Sorting too slow - performance

So, I'm doing a project for my programming languages class, and i have to create a structure, sort it, and then show the time it takes to do it, the thing is bubble sorting(case 1) takes 60 sec to do it, insertion(case 2) 5 sec and selection (case 4) takes 10 sec. All this sorting 100000 elements. shell only takes 0.03 so i started thinking i might have something wrong with my algorithms. can some one help me?
void ordenesc(compleja * vd, int tam)
{
int i=0,j=0,k=0,aux=0,op=0,inc=0,minimo=0;
char auxcad[20];
clock_t start, end;
double tiempo;
op=menus(3);
start = clock();
switch(op)
{
case 1://Burbujeo
for(i=1;i<=tam;i++)
{
for(j=0;j<tam-1;j++)
{
if(vd[j].nro>vd[j+1].nro)
{
aux=vd[j].nro;
vd[j].nro=vd[j+1].nro;
vd[j+1].nro=aux;
strcpy(auxcad,vd[j].cad);
strcpy(vd[j].cad,vd[j+1].cad);
strcpy(vd[j+1].cad,auxcad);
}
}
}
break;
case 2://Inserccion
for(i = 1; i < tam; i++)
{
aux=vd[i].nro;
strcpy(auxcad,vd[i].cad);
for (j = i - 1; j >= 0 && vd[j].nro > aux; j--)
{
vd[j+1].nro=vd[j].nro;
strcpy(vd[j+1].cad,vd[j].cad);
j--;
}
vd[j+1].nro=aux;
strcpy(vd[j+1].cad,auxcad);
}
break;
case 3://Shell
inc=(tam/2);
while (inc > 0)
{
for (i=0; i < tam; i++)
{
j = i;
aux = vd[i].nro;
strcpy(auxcad,vd[i].cad);
while ((j >= inc) && (vd[j-inc].nro > aux))
{
vd[j].nro = vd[j - inc].nro;
strcpy(vd[j].cad,vd[j-inc].cad);
j = j - inc;
}
vd[j].nro = aux;
strcpy(vd[j].cad,auxcad);
}
if (inc == 2)
inc = 1;
else
inc = inc * 5 / 11;
}
break;
case 4://Seleccion
for(i=0;i<tam-1;i++)
{
minimo=i;
for(j=i+1;j<tam;j++)
{
if(vd[minimo].nro > vd[j].nro) minimo=j;
}
aux=vd[minimo].nro;
vd[minimo].nro=vd[i].nro;
vd[i].nro=aux;
strcpy(auxcad,vd[minimo].cad);
strcpy(vd[minimo].cad,vd[i].cad);
strcpy(vd[i].cad,auxcad);
}
break;
case 9:
break;
default:
break;
}
end = clock();
tiempo = ((double) (end - start)) / CLOCKS_PER_SEC;
//system("cls");
i=0;
for(i=0;i<tam;i++){
printf("%d %s \n",vd[i].nro,vd[i].cad);}
printf("\n Tardo %f segundos \n", tiempo);
return;
}
P.d:Edited the text sorry for my english is not my first language and my brain is failing due to this.

To make sure your sort algorithm works as expected, you could add a check to the final loop that the elements are actually ordered when you print them. Its relatively unlikely that there is a fundamental error in the algorithm and it still sorts correctly.
One point of the exercise may be to show that sorting algorithms really matter, and selection sort is the only algorithm that has a better performance than O(n^2) in your list. So I wouldn't be too surprised by wide differences in performance.
One improvement you could make to bubble sort is that you only need to iterate over i elements in the inner loop (instead of tam), as the i-largest element will have bubbled up all the way in the inner loop.
Another improvement may be to just copy the pointers instead of the contents of the char arrays, e.g.
instead of
char auxcad[20];
...
strcpy(auxcad, vd[j].cad);
strcpy(vd[j].cad, vd[j+1].cad);
strcpy(vd[j+1].cad, auxcad);
you may want to write
char* auxcad;
...
auxcad = vd[j].cad;
vd[j].cad = vd[j+1].cad;
vd[j+1].cad = auxcad;

Related

How much can we trust to warnings generated by static analysis tools for vulnerablity detection?

