Bloomberg LP Interview Question for Financial Software Developers

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Country: United States

Comment hidden because of low score. Click to expand.
13
of 13 vote

Algorithm for problem
j=1
for i = 1 to N
if (A[i] > 0)
A[j] = A[i]
j++

for i = j to N
a[i] = 0

This takes O(n) without using any buffer

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0

It requires only one iteration. Time complexity if O(n).

``````using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.IO;

namespace ConsoleApplication1
{
class Program
{
static void Main(string[] args)
{
int[] test = { 1, 2, 0, 4, 6, 7, 0, 9, 12, 45, 0, 49, 0, 99, 0 };

MoveZeroAtTheEnd(test);

Console.WriteLine(test.ToString());
}

static void  MoveZeroAtTheEnd(int[] array)
{
int nZero = 0;

for (int i = 0; i < array.Length; ++i)
{
if (array[i] == 0)
{
nZero++;
continue;
}

if( nZero > 0 )
{
array[i - nZero] = array[i];

array[i] = 0;
}
}
}
}
}``````

Comment hidden because of low score. Click to expand.
0

It requires only one iteration. Time complexity if O(n).

``````using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.IO;

namespace ConsoleApplication1
{
class Program
{
static void Main(string[] args)
{
int[] test = { 1, 2, 0, 4, 6, 7, 0, 9, 12, 45, 0, 49, 0, 99, 0 };

MoveZeroAtTheEnd(test);

Console.WriteLine(test.ToString());
}

static void  MoveZeroAtTheEnd(int[] array)
{
int nZero = 0;

for (int i = 0; i < array.Length; ++i)
{
if (array[i] == 0)
{
nZero++;
continue;
}

if( nZero > 0 )
{
array[i - nZero] = array[i];

array[i] = 0;
}
}
}
}
}``````

Comment hidden because of low score. Click to expand.
0

Even shorter:

``````public int[] MoveZeroAtTheEnd(int[] org){
int[] ret = new int[org.length];
int retForwardIndex = 0;
int retBackwardIndex = org.length-1;
for(int i=0;i<org.length;i++){
if(org[i] == 0){
ret[retBackwardIndex--] = org[i];
}else{
ret[retForwardIndex++] = org[i];
}
}
return ret;
}``````

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3
of 3 vote

This just copying the non zero elements forward to the positions where it supposed to be. and using the zero counter, adding the zeros after the numbers into the array.

``````public static void main(String args[]){
int[] arrayZeros = {1,3,0,8,12,0,4,0,7};

int zeroCounter = 0;
int indexPointer = -1;
for(int i=0;i<arrayZeros.length;i++){

if(arrayZeros[i]!=0){
indexPointer++;
if(i>indexPointer)
arrayZeros[indexPointer] = arrayZeros[i];
}
else{
zeroCounter++;
}
}
int startIndex = arrayZeros.length - zeroCounter;
for(int i=1;i<=zeroCounter;i++){
arrayZeros[startIndex++] = 0;
}

for(int i=0;i<arrayZeros.length;i++){
System.out.println("["+arrayZeros[i]+"]");
}
}``````

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0

Excellent! Thanks..

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0

just awesome

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0
of 0 vote

Code in c# :

``````Int32[] sortArrayPlacingZeroAtEnd(Int32[] inarray)
{
Int32[] outarray = new Int32[inarray.Length];
int j = 0;
for (int i = 0; i <= outarray.Length - 1; i++)
{
if (inarray[i] != 0)
{
outarray[j++] = inarray[i];
}
}
return outarray;
}``````

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0

Sorry, I forgot to clarify; You can't use another buffer.

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0
of 0 vote

``````#include<stdio.h>
#include<stdlib.h>

void print(int *a, int n) {
int i;
for(i=0;i<n;i++)
printf("%d, ", a[i]);
printf("\n");
}

void swap(int *a, int *b) {
int tmp;
tmp=*a;
*a=*b;
*b=tmp;
}

int main(void) {
int *a, n, i, end;
scanf("%d", &n);
a=(int *)calloc(n,sizeof(int));
for(i=0;i<n;i++)
scanf("%d", &a[i]);
print(a,n);
end=i=n-1;
while(i>=0){
if(a[i]) {
if(i<end)
swap(&a[i],&a[end]);
end--;
}
i--;
}
print(a,n);
free(a);
return 0;
}``````

