Sorting Numbers with arrays - arrays

Im really new to programming in Java so any answers don't be shy in really dumbing it down as much as possible.
I'm trying to create a program that will take an array value and sort it from smallest to largest number. This is what I've got so far:
public class ArraySwap
{
public static void main(String[] args)
{
int[a] = new int[4];
a[0] = 5;
a[1] = 7;
a[2] = 2;
a[3] = 1;
for (int i = a.length-1;
Thats what I've got so far, but I've no idea what to use in the for loop, it has to be an actual code formula with a for loop so no using array.sort or anything like that.
The output should re-arrange the numbers so they display 1 2 5 7 instead of 5 7 2 1 which is what they would be if I just had it print them out down the list.
My teacher gave me an example of what to use as this:
void swap (int x, int y)
{
int temp;
temp = x
x = y
y = temp;
}
But I have no idea how to use this in the program.

As mentioned by others, it would be good to read up on bubble sorting algorithms.
To answer your question, the swap function would be used every time two elements are out of order (when a larger number is before a smaller number). A pseudo-code example would be:
loop until no element changes through one cycle
for every element in the array minus one
if one element is greater than the element after it
swap()
And that is bubble sort! I hope this helps.

This is where you should use the simplest sorting algorithm in the world: Bubble Sort. Click here for the Wikipedia article describing step by step how to do it.
If you are still having trouble, leave a comment to this response.