I am running flawfinder on a set of libraries written in C/C++. I have a lot of generated warnings by flawfinder. My question is that, how much I can rely on these generated warnings? For example, consider the following function from numpy library (https://github.com/numpy/numpy/blob/4ada0641ed1a50a2473f8061f4808b4b0d68eff5/numpy/f2py/src/fortranobject.c):
static PyObject *
fortran_doc(FortranDataDef def)
{
char *buf, *p;
PyObject *s = NULL;
Py_ssize_t n, origsize, size = 100;
if (def.doc != NULL) {
size += strlen(def.doc);
}
origsize = size;
buf = p = (char *)PyMem_Malloc(size);
if (buf == NULL) {
return PyErr_NoMemory();
}
if (def.rank == -1) {
if (def.doc) {
n = strlen(def.doc);
if (n > size) {
goto fail;
}
memcpy(p, def.doc, n);
p += n;
size -= n;
}
else {
n = PyOS_snprintf(p, size, "%s - no docs available", def.name);
if (n < 0 || n >= size) {
goto fail;
}
p += n;
size -= n;
}
}
else {
PyArray_Descr *d = PyArray_DescrFromType(def.type);
n = PyOS_snprintf(p, size, "'%c'-", d->type);
Py_DECREF(d);
if (n < 0 || n >= size) {
goto fail;
}
p += n;
size -= n;
if (def.data == NULL) {
n = format_def(p, size, def) == -1;
if (n < 0) {
goto fail;
}
p += n;
size -= n;
}
else if (def.rank > 0) {
n = format_def(p, size, def);
if (n < 0) {
goto fail;
}
p += n;
size -= n;
}
else {
n = strlen("scalar");
if (size < n) {
goto fail;
}
memcpy(p, "scalar", n);
p += n;
size -= n;
}
}
if (size <= 1) {
goto fail;
}
*p++ = '\n';
size--;
/* p now points one beyond the last character of the string in buf */
#if PY_VERSION_HEX >= 0x03000000
s = PyUnicode_FromStringAndSize(buf, p - buf);
#else
s = PyString_FromStringAndSize(buf, p - buf);
#endif
PyMem_Free(buf);
return s;
fail:
fprintf(stderr, "fortranobject.c: fortran_doc: len(p)=%zd>%zd=size:"
" too long docstring required, increase size\n",
p - buf, origsize);
PyMem_Free(buf);
return NULL;
}
There are two memcpy() API calls, and flawfinder tells me that:
['vul_fortranobject.c:216: [2] (buffer) memcpy:\\n Does not check for buffer overflows when copying to destination (CWE-120).\\n Make sure destination can always hold the source data.\\n memcpy(p, "scalar", n);']
I am not sure whether the report is true.
To answer your question: static analysis tools (like FlawFinder) can generate a LOT of "false positives".
I Googled to find some quantifiable information for you, and found an interesting article about "DeFP":
https://arxiv.org/pdf/2110.03296.pdf
Static analysis tools are frequently used to detect potential
vulnerabilities in software systems. However, an inevitable problem of
these tools is their large number of warnings with a high false
positive rate, which consumes time and effort for investigating. In
this paper, we present DeFP, a novel method for ranking static analysis warnings.
Based on the intuition that warnings which have
similar contexts tend to have similar labels (true positive or false
positive), DeFP is built with two BiLSTM models to capture the
patterns associated with the contexts of labeled warnings. After that,
for a set of new warnings, DeFP can calculate and rank them according
to their likelihoods to be true positives (i.e., actual
vulnerabilities).
Our experimental results on a dataset of 10
real-world projects show that using DeFP, by investigating only 60% of
the warnings, developers can find
+90% of actual vulnerabilities. Moreover, DeFP improves the state-of-the-art approach 30% in both Precision and Recall.
Apparently, the authors built a neural network to analyze FlawFinder results, and rank them.
I doubt DeFP is a practical "solution" for you. But yes: if you think that specific "memcpy()" warning is a "false positive" - then I'm inclined to agree. It very well could be :)