Comment hidden because of low score. Click to expand.
0

Wait, if it's 1 2 3 0 7,
when i = 4 and end = 4, a[4] !=0, but i==end, so both i and end decrement.
i = 3, end = 3, a[3]==0, so only i decrements.
i=2, end=3, a[2] = 3, and i<end, so they swap.
12037.
I do not think it is working... There is no way you will swap the end elements 3, 7 with the zero element in the middle at this point... isn't it?

Comment hidden because of low score. Click to expand.
0

You are right "sunghw", the code above would push non-zero integers toward right of the array and zeros toward left ( for input 1 2 3 0 7, out put would be 0 1 2 3 7). *Didn't notice the output formated asked in the question*. Below is the corrected code :

``````#include<stdio.h>
#include<stdlib.h>

void print(int *a, int n) {
int i;
for(i=0;i<n;i++)
printf("%d, ", a[i]);
printf("\n");
}

void swap(int *a, int *b) {
int tmp;
tmp=*a;
*a=*b;
*b=tmp;
}

int main(void) {
int *a, n, i=0, start=0;
scanf("%d", &n);
a=(int *)calloc(n,sizeof(int));
for(i=0;i<n;i++)
scanf("%d", &a[i]);
print(a,n);
i=0;
while(i<n){
if(a[i]) {
if(i>start)
swap(&a[i],&a[start]);
start++;
}
i++;
}
print(a,n);
free(a);
return 0;
}``````

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0
of 0 vote

is there any restriction on the usage of extra space. because, we can iterate through the array and add non-zero's to a queue simulataneously zeroing each element.

Once complete, we can deque elements in queue and add it back to array.
time: O(n)
size: O(n)

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0

no, that would be easy. you can't use any additional buffer.

Comment hidden because of low score. Click to expand.
0

in this one, we will divide and merge the sets recursively. except that while merging new set will have non zero's first and zero's last.

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0
of 0 vote

``````public static void moveZero(int[] arr) {
if (arr == null || arr.length == 0) return;
for (int i = 0; i < arr.length - 1; i++) {
if (arr[i] == 0) {
for (int j = i + 1; j < arr.length; j++) {
if (arr[j] != 0) {
swap(arr, i, j);
break;
}
}
if (arr[i] == 0) return;
}
}
}

private static void swap(int[] arr, int i, int j) {
int temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
}``````

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0
of 0 vote

``````public static void moveZero(int[] arr) {
if (arr == null || arr.length == 0) return;
for (int i = 0; i < arr.length - 1; i++) {
if (arr[i] == 0) {
for (int j = i + 1; j < arr.length; j++) {
if (arr[j] != 0) {
swap(arr, i, j);
break;
}
}
if (arr[i] == 0) return;
}
}
}

private static void swap(int[] arr, int i, int j) {
int temp = arr[i];
arr[i] = arr[j];
arr[j] = temp;
}``````

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0
of 0 vote

/*
A program to add all zero at the end of array

*/
#include<stdio.h>
void zero(int a[],int n)
{

int i,j,tmp;
i=0;
while(i<n) //find first zero
{
if(a[i]==0)
break;
else
i++;
}

if(i==n-1||i==n) // if last element is zero or no zero element
return ;

j=i+1;

while(j<n&&i<n)
{
if(a[j]!=0)
{
tmp=a[i];
a[i]=a[j];
a[j]=tmp;
i++;
j++;
}
else
j++;
}
}
int main()
{

int a[]= {0,1 ,2 ,0 , 3,0,4,0,0,0,0,5,6,7,8,9};
int n=sizeof(a)/sizeof(int);
zero(a,n);

int i;

for(i=0;i<n;i++)
printf("%d",a[i]);

return 0;
}

Comment hidden because of low score. Click to expand.
0
of 0 vote

Is this okay ?

