because in my system it rips the values out of a UI). So, this means the delimiters will be taking up extra slots: To use your sample data above:
string delimitedArray[] = {"X","Y","Z","|","A","B","|","1","2","3","4","|"};
Of course you can concatenate as many arrays as you like.
string[] getPerms( string delimitedArray[]) {
string result[];
string delimiter("|");
string compactArray[]; // will be the same as delimitedArray, but without the "|" delimiters
int arraySizes[]; // will hold number of vals for each array
int offsets[]; // offsets will holds the indices where each new array starts.
int counters[]; // the values that will increment in the following loops, like pegs in each array
int nPemutations = 1;
int arrSize, offset, nArrays;
// do a prepass to find some information about the structure, and to build the compact array
for (s in delimitedArray) {
if (s == delimiter) {
nPemutations *= arrSize; // arrSize will have been counting elements
arraySizes[nArrays] = arrSize;
counters[nArrays] = 0; // reset the counter
nArrays ++; // nArrays goes up every time we find a new array
offsets.append(offset - arrSize) ; //its here, at the end of an array that we store the offset of this array
arrSize=0;
} else { // its one of the elements, not a delimiter
compactArray.append(s);
arrSize++;
offset++;
}
}
// put a bail out here if you like
if( nPemutations > 256) error("too many permutations " + nPemutations+". max is 256");
// now figure out the permutations
for (p=0;p<nPemutations;p++) {
string perm ="";
// In each array at the position of that array's counter
for (i=0;i<nArrays ;i++) {
int delimitedArrayIndex = counters[i] + offsets[i] ;
// build the string
perm += (compactArray[delimitedArrayIndex]);
}
result.append(perm);
// the interesting bit
// increment the array counters, but in fact the program
// will only get to increment a counter if the previous counter
// reached the end of its array, otherwise we break
for (i = 0; i < nArrays; ++i) {
counters[i] += 1;
if (counters[i] < arraySizes[i])
break;
counters[i] = 0;
}
}
return result;
}
If I understand the question correctly, I think you could put all your arrays into another array, thereby creating a jagged array.
Then, loop through all the arrays in your jagged array creating all the permutations you need.
Does that make sense?
it sounds like you've almost got it figured out already.
What if you put in there one more array, call it, say ArrayHolder , that holds all of your unknown number of arrays of unknown length. Then, you just need another loop, no?
I have an interview in 2 days and I am having a very hard time finding a solutions for this question:
What I want to do is .. for any phone number .. the program should print out all the possible strings it represents. For eg.) A 2 in the number can be replaced by 'a' or 'b' or 'c', 3 by 'd' 'e' 'f' etc. In this way how many possible permutations can be formed from a given phone number.
I don't want anyone to write code for it ... a good algorithm or psuedocode would be great.
Thank you
This is the popular correspondence table:
d = { '2': "ABC",
'3': "DEF",
'4': "GHI",
'5': "JKL",
'6': "MNO",
'7': "PQRS",
'8': "TUV",
'9': "WXYZ",
}
Given this, or any other d, (executable) pseudocode to transform a string of digits into all possible strings of letters:
def digstolets(digs):
if len(digs) == 0:
yield ''
return
first, rest = digs[0], digs[1:]
if first not in d:
for x in digstolets(rest): yield first + x
return
else:
for x in d[first]:
for y in digstolets(rest): yield x + y
tweakable depending on what you want to do for characters in the input string that aren't between 2 and 9 included (this version just echoes them out!-).
For example,
print list(digstolets('1234'))
in this version emits
['1ADG', '1ADH', '1ADI', '1AEG', '1AEH', '1AEI', '1AFG', '1AFH', '1AFI',
'1BDG', '1BDH', '1BDI', '1BEG', '1BEH', '1BEI', '1BFG', '1BFH', '1BFI',
'1CDG', '1CDH', '1CDI', '1CEG', '1CEH', '1CEI', '1CFG', '1CFH', '1CFI']
Edit: the OP asks for more explanation, here's an attempt. Function digstolets (digits to letters) takes a string of digits digs and yields a sequence of strings of characters which can be letters or "non-digits". 0 and 1 count as non-digits here because they don't expand into letters, just like spaces and punctuations don't -- only digits 2 to 9 included expand to letters (three possibilities each in most cases, four in two cases, since 7 can expand to any of PQRS and 9 can expand to any of WXYZ).
First, the base case: if nothing is left (string digs is empty), the only possible result is the empty string, and that's all, this recursive call is done, finished, kaput.
If digs is non-empty it can be split into a "head", the first character, and a "tail", all the rest (0 or more characters after the first one).
The "head" either stays as it is in the output, if a non-digit; or expands to any of three or four possibilities, if a digit. In either case, the one, three, or four possible expansions of the head must be concatenated with every possible expansion of the tail -- whence, the recursive call, to get all possible expansions of the tail (so we loop over all said possible expansion of the tail, and yield each of the one, three, or four possible expansions of the head concatenated with each possible expansion of the tail). And then, once again, th-th-that's all, folks.