Related

Making a character array rotate its cells left/right n times

I'm totally new here but I heard a lot about this site and now that I've been accepted for a 7 months software development 'bootcamp' I'm sharpening my C knowledge for an upcoming test.
I've been assigned a question on a test that I've passed already, but I did not finish that question and it bothers me quite a lot.
The question was a task to write a program in C that moves a character (char) array's cells by 1 to the left (it doesn't quite matter in which direction for me, but the question specified left). And I also took upon myself NOT to use a temporary array/stack or any other structure to hold the entire array data during execution.
So a 'string' or array of chars containing '0' '1' '2' 'A' 'B' 'C' will become
'1' '2' 'A' 'B' 'C' '0' after using the function once.
Writing this was no problem, I believe I ended up with something similar to:
void ArrayCharMoveLeft(char arr[], int arrsize, int times) {
int i;
for (i = 0; i <= arrsize ; i++) {
ArraySwap2CellsChar(arr, i, i+1);
}
}
As you can see the function is somewhat modular since it allows to input how many times the cells need to move or shift to the left. I did not implement it, but that was the idea.
As far as I know there are 3 ways to make this:
Loop ArrayCharMoveLeft times times. This feels instinctively inefficient.
Use recursion in ArrayCharMoveLeft. This should resemble the first solution, but I'm not 100% sure on how to implement this.
This is the way I'm trying to figure out: No loop within loop, no recursion, no temporary array, the program will know how to move the cells x times to the left/right without any issues.
The problem is that after swapping say N times of cells in the array, the remaining array size - times are sometimes not organized. For example:
Using ArrayCharMoveLeft with 3 as times with our given array mentioned above will yield
ABC021 instead of the expected value of ABC012.
I've run the following function for this:
int i;
char* lastcell;
if (!(times % arrsize))
{
printf("Nothing to move!\n");
return;
}
times = times % arrsize;
// Input checking. in case user inputs multiples of the array size, auto reduce to array size reminder
for (i = 0; i < arrsize-times; i++) {
printf("I = %d ", i);
PrintArray(arr, arrsize);
ArraySwap2CellsChar(arr, i, i+times);
}
As you can see the for runs from 0 to array size - times. If this function is used, say with an array containing 14 chars. Then using times = 5 will make the for run from 0 to 9, so cells 10 - 14 are NOT in order (but the rest are).
The worst thing about this is that the remaining cells always maintain the sequence, but at different position. Meaning instead of 0123 they could be 3012 or 2301... etc.
I've run different arrays on different times values and didn't find a particular pattern such as "if remaining cells = 3 then use ArrayCharMoveLeft on remaining cells with times = 1).
It always seem to be 1 out of 2 options: the remaining cells are in order, or shifted with different values. It seems to be something similar to this:
times shift+direction to allign
1 0
2 0
3 0
4 1R
5 3R
6 5R
7 3R
8 1R
the numbers change with different times and arrays. Anyone got an idea for this?
even if you use recursion or loops within loops, I'd like to hear a possible solution. Only firm rule for this is not to use a temporary array.
Thanks in advance!
If irrespective of efficiency or simplicity for the purpose of studying you want to use only exchanges of two array elements with ArraySwap2CellsChar, you can keep your loop with some adjustment. As you noted, the given for (i = 0; i < arrsize-times; i++) loop leaves the last times elements out of place. In order to correctly place all elements, the loop condition has to be i < arrsize-1 (one less suffices because if every element but the last is correct, the last one must be right, too). Of course when i runs nearly up to arrsize, i+times can't be kept as the other swap index; instead, the correct index j of the element which is to be put at index i has to be computed. This computation turns out somewhat tricky, due to the element having been swapped already from its original place. Here's a modified variant of your loop:
for (i = 0; i < arrsize-1; i++)
{
printf("i = %d ", i);
int j = i+times;
while (arrsize <= j) j %= arrsize, j += (i-j+times-1)/times*times;
printf("j = %d ", j);
PrintArray(arr, arrsize);
ArraySwap2CellsChar(arr, i, j);
}
Use standard library functions memcpy, memmove, etc as they are very optimized for your platform.
Use the correct type for sizes - size_t not int
char *ArrayCharMoveLeft(char *arr, const size_t arrsize, size_t ntimes)
{
ntimes %= arrsize;
if(ntimes)
{
char temp[ntimes];
memcpy(temp, arr, ntimes);
memmove(arr, arr + ntimes, arrsize - ntimes);
memcpy(arr + arrsize - ntimes, temp, ntimes);
}
return arr;
}
But you want it without the temporary array (more memory efficient, very bad performance-wise):
char *ArrayCharMoveLeft(char *arr, size_t arrsize, size_t ntimes)
{
ntimes %= arrsize;
while(ntimes--)
{
char temp = arr[0];
memmove(arr, arr + 1, arrsize - 1);
arr[arrsize -1] = temp;
}
return arr;
}
https://godbolt.org/z/od68dKTWq
https://godbolt.org/z/noah9zdYY
Disclaimer: I'm not sure if it's common to share a full working code here or not, since this is literally my first question asked here, so I'll refrain from doing so assuming the idea is answering specific questions, and not providing an example solution for grabs (which might defeat the purpose of studying and exploring C). This argument is backed by the fact that this specific task is derived from a programing test used by a programing course and it's purpose is to filter out applicants who aren't fit for intense 7 months training in software development. If you still wish to see my code, message me privately.
So, with a great amount of help from #Armali I'm happy to announce the question is answered! Together we came up with a function that takes an array of characters in C (string), and without using any previously written libraries (such as strings.h), or even a temporary array, it rotates all the cells in the array N times to the left.
Example: using ArrayCharMoveLeft() on the following array with N = 5:
Original array: 0123456789ABCDEF
Updated array: 56789ABCDEF01234
As you can see the first cell (0) is now the sixth cell (5), the 2nd cell is the 7th cell and so on. So each cell was moved to the left 5 times. The first 5 cells 'overflow' to the end of the array and now appear as the Last 5 cells, while maintaining their order.
The function works with various array lengths and N values.
This is not any sort of achievement, but rather an attempt to execute the task with as little variables as possible (only 4 ints, besides the char array, also counting the sub function used to swap the cells).
It was achieved using a nested loop so by no means its efficient runtime-wise, just memory wise, while still being self-coded functions, with no external libraries used (except stdio.h).
Refer to Armali's posted solution, it should get you the answer for this question.