String permutation with duplicate characters

I have string "0011" and want all of the combinations without duplicate.
that's means I want a string with a combination of two '0' and two '1';
for example : [0011,0101,0110,1001,1010,1100]
I tried with this and the result is exactly what i need.
private void permutation(String result, String str, HashSet hashset) {
if (str.length()==0 && !hashSet.contains(result)){
System.out.println(result);
hashSet.add(result);
return;
}
IntStream.range(0,str.length()).forEach(pos->permutation(result+ str.charAt(pos), str.substring(0, pos) + str.substring(pos+1),hashset));
}
if i remove HashSet, this code will produce 24 results instead of 6 results.
but the time complexity of this code is O(n!).
how to avoid it to create a duplicate string and reduce the time complexity?
Probably something like this can be faster than n! even on small n
The idea is to count how many bits we need should be in resulting item and
iterate through all posible values and filter only those than have same number of bits. It will work similar amount of time with only one 1 and for 50%/50% of 0 and 1
function bitCount(n) {
n = n - ((n >> 1) & 0x55555555)
n = (n & 0x33333333) + ((n >> 2) & 0x33333333)
return ((n + (n >> 4) & 0xF0F0F0F) * 0x1010101) >> 24
}
function perm(inp) {
const bitString = 2;
const len = inp.length;
const target = bitCount(parseInt(inp, bitString));
const min = (Math.pow(target, bitString) - 1);
const max = min << (len - target);
const result = [];
for (let i = min; i < max + 1; i++) {
if (bitCount(i) === target) {
result.push(i.toString(bitString).padStart(len, '0'));
}
}
return result;
}
const inp = '0011';
const res = perm(inp);
console.log('result',res);
P.s. My first idea was probably faster than upper code. But upper is easier to implement
first idea was to convert string to int
and use bitwise left shift but only for one digit every time. it still depends on n. and can be larger or smaller than upper solution. but bitwise shift is faster itself.
example
const input = '0011'
const len = input.length;
step1: calc number of bits = 2;
then generate first element = 3(Dec) is = '0011' in bin
step2 move last from the right bit one position left with << operator: '0101'
step3 move again: '1001'
step4: we are reached `len` so use next bit:100'1' : '1010'
step5: repeat:'1100'
step6: move initial 3 << 1: '0110'
repeat above steps: '1010'
step8: '1100'
it will generate duplicates so probably can be improved
Hope it helps
The worst case time complexity cannot be improved because there can be no duplicates in a string. However, in case of a multi-set, we could prune a lot of sub-trees to prevent duplicates.
The key idea is to permute the string using traditional backtracking algorithm but prevent swapping if the character has been previously swapped to prevent duplicates.
Here is a C++ code snippet that prevents duplicates and doesn't use any memory for lookup.
bool shouldSwap(const string& str, size_t start, size_t index) {
for (auto i = start; i < index; ++i) {
if (str[i] == str[index])
return false;
}
return true;
}
void permute(string& str, size_t index)
{
if (index >= str.size()) {
cout << str << endl;;
return;
}
for (size_t i = index; i < str.size(); ++i) {
if(shouldSwap(str, index, i)) {
swap(str[index], str[i]);
permute(str, index + 1);
swap(str[index], str[i]);
}
}
}
Running demo. Also refer to SO answer here and Distinct permutations for more references.
Also, note that the time complexity of this solution is O(n2 n!)
O(n) for printing a string
O(n) for iterating over the string to generate swaps and recurrence.
O(n!) possible states for the number of permutations.

