Write a program that removes duplicates from a set of 10000 random numbers. Use
ID: 3689638 • Letter: W
Question
Write a program that removes duplicates from a set of 10000 random numbers. Use each of the sorting methods in Chapter 10. Display the elapsed times for each sort. Display the sort method, list of duplicates removed, and the elapsed time in milliseconds for each sort.
I have been trying to figure out why my code is not working. I am getting an IndexOutOfBoundsException. Thank you in advance.
import java.util.*;
import java.text.DecimalFormat;
public class P6
{
static int SIZE = 10000;
static ArrayList<Integer> values = new ArrayList<Integer>();
//static int[] values = new int[SIZE]; // values to be sorted
static List<Integer> dup = new ArrayList<Integer>();
static void initValues()
// Initializes the values array with random integers from 0 to 99.
{
Random rand = new Random();
for (int index = 0; index < SIZE; index++)
values.add(Math.abs(rand.nextInt()) % 10000);
}
static public boolean isSorted()
// Returns true if the array values are sorted and false otherwise.
{
boolean sorted = true;
for (int index = 0; index < (SIZE - 1); index++)
if (values.get(index) > values.get(index+1))
sorted = false;
return sorted;
}
static public void deleteRepeats(ArrayList<Integer> values){
for(int index = 0; index <(values.size()); index++){
if(values.get(index)==values.get(index+1)){
dup.add(index);
values.remove(index);
System.out.print(dup);
SIZE--;
}
}
}
static public void swap(int index1, int index2)
// Precondition: index1 and index2 are >= 0 and < SIZE.
//
// Swaps the integers at locations index1 and index2 of the values array.
{
int temp = values.get(index1);
values.set(index1, values.get(index2));
values.set(index2,temp);
}
static public void printValues()
// Prints all the values integers.
{
int value;
DecimalFormat fmt = new DecimalFormat("00");
System.out.println("The values array is:");
for (int index = 0; index < SIZE; index++)
{
value = values.get(index);
if (((index + 1) % 10) == 0)
System.out.println(fmt.format(value));
else
System.out.print(fmt.format(value) + " ");
}
System.out.println();
}
/////////////////////////////////////////////////////////////////
//
// Selection Sort
static int minIndex(int startIndex, int endIndex)
// Returns the index of the smallest value in
// values[startIndex]..values[endIndex].
{
int indexOfMin = startIndex;
for (int index = startIndex + 1; index <= endIndex; index++)
if (values.get(index) < values.get(indexOfMin))
indexOfMin = index;
return indexOfMin;
}
static void selectionSort()
// Sorts the values array using the selection sort algorithm.
{
int endIndex = SIZE - 1;
for (int current = 0; current < endIndex; current++){
swap(current, minIndex(current, endIndex));
}
for (int current = 0; current < endIndex; current++){
deleteRepeats(values);
}
}
/////////////////////////////////////////////////////////////////
//
// Bubble Sort
static void bubbleUp(int startIndex, int endIndex)
// Switches adjacent pairs that are out of order
// between values[startIndex]..values[endIndex]
// beginning at values[endIndex].
{
for (int index = endIndex; index > startIndex; index--)
if (values.get(index) < values.get(index-1))
swap(index, index - 1);
}
static void bubbleSort()
// Sorts the values array using the bubble sort algorithm.
{
int current = 0;
while (current < (SIZE - 1))
{
bubbleUp(current, SIZE - 1);
current++;
}
}
/////////////////////////////////////////////////////////////////
//
// Short Bubble Sort
static boolean bubbleUp2(int startIndex, int endIndex)
// Switches adjacent pairs that are out of order
// between values[startIndex]..values[endIndex]
// beginning at values[endIndex].
//
// Returns false if a swap was made; otherwise, returns true.
{
boolean sorted = true;
for (int index = endIndex; index > startIndex; index--)
if (values.get(index) < values.get(index-1))
{
swap(index, index - 1);
sorted = false;
}
return sorted;
}
static void shortBubble()
// Sorts the values array using the bubble sort algorithm.
// The process stops as soon as values is sorted.
{
int current = 0;
boolean sorted = false;
while ((current < (SIZE - 1)) && !sorted)
{
sorted = bubbleUp2(current, SIZE - 1);
current++;
}
}
/////////////////////////////////////////////////////////////////
//
// Insertion Sort
static void insertItem(int startIndex, int endIndex)
// Upon completion, values[0]..values[endIndex] are sorted.