``````static void Main(string[] args)
{
int[] a = {1,2,3,4,4,5,5,6,6,6};

int i=0, j=0;

while (j < a.Length)
{
if (a[j] != 0)
{
a[i++] = a[j];
}
j++;
}

while (i < a.Length)
{
a[i++] = 0;
}

for (int n = 0; n < a.Length; n++)
{
Console.Write("{0} ", a[n]);
}

}``````

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0

I think it pretty good

Comment hidden because of low score. Click to expand.
0
of 0 vote

Have 2 indexes i & j, both initialized to 0. as long as a[j] is not zero, copy it into a[i].
increment i when u copy from a[j]; The moment u reach the end of the array, you would have copied all the non zero elements to the left.
from this point on, fill the elements at a[i] with zeroes.

I guess it should work fine.

Comment hidden because of low score. Click to expand.
0
of 0 vote

hope this is what you are looking for

``````#include<iostream>
using namespace std;

int main()
{
int a[]={1,0,2,0,0,3,0,4,0};
int count = 0;
int temp;

for(int i=0;i<8;i++)
{
for(int j=0;j<8-i;j++)
{
if(a[j] == 0)
{
while(a[j+1] !=0)
{temp=a[j];
a[j]=a[j+1];
a[j+1]=temp;j++;}
}
}

}

for(int i=0;i<8;i++)
{
cout << a[i];
}

return 0;
}``````

Comment hidden because of low score. Click to expand.
0
of 0 vote

If we have extra space, we can allocate a new array buffer.

if the current element in the original array is non-zero, copy it to the new array and increase new array's index.
Otherwise just continue without updating new array's index.
When we reach the end of the original array, fill the new array with 0s.

This algorithm takes extra n space and takes liner time.

Comment hidden because of low score. Click to expand.
0
of 0 vote

I wrote a code using vector hope this helps

``````for(int i=0;i<n;){
if(b[i]==0){
b.erase(b.begin()+i);
b.push_back(0);
n=n-1;
}
else
i++;
}``````

here I used erase the number 0 from a list and pushed a 0 at the back of the vector

Comment hidden because of low score. Click to expand.
0
of 0 vote

``````int a[] ={1,3,0,0,4,10,0,18,3,0,6,0,1,4};
int current_zero_index = 0;
int count =0 ,flag=0;

for (int i=0; i<a.length;i++) {

if(a[i]==0 && flag==0) {
current_zero_index=i-count;
flag=1;
//	count++;
}

if(a[i]>0 && current_zero_index>0) {
a[current_zero_index++] = a[i];
count++;
a[i]=0;
flag=0;
}

}``````

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0
of 0 vote

public class fixArray {
public static void main(String[] args) {
int[] arr = {5,0,3,7,8,0,1,0};
int j = 0;
for(int i = 0; i < arr.length; i++) {
if (arr[i] != 0) {
arr[j] = arr[i];
if(i != j) arr[i] = 0;
++j;
}
}
for(int i = 0; i < arr.length; i++) {
System.out.println(arr[i]);
}
}
}

Comment hidden because of low score. Click to expand.
0

Just a minor comment:

if (arr[i] != 0) {
if(i != j) {
arr[j] = arr[i]; // this can be done only if i not equal to j
arr[i] = 0;
}
++j;
}

Comment hidden because of low score. Click to expand.
0
of 0 vote

This works!!