Implementing Radix sort in java - quite a few questions

Although it is not clearly stated in my excercise, I am supposed to implement Radix sort recursively. I've been working on the task for days, but yet, I only managed to produce garbage, unfortunately. We are required to work with two methods. The sort method receives a certain array with numbers ranging from 0 to 999 and the digit we are looking at. We are supposed to generate a two-dimensional matrix here in order to distribute the numbers inside the array. So, for example, 523 is positioned at the fifth row and 27 is positioned at the 0th row since it is interpreted as 027.
I tried to do this with the help of a switch-case-construct, dividing the numbers inside the array by 100, checking for the remainder and then position the number with respect to the remainder. Then, I somehow tried to build buckets that include only the numbers with the same digit, so for example, 237 and 247 would be thrown in the same bucket in the first "round". I tried to do this by taking the whole row of the "fields"-matrix where we put in the values before.
In the putInBucket-method, I am required to extent the bucket (which I managed to do right, I guess) and then returning it.
I am sorry, I know that the code is total garbage, but maybe there's someone out there who understands what I am up to and can help me a little bit.
I simply don't see how I need to work with the buckets here, I even don't understand why I have to extent them, and I don't see any way to returning it back to the sort-method (which, I think, I am required to do).
Further description:
The whole thing is meant to work as follows: We take an array with integers ranging from 0 to 999. Every number is then sorted by its first digit, as mentioned above. Imagine you have buckets denoted with the numbers ranging from 0 to 9. You start the sorting by putting 523 in bucket 5, 672 in bucket 6 and so on. This is easy when there is only one number (or no number at all) in one of the buckets. But it gets harder (and that's where recursion might come in hand) when you want to put more than one number in one bucket. The mechanism now goes as follows: We put two numbers with the same first digit in one bucket, for example 237 and 245. Now, we want to sort these numbers again by the same algorithm, meaning we call the sort-method (somehow) again with an array that only contains these two numbers and sorting them again, but now my we do by looking at the second digit, so we would compare 3 and 4. We sort every number inside the array like this, and at the end, in order to get a sorted array, we start at the end, meaning at bucket 9, and then just put everything together. If we would be at bucket 2, the algorithm would look into the recursive step and already receive the sorted array [237, 245] and deliver it in order to complete the whole thing.
My own problems:
I don't understand why we need to extent a bucket and I can't figure it out from the description. It is simply stated that we are supposed to do so. I'd imagine that we would to it to copy another element inside it, because if we have the buckets from 0 to 9, putting in two numbers inside the same bucket would just mean that we would overwrite the first value. This might be the reason why we need to return the new, extended bucket, but I am not sure about that. Plus, I don't know how to go further from there. Even if I have an extened bucket now, it's not like I can simply stick it to the old matrix and copy another element into it again.
public static int[] sort(int[] array, int digit) {
if (array.length == 0)
return array;
int[][] fields = new int[10][array.length];
int[] bucket = new int[array.length];
int i = 0;
for (int j = 0; j < array.length; j++) {
switch (array[j] / 100) {
case 0: i = 0; break;
case 1: i = 1; break;
...
}
fields[i][j] = array[j]
bucket[i] = fields[i][j];
}
return bucket;
}
private static int[] putInBucket(int [] bucket, int number) {
int[] bucket_new = int[bucket.length+1];
for (int i = 1; i < bucket_new.length; i++) {
bucket_new[i] = bucket[i-1];
}
return bucket_new;
}
public static void main (String [] argv) {
int[] array = readInts("Please type in the numbers: ");
int digit = 0;
int[] bucket = sort(array, digit);
}
You don't use digit in sort, that's quite suspicious
The switch/case looks like a quite convoluted way to write i = array[j] / 100
I'd recommend to read the wikipedia description of radix sort.
The expression to extract a digit from a base 10 number is (number / Math.pow(10, digit)) % 10.
Note that you can count digits from left to right or right to left, make sure you get this right.
I suppose you first want to sort for digit 0, then for digit 1, then for digit 2. So there should be a recursive call at the end of sort that does this.
Your buckets array needs to be 2-dimensional. You'll need to call it this way: buckets[i] = putInBucket(buckets[i], array[j]). If you handle null in putInBuckets, you don't need to initialize it.
The reason why you need a 2d bucket array and putInBucket (instead of your fixed size field) is that you don't know how many numbers will end up in each bucket
The second phase (reading back from the buckets to the array) is missing before the recursive call
make sure to stop the recursion after 3 digits
Good luck