Make unique array with minimal sum

It is a interview question. Given an array, e.g., [3,2,1,2,7], we want to make all elements in this array unique by incrementing duplicate elements and we require the sum of the refined array is minimal. For example the answer for [3,2,1,2,7] is [3,2,1,4,7] and its sum is 17. Any ideas?
It's not quite as simple as my earlier comment suggested, but it's not terrifically complicated.
First, sort the input array. If it matters to be able to recover the original order of the elements then record the permutation used for the sort.
Second, scan the sorted array from left to right (ie from low to high). If an element is less than or equal to the element to its left, set it to be one greater than that element.
Pseudocode
sar = sort(input_array)
for index = 2:size(sar) ! I count from 1
if sar(index)<=sar(index-1) sar(index) = sar(index-1)+1
forend
Is the sum of the result minimal ? I've convinced myself that it is through some head-scratching and trials but I haven't got a formal proof.
If you only need to find ONE of the best solution, here's the algorythm with some explainations.
The idea of this problem is to find an optimal solution, which can be found only by testing all existing solutions (well, they're infinite, let's stick with the reasonable ones).
I wrote a program in C, because I'm familiar with it, but you can port it to any language you want.
The program does this: it tries to increment one value to the max possible (I'll explain how to find it in the comments under the code sections), than if the solution is not found, decreases this value and goes on with the next one and so on.
It's an exponential algorythm, so it will be very slow on large values of duplicated data (yet, it assures you the best solution is found).
I tested this code with your example, and it worked; not sure if there's any bug left, but the code (in C) is this.
#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
typedef int BOOL; //just to ease meanings of values
#define TRUE 1
#define FALSE 0
Just to ease comprehension, I did some typedefs. Don't worry.
typedef struct duplicate { //used to fasten the algorythm; it uses some more memory just to assure it's ok
int value;
BOOL duplicate;
} duplicate_t;
int maxInArrayExcept(int *array, int arraySize, int index); //find the max value in array except the value at the index given
//the result is the max value in the array, not counting th index
int *findDuplicateSum(int *array, int arraySize);
BOOL findDuplicateSum_R(duplicate_t *array, int arraySize, int *tempSolution, int *solution, int *totalSum, int currentSum); //resursive function used to find solution
BOOL check(int *array, int arraySize); //checks if there's any repeated value in the solution
These are all the functions we'll need. All split up for comprehension purpose.
First, we have a struct. This struct is used to avoid checking, for every iteration, if the value on a given index was originally duplicated. We don't want to modify any value not duplicated originally.
Then, we have a couple functions: first, we need to see the worst case scenario: every value after the duplicated ones is already occupied: then we need to increment the duplicated value up to the maximum value reached + 1.
Then, there are the main Function we'll discute later about.
The check Function only checks if there's any duplicated value in a temporary solution.
int main() { //testing purpose
int i;
int testArray[] = { 3,2,1,2,7 }; //test array
int nTestArraySize = 5; //test array size
int *solutionArray; //needed if you want to use the solution later
solutionArray = findDuplicateSum(testArray, nTestArraySize);
for (i = 0; i < nTestArraySize; ++i) {
printf("%d ", solutionArray[i]);
}
return 0;
}
This is the main Function: I used it to test everything.
int * findDuplicateSum(int * array, int arraySize)
{
int *solution = malloc(sizeof(int) * arraySize);
int *tempSolution = malloc(sizeof(int) * arraySize);
duplicate_t *duplicate = calloc(arraySize, sizeof(duplicate_t));
int i, j, currentSum = 0, totalSum = INT_MAX;
for (i = 0; i < arraySize; ++i) {
tempSolution[i] = solution[i] = duplicate[i].value = array[i];
currentSum += array[i];