``````#include <iostream>
using namespace std;

int main()
{
int n = 15;
int a[15] = {1,0,0,8,12,0,4,0,7,0,0,0,0,1,1};
int i = 0, j= 0;
for (int k = 0; k<n; k++) cout <<a[k]<<'\t';
cout <<'\n'<<'\n';
while(j<n)
{

if(a[j]==0 && a[i]!=0)i=j++;

else if(a[i]==0 && a[j]!=0)
{
int temp = a[i];
a[i] = a[j];
a[j] = temp;
i++;j++;
}
else if (a[j]==0 && a[i] ==0) j++;
else j++;
}
cout <<'\n'<<'\n';
for (int k = 0; k<n; k++) cout <<a[k]<<'\t';
}``````

Comment hidden because of low score. Click to expand.
0

This works in O(n). crawling the array just ones

Comment hidden because of low score. Click to expand.
0
of 0 vote

for(i=0; i<5; i++)
{
if(arr[i]== 0)
{
shift_left++;
}
else
{
arr[i-shift_left] = arr[i];
if(shift_left!=0)
{
arr[i] = 0;
}
}
}

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0
of 0 vote

void PutZroatEnd(int src[],int size)
{
int distancetoCursor = 1;
for(int i =0;i<size-distancetoCursor;++i)
{
if(src[i] == 0)
{
if(src[i+distancetoCursor] == 0)
++distancetoCursor;
int temp = src[i+distancetoCursor];
src[i+distancetoCursor] = src[i];
src[i] = temp;
}
}
}

Comment hidden because of low score. Click to expand.
0
of 0 vote

This one works for the data set provided in the code. I guess I can improve this a lot. There is a bug though. The code is getting into infinite loop if I have zeros in the beginning.

The code is in C# (Windows Forms)

``````private void button1_Click(object sender, EventArgs e)
{
int[] a = new int[] { 13, 8, 0, 12, 0, 4, 7, 0, 8, 9, 0, 5, 6, 0, 17, 12, 34, 56, 78, 0, 98, 87, 0, 65, 0, 54, 0, 0, 0, 101, 0, 1, 0, 2, 0, 3, 0, 4 };
int nextcurr = -1;
int noofzeros = 0;
int count = 0;

// 1 iteration to get the number of zeros
for (int i = 0; i < a.Length; i++)
{
if (a[i] == 0)
noofzeros++;
}

int curr = 0;

while (nextcurr != (a.Length - noofzeros))
{
// Check to swap
if (curr < a.Length - 1)
{
if (a[curr] == 0 && a[curr + 1] != 0)
Swap(a, curr, curr + 1);
else if (a[curr] == 0 && a[curr + 1] == 0 && nextcurr < 0)
nextcurr = curr;

curr++;
Display(a);
}
else if (curr >= a.Length - 1 && nextcurr > 0)
{
curr = nextcurr;
nextcurr = -1;
}

count++;
}

richTextBox1.AppendText("\nTotal iterations: " + count.ToString());
}``````

Comment hidden because of low score. Click to expand.
0
of 0 vote

``````Here is the output for the code above:

13 ,8 ,0 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,0 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,0 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,0 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,0 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,0 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,0 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,0 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,0 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,0 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,0 ,2 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,0 ,3 ,0 ,4
13 ,8 ,12 ,0 ,4 ,7 ,0 ,8 ,9 ,0 ,5 ,6 ,0 ,17 ,12 ,34 ,56 ,78 ,0 ,98 ,87 ,0 ,65 ,0 ,54 ,0 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,0 ,4
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13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,0 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,2 ,0 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,2 ,0 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,0 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,3 ,0 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,3 ,0 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,0 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,3 ,0 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,3 ,0 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,0 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,0 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
13 ,8 ,12 ,4 ,7 ,8 ,9 ,5 ,6 ,17 ,12 ,34 ,56 ,78 ,98 ,87 ,65 ,54 ,101 ,1 ,2 ,3 ,4 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0