Given a list of n integers , find the minimum subset sum greater than X

Given an unsorted set of integers in the form of array, find minimum subset sum greater than or equal to a const integer x.
eg:- Our set is {4 5 8 10 10} and x=15
so the minimum subset sum closest to x and >=x is {5 10}
I can only think of a naive algorithm which lists all the subsets of set and checks if sum of subset is >=x and minimum or not, but its an exponential algorithm and listing all subsets requires O(2^N). Can I use dynamic programming to solve it in polynomial time?
If the sum of all your numbers is S, and your target number is X, you can rephrase the question like this: can you choose the maximum subset of the numbers that is less than or equal to S-X?
And you've got a special case of the knapsack problem, where weight and value are equal.
Which is bad news, because it means your problem is NP-hard, but on the upside you can just use the dynamic programming solution of the KP (which still isn't polynomial). Or you can try a polynomial approximation of the KP, if that's good enough for you.
I was revising DP. I thought of this question. Then I searched and I get this question but without a proper answer.
So here is the complete code (along with comments ): Hope it is useful.
sample image of table
//exactly same concept as subset-sum(find the minimum difference of subset-sum)
public class Main
{
public static int minSubSetSum(int[] arr,int n,int sum,int x){
boolean[][] t=new boolean[n+1][sum+1];
//initailization if n=0 return false;
for(int i=0;i<sum+1;i++)
t[0][i]=false;
//initialization if sum=0 return true because of empty set (a set can be empty)
for(int i=0;i<n+1;i++)
t[i][0]=true; //here if(n==0 && sum==0 return true) has been also initialized
//now DP top-down
for(int i=1;i<n+1;i++)
for(int j=1;j<sum+1;j++)
{
if(arr[i-1]<=j)
t[i][j]=t[i-1][j-arr[i-1]] || t[i-1][j]; // either include arr[i-1] or not
else
t[i][j]=t[i-1][j]; //not including arr[i-1] so sum is not deducted from j
}
//now as per question we have to take all element as it can be present in set1
//if not in set1 then in set2 ,so always all element will be a member of either set
// so we will look into last row(when i=n) and we have to find min_sum(j)
int min_sum=Integer.MAX_VALUE;
for(int j=x;j<=sum;j++)
if(t[n][j]==true){ //if in last row(n) w.r.t J , if the corresponding value true then
min_sum=j; //then that sum is possible
break;
}
if(min_sum==Integer.MAX_VALUE)
return -1;// because that is not possible
return min_sum;
}
public static void main(String[] args) {
int[] arr=new int[]{4,5,8,10,10};
int x=15;
int n=arr.length;
int sum=0;
for(int i=0;i<n;i++)
sum=sum+arr[i];
System.out.println("Min sum can formed greater than X is");
int min_sum=minSubSetSum(arr,n,sum,x);
System.out.println(min_sum);
}
}
As the problem was N-P complete so with DP time complexity reduces to
T(n)=O(n*sum)
and space complexity =O(n*sum);
As already mentioned, this is NP-complete. Another way of seeing that is, if one can solve this in polynomial time, then subset-sum problem could also be solved in polynomial time (if solution exist then it will be same).
I believe the other answers are incorrect. Your problem is actually a variation of the 0-1 knapsack problem (i.e. without repetitions) which is solvable in polynomial time with dynamic programming. You just need to formulate your criteria as in #biziclop's answer.
How about a greedy approach?
First we sort the list in descending order. Then we recursively pop the first element of the sorted list, subtract its value from x, and repeat until x is 0 or less.
In pseudocode:
sort(array)
current = 0
solution = []
while current < x:
if len(array) < 0:
return -1 //no solution possible
current += array[0]
solution.append(array.pop(0))
return solution