for (j = 0; j < i; ++j) { //to find ALL the best solutions, we should also put the first found value as true; it's just a line more
//yet, it saves the algorythm half of the duplicated numbers (best/this case scenario)
if (array[j] == duplicate[i].value) {
duplicate[i].duplicate = TRUE;
}
}
}
if (findDuplicateSum_R(duplicate, arraySize, tempSolution, solution, &totalSum, currentSum));
else {
printf("No solution found\n");
}
free(tempSolution);
free(duplicate);
return solution;
}
This Function does a lot of things: first, it sets up the solution array, then it initializes both the solution values and the duplicate array, that is the one used to check for duplicated values at startup. Then, we find the current sum and we set the maximum available sum to the maximum integer possible.
Then, the recursive Function is called; this one gives us the info about having found the solution (that should be Always), then we return the solution as an array.
int findDuplicateSum_R(duplicate_t * array, int arraySize, int * tempSolution, int * solution, int * totalSum, int currentSum)
{
int i;
if (check(tempSolution, arraySize)) {
if (currentSum < *totalSum) { //optimal solution checking
for (i = 0; i < arraySize; ++i) {
solution[i] = tempSolution[i];
}
*totalSum = currentSum;
}
return TRUE; //just to ensure a solution is found
}
for (i = 0; i < arraySize; ++i) {
if (array[i].duplicate == TRUE) {
if (array[i].duplicate <= maxInArrayExcept(solution, arraySize, i)) { //worst case scenario, you need it to stop the recursion on that value
tempSolution[i]++;
return findDuplicateSum_R(array, arraySize, tempSolution, solution, totalSum, currentSum + 1);
tempSolution[i]--; //backtracking
}
}
}
return FALSE; //just in case the solution is not found, but we won't need it
}
This is the recursive Function. It first checks if the solution is ok and if it is the best one found until now. Then, if everything is correct, it updates the actual solution with the temporary values, and updates the optimal condition.
Then, we iterate on every repeated value (the if excludes other indexes) and we progress in the recursion until (if unlucky) we reach the worst case scenario: the check condition not satisfied above the maximum value.
Then we have to backtrack and continue with the iteration, that will go on with other values.
PS: an optimization is possible here, if we move the optimal condition from the check into the for: if the solution is already not optimal, we can't expect to find a better one just adding things.
The hard code has ended, and there are the supporting functions:
int maxInArrayExcept(int *array, int arraySize, int index) {
int i, max = 0;
for (i = 0; i < arraySize; ++i) {
if (i != index) {
if (array[i] > max) {
max = array[i];
}
}
}
return max;
}
BOOL check(int *array, int arraySize) {
int i, j;
for (i = 0; i < arraySize; ++i) {
for (j = 0; j < i; ++j) {
if (array[i] == array[j]) return FALSE;
}
}
return TRUE;
}
I hope this was useful.
Write if anything is unclear.
Well, I got the same question in one of my interviews.
Not sure if you still need it. But here's how I did it. And it worked well.
num_list1 = [2,8,3,6,3,5,3,5,9,4]
def UniqueMinSumArray(num_list):
max=min(num_list)
for i,V in enumerate(num_list):
while (num_list.count(num_list[i])>1):
if (max > num_list[i]+1) :
num_list[i] = max + 1
else:
num_list[i]+=1
max = num_list[i]
i+=1
return num_list
print (sum(UniqueMinSumArray(num_list1)))
You can try with your list of numbers and I am sure it will give you the correct unique minimum sum.
I got the same interview question too. But my answer is in JS in case anyone is interested.
For sure it can be improved to get rid of for loop.
function getMinimumUniqueSum(arr) {
// [1,1,2] => [1,2,3] = 6
// [1,2,2,3,3] = [1,2,3,4,5] = 15
if (arr.length > 1) {
var sortedArr = [...arr].sort((a, b) => a - b);
var current = sortedArr[0];
var res = [current];
for (var i = 1; i + 1 <= arr.length; i++) {
// check current equals to the rest array starting from index 1.
if (sortedArr[i] > current) {
res.push(sortedArr[i]);
current = sortedArr[i];
} else if (sortedArr[i] == current) {
current = sortedArr[i] + 1;
// sortedArr[i]++;
res.push(current);
} else {
current++;
res.push(current);
}
}
return res.reduce((a,b) => a + b, 0);
} else {
return 0;
}
}