Total iterations: 349``````

Comment hidden because of low score. Click to expand.
0
of 0 vote

``````#include <iostream>
using namespace std;

// version 1: using a separate buffer
//void separateZeros(int *input, int *output, int size){
//     for(int i=0, j=0, k=size-1; i<size; ++i){
//          if(input[i] != 0){
//               output[j++] = input[i];
//          }
//          else{
//               output[k--] = input[i];
//          }
//     }
//}

// version 2: no extra buffer
void separateZeros(int *arr, int size){
int i = 0;
while(i < size && arr[i] != 0)
++i;     //find first 0

if(i < size-1){
int j = i+1;
while(j < size){
if(arr[j] == 0){
++j;
}
else{
arr[i] = arr[j];
arr[j] = 0;
++i;
++j;
}
}
}
}

int main(){
int a[] = {1, 3, 0, 8, 12, 0, 4, 0, 7};
int n = sizeof(a)/sizeof(a[0]);

separateZeros(a, n);
cout << "after separating 0's and non-0's: " << endl;
for(int i=0; i<n; ++i){
cout << a[i] << " ";
}
cout << endl;

return 0;
}``````

Comment hidden because of low score. Click to expand.
0
of 0 vote

Use stable_sort to sort and preserve ordering of certain elements.

``````bool q1_comp(int i_first,int i_second){return (i_first==0)<(i_second==0);}
void main(){
int q1_ints[]={1,3,0,8,12,0,4,0,7};
vector<int> q1_array(q1_ints,q1_ints+sizeof(q1_ints)/sizeof(q1_ints[0]));
stable_sort(q1_array.begin(),q1_array.end(),q1_comp);
}``````

Comment hidden because of low score. Click to expand.
0
of 0 vote

for(int j=0; j<n; j++)
{
for(i=0;i<n&&a[i]=0;i++)
{
int temp=a[i];
a[i]=a[i+1];
}
a[i]=temp;
}

Comment hidden because of low score. Click to expand.
0
of 0 vote

for(int j=0; j<n; j++)
{
for(i=0;i<n&&a[i]=0;i++)
{
int temp=a[i];
a[i]=a[i+1];
}
a[i]=temp;
}

Comment hidden because of low score. Click to expand.
0
of 0 vote

``````#include<iostream>
using namespace std;

void swap(int a[],int length)
{
int zeroPointer = 0;
int nonZeroPointer = 0;
while((zeroPointer < length) &&(nonZeroPointer < length))
{
while(a[zeroPointer] != 0)
{
zeroPointer++;
if(zeroPointer == length)
{
break;
}
}
while((nonZeroPointer < zeroPointer) || (a[nonZeroPointer] == 0))
{
nonZeroPointer++;
if(nonZeroPointer == length)
{
break;
}
}
if((zeroPointer < length) && (nonZeroPointer < length))
{
int temp = a[nonZeroPointer];
a[nonZeroPointer] = a[zeroPointer];
a[zeroPointer]= temp;
if(a[zeroPointer + 1] == 0)
{
zeroPointer++;
}
}
}
}
int main()
{
int a[]={0,1,3,0,0,8,12,4,7};
swap(a,9);
for(int i=0;i<9;i++)
{
cout << a[i] << " ";
}
cout << endl
}``````

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of 0 vote

import java.util.Arrays;

public class CareerUp_ArrayIndex {

public static void main(String[] args) {
process();
}

public static void process() {

int[] price = {1,3,0,8,12, 0, 4, 0,7};
int[] _price = new int[price.length];
int j = price.length-1;
int k = 0;

for (int i=0;i<price.length;i++){
if (price[i] != 0){
_price[k] = price[i];
k++;
}
if (price[i] == 0){
_price[j] = price[i];
j--;
}
}
System.out.println(Arrays.toString(_price));
}
}

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of 0 vote

``````// Move all zeros to the end
void MoveZerosToEnd(int a[], size_t n)
{
size_t nCurIndex = 0;
for (size_t i = 0; i < n; ++i)
{
if (0 != a[i])
{
a[nCurIndex] = a[i];
++nCurIndex;
}
}
for (int i = nCurIndex; i < n ; ++i)
{
a[i] = 0;
}
}``````

Comment hidden because of low score. Click to expand.
0

#include <stdlib.h>
#include <stdio.h>

void printarray(int *a, int n);

void main()
{
int A[]={0, 3, 0, 5, 7, 0, 0, 8};
int i, j, k;
int n = sizeof(A)/sizeof(int);

printarray(A, n);
for (i=0; i<n; i++)
{
if (A[i]==0)
{
for (j=i+1; j<n;j++)
{
if (A[j]!=0)
{
k=A[i];
A[i] = A[j];
A[j] = k;
break;
}
}
}
}
printarray(A, n);