Logic challenge: sorting arrays alphabetically in C

I'm new to programming, currently learning C. I've been working at this problem for a week now, and I just can't seem to get the logic straight. This is straight from the book I'm using:
Build a program that uses an array of strings to store the following names:
"Florida"
"Oregon"
"Califoria"
"Georgia"
Using the preceding array of strings, write your own sort() function to display each state's name in alphabetical order using the strcmp() function.
So, let's say I have:
char *statesArray[4] = {"Florida", "Oregon", "California", "Georgia"};
Should I do nested for loops, like strcmp(string[x], string[y])...? I've hacked and hacked away. I just can't wrap my head around the algorithm required to solve this even somewhat efficiently. Help MUCH appreciated!!!
imagine you had to sort the array - think of each state written on a card. HOw would you sort it into order. There are many ways of doing it. Each one is called an algorithm
One way is to find the first state by looking at every card and keeping track in your head of the lowest one you have seen. After looking at each card you will have the lowest one. Put that in a new pile. NOw repeat - trying to find the lowest of the ones you have left.
repeat till no cards left in original pile
This is a well known simple but slow algorithm. Its the one i would do first
there are other ones too
Yes, you can sort by using nested for loops. After you understand how strcmp() works it should be fairly straight forward:
strcmp(char *string1, char *string2)
if Return value is < 0 then it indicates string1 is less than string2
if Return value is > 0 then it indicates string2 is less than string1
if Return value is = 0 then it indicates string1 is equal to string2
You can then choose any of the sorting methods once from this point
This site has a ton of great graphical examples of various sorts being performed and includes the pseudo code for the given algorithms.
Do you need "any" sorting algorithm, or an "efficient" sorting algorithm?
For simplicity, I can show you how to implement an easy, but not efficient, sorting algorithm.
It's the double for method!!
Then, with the same ideas, you can modify it to any other efficient algorithm (like shell, or quicksort).
For numbers, you could put arrays ir order, as follows (as you probably know):
int intcmp(int a, int b) {
return (a < b)? -1: ((a > b)? +1: 0);
}
int main(void) {
int a[5] = {3, 4, 22, -13, 9};
for (int i = 0; i < 5; i++) {
for (int j = i+1; j < 5; j++)
if (intcmp(a[i], a[j]) > 0) {
int temp = a[i];
a[i] = a[j];
a[j] = temp;
}
printf("%d ", a[i]);
}
}
The only thing that has changed now is that you have strings intead integers.
So, you have to consider an array of strings:
char *a[] = {"Florida", "Oregon", "Califoria", "Georgia"};
Then, you have to change the type of temp to char*,
and finally you put the function strcmp() instead of intcmp().
The function strcmp(s1, s2) (from < string.h >)
returns a number < 0 if s1 is a string "less than" s2, == 0 if s1 is
"equal to" s2, and > 1 else.
The program looks like this:
#include <stdio.h>
#include <string.h>
int main(void) {
char *a[] = {"Florida", "Oregon", "Califoria", "Georgia"};
for (int i = 0; i < 4; i++) {
for (int j = i+1; j < 4; j++)
if (strcmp(a[i], a[j]) > 0) {
char* temp = a[i];
a[i] = a[j];
a[j] = temp;
}
printf("%s ", a[i]);
}
getchar();
return 0;
}
Note that for the printf() sentence, we have changed "%d " by "%s ", in order to properly show strings.
Final comment: When you program a better algorithm, like quick-sort, it is enough that you change the comparisson function, because the algorithm it is the same, in despite of the type of data you are comparing.
Remark: I have used a "tricky" method. As you can see, I have defined the variable a as a pointer to string. The initializer has taken a constant array of strings and then initialized the variable a with it. The variable a now can be safely treated and indexed as an array of exactly 4 pointer-to-strings.
That is the reason why the "swap" works fine in the double-for algorithm: The memory addresses are swapped instead the entire strings.
Steps you likely should take:
Populate array with state names
Create method to swap two states in place in the array
At this point you have all the tools necessary to use strcmp to implement any sorting algorithm you choose
Most sorting methods rely on two things.
Being able to rearrange a list (i.e. swap)
Being able to compare items in list to see if they should be swapped
I would work on getting those two things working correctly and the rest should just be learning a particular sorting algorithm
Beware of a little headaching problem: Strings are sorted by ascii numeric representations, so if you sort alphabetically like this, any capital letter will come before a lowercase letter e.g. "alpha", "beta", "gamma", "Theta" will be sorted as:
Theta, alpha, beta, gamma
When it comes to the sample array you have listed here the simple algorithm mentioned earlier might actually be the most efficient. The algorithm I'm referring to is the one where you start with the first element and then compare it to the others and substitute with the smallest you find and then going to the next element to do the same only dont compare it to the already sorted elements.
While this algorithm has an execution time of O(n^2). Where n is the number of elements in the array. It will usually be faster than something like quick sort (execution time O(n*log(n)) for smaller arrays. The reason being that quick sort has more overhead. For larger arrays quick sort will serve you better than the other method, which if memory serves me right is called substitution sort although I see it mentioned as "double for" in a different answer.