OpenACC bitonic sort is much slower on GPU than on CPU

I have the following bit of code to sort double values on my GPU:
void bitonic_sort(double *data, int length) {
#pragma acc data copy(data[0:length], length)
{
int i,j,k;
for (k = 2; k <= length; k *= 2) {
for (j=k >> 1; j > 0; j = j >> 1) {
#pragma acc parallel loop gang worker vector independent
for (i = 0; i < length; i++) {
int ixj = i ^ j;
if ((ixj) > i) {
if ((i & k) == 0 && data[i] > data[ixj]) {
_ValueType buffer = data[i];
data[i] = data[ixj];
data[ixj] = buffer;
}
if ((i & k) != 0 && data[i] < data[ixj]) {
_ValueType buffer = data[i];
data[i] = data[ixj];
data[ixj] = buffer;
}
}
}
}
}
}
}
This is a bit slower on my GPU than on my CPU. I'm using GCC 6.1. I can't figure out, how to run the whole code on my GPU. So far, only the parallel loop is executed on the cpu and it switches between CPU and GPU for each one of the outer loops.
I'd like to run the whole content of the function on the GPU, but I can't figure out how. One major problem for me now is that the GCC implementation currently doesn't allow nested parallelism, so I can't use a parallel construct inside another parallel construct. Is there any way to get around that?
I've tried putting a kernels construct on top of the first loop but that slows it down by a factor of about 10. If I use a parallel construct above the first loop instead, the result isn't sorted any more, which makes sense. The two outer loops need to be executed sequentially for the algorithm to work.
If you have any other suggestions on how I could improve performance, I would be grateful as well.