I don't know how to put this in terms that are any more elementary -- if the OP is still lost after THIS, I can only recommend a serious, total review of everything concerning recursion. Removing the recursion in favor of an explicitly maintained stack cannot simplify this conceptual exposition -- depending on the language involved (it would be nice to hear about what languages the OP is totally comfortable with!), recursion elimination can be an important optimization, but it's never a conceptual simplification...!-)
If asked this in an interview, I'd start by breaking the problem down. What are the problems you have to solve?
First, you need to map a number to a set of letters. Some numbers will map to different numbers of letters. So start by figuring out how to store that data. Basically you want a map of a number to a collection of letters.
Once you're there, make it easier, how would you generate all the "words" for a 1-digit number? Basically how to iterate through the collection that's mapped to a given number. And how many possibilities are there?
OK, now the next step is, you've got two numbers and want to generate all the words. How would you do this if you were just gonna do it manually? You'd start with the first letter for the first number, and the first letter for the second number. Then go to the next letter for the second number, keeping the first letter for the first, etc. Think about it as numbers (basically indices into the collections for two numbers which each map to 3 letters):
00,01,02,10,11,12,20,21,22
So how would you generate that sequence of numbers in code?
Once you can do that, translating it to code should be trivial.
Good luck!
Another version in Java.
First it selects character arrays based on each digit of the phone number. Then using recursion it generates all possible permutations.
public class PhonePermutations {
public static void main(String[] args) {
char[][] letters =
{{'0'},{'1'},{'A','B','C'},{'D','E','F'},{'G','H','I'},{'J','K','L'},
{'M','N','O'},{'P','Q','R','S'},{'T','U','V'},{'W','X','Y','Z'}};
String n = "1234";
char[][] sel = new char[n.length()][];
for (int i = 0; i < n.length(); i++) {
int digit = Integer.parseInt("" +n.charAt(i));
sel[i] = letters[digit];
}
permutations(sel, 0, "");
}
public static void permutations(char[][] symbols, int n, String s) {
if (n == symbols.length) {
System.out.println(s);
return;
}
for (int i = 0; i < symbols[n].length; i ++) {
permutations(symbols, n+1, s + symbols[n][i]);
}
}
}
This is a counting problem, so it usually helps to find a solution for a smaller problem, then think about how it expands to your general case.
If you had a 1 digit phone number, how many possibilities would there be? What if you had 2 digits? How did you move from one to the other, and could you come up with a way to solve it for n digits?
Here's what I came up with:
import java.util.*;
public class PhoneMmemonics {
/**
* Mapping between a digit and the characters it represents
*/
private static Map<Character,List<Character>> numberToCharacters = new HashMap<Character,List<Character>>();
static {
numberToCharacters.put('0',new ArrayList<Character>(Arrays.asList('0')));
numberToCharacters.put('1',new ArrayList<Character>(Arrays.asList('1')));
numberToCharacters.put('2',new ArrayList<Character>(Arrays.asList('A','B','C')));
numberToCharacters.put('3',new ArrayList<Character>(Arrays.asList('D','E','F')));
numberToCharacters.put('4',new ArrayList<Character>(Arrays.asList('G','H','I')));
numberToCharacters.put('5',new ArrayList<Character>(Arrays.asList('J','K','L')));
numberToCharacters.put('6',new ArrayList<Character>(Arrays.asList('M','N','O')));
numberToCharacters.put('7',new ArrayList<Character>(Arrays.asList('P','Q','R')));
numberToCharacters.put('8',new ArrayList<Character>(Arrays.asList('T','U','V')));
numberToCharacters.put('9',new ArrayList<Character>(Arrays.asList('W','X','Y','Z')));
}
/**
* Generates a list of all the mmemonics that can exists for the number
* #param phoneNumber
* #return
*/
public static List<String> getMmemonics(int phoneNumber) {
// prepare results
StringBuilder stringBuffer = new StringBuilder();
List<String> results = new ArrayList<String>();
// generate all the mmenonics
generateMmemonics(Integer.toString(phoneNumber), stringBuffer, results);
// return results
return results;
}
/**
* Recursive helper method to generate all mmemonics
*
* #param partialPhoneNumber Numbers in the phone number that haven't converted to characters yet
* #param partialMmemonic The partial word that we have come up with so far
* #param results total list of all results of complete mmemonics
*/
private static void generateMmemonics(String partialPhoneNumber, StringBuilder partialMmemonic, List<String> results) {
// are we there yet?
if (partialPhoneNumber.length() == 0) {
//Printing the pnemmonics
//System.out.println(partialMmemonic.toString());
// base case: so add the mmemonic is complete
results.add(partialMmemonic.toString());
return;
}
// prepare variables for recursion
int currentPartialLength = partialMmemonic.length();
char firstNumber = partialPhoneNumber.charAt(0);
String remainingNumbers = partialPhoneNumber.substring(1);
// for each character that the single number represents
for(Character singleCharacter : numberToCharacters.get(firstNumber)) {
// append single character to our partial mmemonic so far
// and recurse down with the remaining characters
partialMmemonic.setLength(currentPartialLength);
generateMmemonics(remainingNumbers, partialMmemonic.append(singleCharacter), results);
}
}
}
Use recursion and a good data structure to hold the possible characters. Since we are talking numbers, an array of array would work.
char[][] toChar = {{'0'}, {'1'}, {'2', 'A', 'B', 'C'}, ..., {'9', 'W', 'X'. 'Y'} };
Notice that the ith array in this array of arrays holds the characters corresponding to the ith button on the telephone. I.e., tochar[2][0] is '2', tochar[2][1] is 'A', etc.