Improving Mergesort. Improvement 3). Use one less copy between input and temp arrays

I am currently working on a project for my algorithms class and am at a bit of a standstill. We were assigned to do improvements to merge sort, that was in the book, by implementing specific changes. I have worked fine through the first 2 changes but the 3'rd one is killer.
Merge sort, the one we are improving, copies the contents of the input array into the temporary array, and then copies the temporary array back into the input array. So it recursively sorts the input array, placing the two sorted halves into the temporary array. And then it merges the two halves in the temporary array together, placing the sorted sequence into the input array as it goes.
The improvement is that this double copying is wasteful can be done without. His hint is that: We can make it so that each call to Merge only copies in one direction, but the calls to Merge alternate the direction.
This is supposedly done by blurring the lines between the original and temporary array.
I am not really looking for code as I am confident that I can code this. I just have no idea what i'm supposed to be doing. The professor is gone for the day so I can't ask him until next week when I have his course again.
Has anyone done something like this before? Or can decipher and put it into laymans terms for me :P
The first improvement, simply has it use insertion sort whenever an Array gets small enough that it will benefit greatly, timewise, from doing so.
The second improvement stops allocating two dynamic arrays (the 2 halves that are sorted) and instead allocates 1 array of size n and that is what is used instead of the two dynamic arrays. That's that last one I did. The code for that is :
//#include "InsertionSort.h"
#define INSERTION_CUTOFF 250
#include <limits.h> // needed for INT_MAX (the sentinel)
void merge3(int* inputArray, int p, int q, int r, int* tempArray)
{
int i,j,k;
for (i = p; i <= r; i++)
{
tempArray[i] = inputArray[i];
}
i = p;
j = q+1;
k = p;
while (i <= q && j <= r)
{
if (tempArray[i] <= tempArray[j])
{
inputArray[k++] = tempArray[i++];
}
else
{
inputArray[k++] = tempArray[j++];
}
}
}//merge3()
void mergeSort3Helper(int* inputArray, int p, int r, int* tempArray)
{
if (r - p < INSERTION_CUTOFF)
{
insertionSort(inputArray,p,r);
return;
}
int q = (p+r-1)/2;
mergeSort3Helper(inputArray,p,q,tempArray);
mergeSort3Helper(inputArray,q+1,r,tempArray);
merge3(inputArray,p,q,r,tempArray);
}//mergeSort3Helper()
void mergeSort3(int* inputArray, int p, int r)
{
if (r-p < 1)
{
return;
}
if (r - p < INSERTION_CUTOFF)
{
insertionSort(inputArray,p,r);
return;
}
int* tempArray = malloc((r-p)+1*sizeof(int));
tempArray[r+1] = INT_MAX;
mergeSort3Helper(inputArray,p,r,tempArray);
// This version of merge sort should allocate all the extra space
// needed for merging just once, at the very beginning, instead of
// within each call to merge3().
}//mergeSort3()
The algorithm is like this:
A1: 7 0 2 9 5 1 4 3
A2: (uninitialized)
Step 1:
A1 : unchanged
A2: 0 7 2 9 1 5 3 4
Step 2:
A1: 0 2 7 9 1 3 4 5
A2: unchanged
Step 3:
A1: unchanged
A2: 0 1 2 3 4 5 7 9
This involves you copying only one way each time and follows the steps of mergesort. As your professor said, you blur the lines between the work array and the sorted array by alternating which is which, and only copying once things are sorted.
I suspect it would be difficult and ultimately unprofitable to avoid all copying. What you want to do instead is to avoid the copy you currently do with each merge.
Your current merge3(inputArray, p,q,r, tempArray) returns the merged result in its original array, which requires a copy; it uses its tempArray buffer only as a resource. In order to do better, you need to modify it to something like merge4(inputArray, p,q,r, outputArray), where the result is returned in the second buffer, not the first.
You will need to change the logic in mergeSort3Helper() to deal with this. One approach requires a comparable interface change, to mergeSort4Helper(inputArray, p,q,r, outputArray), such that it also yields its result in its second buffer. This will require a copy at the lowest (insertion sort) level, and a second copy in the top-level mergeSort4() if you want your final result in the same buffer it came in. However, it eliminates all other unnecessary copies.
Alternately, you could add a boolean parameter to mergeSort4Helper() to indicate whether you want the result returned in the first or second buffer. This value would alternate recursively, resulting in at most one copy, at the lowest level.
A final option might be to do the merging non-recursively, and alternate buffers at each pass. This would also result in at most one copy; however, I would expect the resulting access pattern to be inherently less cache-friendly than the recursive one.

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