}

void printarray(int *a, int n)
{
int i;
for (i=0;i<n;i++)
{
printf("%3d", a[i]);
}
printf("\n");

}

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0
of 0 vote

public void moveBackZero(int[] a){
int i, j;

for(i=a.length-1; i>=0; i--){
if(a[i]==0){
j=i;
while(j<a.length-1){
a[j] = a[j+1];
j++;
}
a[j] = 0;
}
}
}

Comment hidden because of low score. Click to expand.
0
of 0 vote

Using the STL

``````int nums[] = { 1, 3, 0, 8, 12, 0, 4, 0, 7 };

std::stable_partition(std::begin(nums), std::end(nums), std::bind(std::greater<int>(), std::placeholders::_1, 0));``````

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0
of 0 vote

FWIW,

``````void zero_sort(int* arr, int length){
int* end=arr+length;
int* write=arr--;
while (++arr!=end) if (*arr!=0) *(write++)=*arr;
while (write!=end) *(write++)=0;
}``````

Comment hidden because of low score. Click to expand.
0
of 0 vote

In place and linear time:

``````public static void fun(int[] data) {
int offset=0;
for (int i=0; i<data.length; i++) {
if (data[i]==0)
offset++;
else
data[i-offset]=data[i];
if (i+offset>=data.length-1)
data[i]=0;
}
}``````

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0
of 0 vote

``````void zerosToEnd(int[] ints)
{
if(ints != null)
{
int insertpos = 0;
while (insertpos < ints.length && ints[insertpos] != 0)
insertpos++;

for (int i = insertpos + 1; i < ints.length; i++)
{
if (ints[i] != 0)
{
ints[insertpos] = ints[i];
insertpos++;
}
}

for (; insertpos < ints.length; insertpos++)
ints[insertpos] = 0;
}
}``````

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0
of 0 vote

``````int arr[] = { 0, 0, 1, 8, 0, 1, 0, 1, 0 };
int n = 9;

int k = 0;
for (int i = 0; i < n; i++)
{
if (arr[i] != 0)
arr[k++] = arr[i];
}

for (; k < n; k++)
arr[k] = 0;``````

Comment hidden because of low score. Click to expand.
0
of 0 vote

Here is a Hybrid ( Iterative-Recursive ) version:

``````...
void ShuffleArray( int a[], int n, int v )
{
if( --n == 0 )
return;
ShuffleArray( &a[1], n, v );
int t;
if( a[0] == v && a[1] != v )
{
t = a[0];
a[0] = a[1];
a[1] = t;
}
}
...
int a[] = { 1, 3, 0, 8, 12, 0, 4, 0, 7 };
int n = 9;
int v = 0;
for( int i = 0; i < n; i++ )
ShuffleArray( &a[i], n-i, v );
...``````

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0
of 0 vote

``````void movezerotoend1(vector<int> & vec){
auto i=vec.begin();
auto j=vec.begin();
while (i!=vec.end()&&j!=vec.end()) {
while (*i!=0) ++i;
j=i;
while (*j==0) ++j;
swap(*(i++), *(j++));
}

}``````

or one line:

``for_each(std::remove_if(vec.begin(), vec.end(), zeroval()),vec.end(),setzero());``

with zeroval() and setzero():

``````class zeroval:public unary_function<int, bool> {

public:
bool operator()(int x);
};
class setzero:public unary_function<int, void> {

public:
void operator()(int &x);
};

bool zeroval::operator()(int x){
return x==0;
}

void setzero::operator()(int& x){
x=0;
}``````

Comment hidden because of low score. Click to expand.
0
of 0 vote

``````public static void movezerotoend(int[]arr){
int startindex,endindex;
startindex=endindex=0;
while(endindex<arr.length){
if(arr[endindex]!=0){
arr[startindex++]=arr[endindex];
}
endindex++;
}
while(startindex<arr.length){
arr[startindex++]=0;
}``````

}

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