Remove duplicate items with minimal auxiliary memory?

What is the most efficient way to remove duplicate items from an array under the constraint that axillary memory usage must be to a minimum, preferably small enough to not even require any heap allocations? Sorting seems like the obvious choice, but this is clearly not asymptotically efficient. Is there a better algorithm that can be done in place or close to in place? If sorting is the best choice, what kind of sort would be best for something like this?
I'll answer my own question since, after posting, I came up with a really clever algorithm to do this. It uses hashing, building something like a hash set in place. It's guaranteed to be O(1) in axillary space (the recursion is a tail call), and is typically O(N) time complexity. The algorithm is as follows:
Take the first element of the array, this will be the sentinel.
Reorder the rest of the array, as much as possible, such that each element is in the position corresponding to its hash. As this step is completed, duplicates will be discovered. Set them equal to sentinel.
Move all elements for which the index is equal to the hash to the beginning of the array.
Move all elements that are equal to sentinel, except the first element of the array, to the end of the array.
What's left between the properly hashed elements and the duplicate elements will be the elements that couldn't be placed in the index corresponding to their hash because of a collision. Recurse to deal with these elements.
This can be shown to be O(N) provided no pathological scenario in the hashing:
Even if there are no duplicates, approximately 2/3 of the elements will be eliminated at each recursion. Each level of recursion is O(n) where small n is the amount of elements left. The only problem is that, in practice, it's slower than a quick sort when there are few duplicates, i.e. lots of collisions. However, when there are huge amounts of duplicates, it's amazingly fast.
Edit: In current implementations of D, hash_t is 32 bits. Everything about this algorithm assumes that there will be very few, if any, hash collisions in full 32-bit space. Collisions may, however, occur frequently in the modulus space. However, this assumption will in all likelihood be true for any reasonably sized data set. If the key is less than or equal to 32 bits, it can be its own hash, meaning that a collision in full 32-bit space is impossible. If it is larger, you simply can't fit enough of them into 32-bit memory address space for it to be a problem. I assume hash_t will be increased to 64 bits in 64-bit implementations of D, where datasets can be larger. Furthermore, if this ever did prove to be a problem, one could change the hash function at each level of recursion.
Here's an implementation in the D programming language:
void uniqueInPlace(T)(ref T[] dataIn) {
uniqueInPlaceImpl(dataIn, 0);
}
void uniqueInPlaceImpl(T)(ref T[] dataIn, size_t start) {
if(dataIn.length - start < 2)
return;
invariant T sentinel = dataIn[start];
T[] data = dataIn[start + 1..$];
static hash_t getHash(T elem) {
static if(is(T == uint) || is(T == int)) {
return cast(hash_t) elem;
} else static if(__traits(compiles, elem.toHash)) {
return elem.toHash;
} else {
static auto ti = typeid(typeof(elem));
return ti.getHash(&elem);
}
}
for(size_t index = 0; index < data.length;) {
if(data[index] == sentinel) {
index++;
continue;
}
auto hash = getHash(data[index]) % data.length;
if(index == hash) {
index++;
continue;
}
if(data[index] == data[hash]) {
data[index] = sentinel;
index++;
continue;
}
if(data[hash] == sentinel) {
swap(data[hash], data[index]);
index++;
continue;
}
auto hashHash = getHash(data[hash]) % data.length;
if(hashHash != hash) {
swap(data[index], data[hash]);
if(hash < index)
index++;
} else {
index++;
}
}
size_t swapPos = 0;
foreach(i; 0..data.length) {
if(data[i] != sentinel && i == getHash(data[i]) % data.length) {
swap(data[i], data[swapPos++]);
}
}
size_t sentinelPos = data.length;
for(size_t i = swapPos; i < sentinelPos;) {
if(data[i] == sentinel) {
swap(data[i], data[--sentinelPos]);
} else {
i++;
}
}
dataIn = dataIn[0..sentinelPos + start + 1];
uniqueInPlaceImpl(dataIn, start + swapPos + 1);
}
Keeping auxillary memory usage to a minimum, your best bet would be to do an efficient sort to get them in order, then do a single pass of the array with a FROM and TO index.
You advance the FROM index every time through the loop. You only copy the element from FROM to TO (and increment TO) when the key is different from the last.
With Quicksort, that'll average to O(n-log-n) and O(n) for the final pass.
If you sort the array, you will still need another pass to remove duplicates, so the complexity is O(NN) in the worst case (assuming Quicksort), or O(Nsqrt(N)) using Shellsort.
You can achieve O(N*N) by simply scanning the array for each element removing duplicates as you go.
Here is an example in Lua:
function removedups (t)
local result = {}
local count = 0
local found
for i,v in ipairs(t) do
found = false
if count > 0 then
for j = 1,count do
if v == result[j] then found = true; break end
end
end
if not found then
count = count + 1
result[count] = v
end
end
return result, count
end
I don't see any way to do this without something like a bubblesort. When you find a dupe, you need to reduce the length of the array. Quicksort is not designed for the size of the array to change.
This algorithm is always O(n^2) but it also use almost no extra memory -- stack or heap.
// returns the new size
int bubblesqueeze(int* a, int size) {
for (int j = 0; j < size - 1; ++j) {
for (int i = j + 1; i < size; ++i) {
// when a dupe is found, move the end value to index j
// and shrink the size of the array
while (i < size && a[i] == a[j]) {
a[i] = a[--size];
}
if (i < size && a[i] < a[j]) {
int tmp = a[j];
a[j] = a[i];
a[i] = tmp;
}
}
}
return size;
}
Is you have two different var for traversing a datadet insted of just one then you can limit the output by dismissing all diplicates that currently are already in the dataset.
Obvious this example in C is not an efficiant sorting algorith but it is just an example on one way to look at the probkem.
You could also blindly sort the data first and then relocate the data for removing dups, but I'm not sure that would be faster.
#define ARRAY_LENGTH 15
int stop = 1;
int scan_sort[ARRAY_LENGTH] = {5,2,3,5,1,2,5,4,3,5,4,8,6,4,1};
void step_relocate(char tmp,char s,int *dataset)
{
for(;tmp<s;s--)
dataset[s] = dataset[s-1];
}
int exists(int var,int *dataset)
{
int tmp=0;
for(;tmp < stop; tmp++)
{
if( dataset[tmp] == var)
return 1;/* value exsist */
if( dataset[tmp] > var)
tmp=stop;/* Value not in array*/
}
return 0;/* Value not in array*/
}
void main(void)
{
int tmp1=0;
int tmp2=0;
int index = 1;
while(index < ARRAY_LENGTH)
{
if(exists(scan_sort[index],scan_sort))
;/* Dismiss all values currently in the final dataset */
else if(scan_sort[stop-1] < scan_sort[index])
{
scan_sort[stop] = scan_sort[index];/* Insert the value as the highest one */
stop++;/* One more value adde to the final dataset */
}
else
{
for(tmp1=0;tmp1<stop;tmp1++)/* find where the data shall be inserted */
{
if(scan_sort[index] < scan_sort[tmp1])
{
index = index;
break;
}
}
tmp2 = scan_sort[index]; /* Store in case this value is the next after stop*/
step_relocate(tmp1,stop,scan_sort);/* Relocated data already in the dataset*/
scan_sort[tmp1] = tmp2;/* insert the new value */
stop++;/* One more value adde to the final dataset */
}
index++;
}
printf("Result: ");
for(tmp1 = 0; tmp1 < stop; tmp1++)
printf( "%d ",scan_sort[tmp1]);
printf("\n");
system( "pause" );
}
I liked the problem so I wrote a simple C test prog for it as you can see above. Make a comment if I should elaborate or you see any faults.

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