The recursive function will take index as a parameter. It will have a for loop that iterates through the replacement chars, replacing the char at that index with one from the array. If the length equals the length of the input string, then it outputs the string.
In Java or C#, you would want to use a string buffer to hold the changing string.
function recur(index)
if (index == input.length) output stringbuffer
else
for (i = 0; i < tochar[input[index]].length; i++)
stringbuffer[index] = tochar[input[index]][i]
recur(index + 1)
A question that comes to my mind is the question of what should 0 and 1 become in such a system? Otherwise, what you have is something where you could basically just recursively go through the letters for each value in the 2-9 range for the simple brute force way to churn out all the values.
Assuming normal phone number length within North America and ignoring special area codes initially there is also the question of how many digits represent 4 values instead of 3 as 7 and 9 tend to get those often unused letters Q and Z, because the count could range from 3^10 = 59,049 to 4^10 = 1,048,576. The latter is 1024 squared, I just noticed.
The OP seems to be asking for an implementation as he is struggling to understand the pseudocode above. Perhaps this Tcl script will help:
array set d {
2 {a b c}
3 {d e f}
4 {g h i}
5 {j k l}
6 {m n o}
7 {p q r s}
8 {t u v}
9 {w x y z}
}
proc digstolets {digits} {
global d
set l [list]
if {[string length $digits] == 0} {
return $l
}
set first [string index $digits 0]
catch {set first $d($first)}
if {[string length $digits] == 1} {
return $first
}
set res [digstolets [string range $digits 1 end]]
foreach x $first {
foreach y $res {
lappend l $x$y
}
}
return $l
}
puts [digstolets "1234"]
#include <sstream>
#include <map>
#include <vector>
map< int, string> keyMap;
void MakeCombinations( string first, string joinThis , vector<string>& eachResult )
{
if( !first.size() )
return;
int length = joinThis.length();
vector<string> result;
while( length )
{
string each;
char firstCharacter = first.at(0);
each = firstCharacter;
each += joinThis[length -1];
length--;
result.push_back(each);
}
first = first.substr(1);
vector<string>::iterator begin = result.begin();
vector<string>::iterator end = result.end();
while( begin != end)
{
eachResult.push_back( *begin);
begin++;
}
return MakeCombinations( first, joinThis, eachResult);
}
void ProduceCombinations( int inNumber, vector<string>& result)
{
vector<string> inputUnits;
vector<string> finalres;
int number = inNumber;
while( number )
{
int lastdigit ;
lastdigit = number % 10;
number = number/10;
inputUnits.push_back( keyMap[lastdigit]);
}
if( inputUnits.size() == 2)
{
MakeCombinations(inputUnits[0], inputUnits[1], result);
}
else if ( inputUnits.size() > 2 )
{
MakeCombinations( inputUnits[0] , inputUnits[1], result);
vector<string>::iterator begin = inputUnits.begin();
vector<string>::iterator end = inputUnits.end();
begin += 2;
while( begin != end )
{
vector<string> intermediate = result;
vector<string>::iterator ibegin = intermediate.begin();
vector<string>::iterator iend = intermediate.end();
while( ibegin != iend)
{
MakeCombinations( *ibegin , *begin, result);
//resultbegin =
ibegin++;
}
begin++;
}
}
else
{
}
return;
}
int _tmain(int argc, _TCHAR* argv[])
{
keyMap[1] = "";
keyMap[2] = "abc";
keyMap[3] = "def";
keyMap[4] = "ghi";
keyMap[5] = "jkl";
keyMap[6] = "mno";
keyMap[7] = "pqrs";
keyMap[8] = "tuv";
keyMap[9] = "wxyz";
keyMap[0] = "";
string inputStr;
getline(cin, inputStr);
int number = 0;
int length = inputStr.length();
int tens = 1;
while( length )
{
number += tens*(inputStr[length -1] - '0');
length--;
tens *= 10;
}
vector<string> r;
ProduceCombinations(number, r);
cout << "[" ;
vector<string>::iterator begin = r.begin();
vector<string>::iterator end = r.end();
while ( begin != end)
{
cout << *begin << "," ;
begin++;
}
cout << "]" ;
return 0;
}
C program:
char *str[] = {"0", "1", "2abc", "3def", "4ghi", "5jkl", "6mno", "7pqrs", "8tuv", "9wxyz"};
const char number[]="2061234569";
char printstr[15];
int len;
printph(int index)
{
int i;
int n;
if (index == len)
{
printf("\n");
printstr[len] = '\0';
printf("%s\n", printstr);
return;
}
n =number[index] - '0';
for(i = 0; i < strlen(str[n]); i++)
{
printstr[index] = str[n][i];
printph(index +1);
}
}
Call
printph(0);