{
boolean finished = false;
int current = endIndex;
boolean moreToSearch = true;
while (moreToSearch && !finished)
{
if (values.get(current) < values.get(current-1))
{
swap(current, current - 1);
current--;
moreToSearch = (current != startIndex);
}
else
finished = true;
}
}
static void insertionSort()
// Sorts the values array using the insertion sort algorithm.
{
for (int count = 1; count < SIZE; count++)
insertItem(0, count);
}
/////////////////////////////////////////////////////////////////
//
// Merge Sort
static void merge (int leftFirst, int leftLast, int rightFirst, int rightLast)
// Preconditions: values[leftFirst]..values[leftLast] are sorted.
// values[rightFirst]..values[rightLast] are sorted.
//
// Sorts values[leftFirst]..values[rightLast] by merging the two subarrays.
{
List<Integer> tempArray = new ArrayList<Integer>(SIZE);
int index = leftFirst;
int saveFirst = leftFirst; // to remember where to copy back
while ((leftFirst <= leftLast) && (rightFirst <= rightLast))
{
if (values.get(leftFirst) < values.get(rightFirst))
{
tempArray.set(index, values.get(leftFirst));
leftFirst++;
}
else
{
tempArray.set(index,values.get(rightFirst));
rightFirst++;
}
index++;
}
while (leftFirst <= leftLast)
// Copy remaining items from left half.
{
tempArray.set(index,values.get(leftFirst));
leftFirst++;
index++;
}
while (rightFirst <= rightLast)
// Copy remaining items from right half.
{
tempArray.set(index,values.get(rightFirst));
rightFirst++;
index++;
}
for (index = saveFirst; index <= rightLast; index++)
values.set(index,tempArray.get(index));
}
static void mergeSort(int first, int last)
// Sorts the values array using the merge sort algorithm.
{
if (first < last)
{
int middle = (first + last) / 2;
mergeSort(first, middle);
mergeSort(middle + 1, last);
merge(first, middle, middle + 1, last);
}
}
/////////////////////////////////////////////////////////////////
//
// Quick Sort
static int split(int first, int last)
{
int splitVal = values.get(first);
int saveF = first;
boolean onCorrectSide;
first++;
do
{
> while (onCorrectSide) // move first toward last
if (values.get(first) > splitVal)
> else
{
first++;
<= last);
}
<= last);
while (onCorrectSide) // move last toward first
if (values.get(last) <= splitVal)
> else
{
last--;
<= last);
}
if (first < last)
{
swap(first, last);
first++;
last--;
}
} while (first <= last);
swap(saveF, last);
return last;
}
static void quickSort(int first, int last)
{
if (first < last)
{
int splitPoint;
splitPoint = split(first, last);
// values[first]..values[splitPoint - 1] <= splitVal
// values[splitPoint] = splitVal
// values[splitPoint+1]..values[last] > splitVal
quickSort(first, splitPoint - 1);
quickSort(splitPoint + 1, last);
}
}
/////////////////////////////////////////////////////////////////
//
// Heap Sort
static int newHole(int hole, int lastIndex, int item)
// If either child of hole is larger than item this returns the index
// of the larger child; otherwise it returns the index of hole.
{
int left = (hole * 2) + 1;
int right = (hole * 2) + 2;
if (left > lastIndex)
// hole has no children
return hole;
else
if (left == lastIndex)
// hole has left child only
if (item < values.get(left))
// item < left child
return left;
else
// item >= left child
return hole;
else
// hole has two children
if (values.get(left) < values.get(right))
// left child < right child
if (values.get(right) <= item)
// right child <= item
return hole;
else
// item < right child
return right;
else
// left child >= right child
if (values.get(left) <= item)
// left child <= item
return hole;
else
// item < left child
return left;
}
static void reheapDown(int item, int root, int lastIndex)
// Precondition: Current root position is "empty".
//
// Inserts item into the tree and ensures shape and order properties.
{
int hole = root; // current index of hole
int newhole; // index where hole should move to
newhole = newHole(hole, lastIndex, item); // find next hole
while (newhole != hole)
{
values.set(hole, values.get(newhole)); // move value up
hole = newhole; // move hole down
newhole = newHole(hole, lastIndex, item); // find next hole
}
values.set(hole,item); // fill in the final hole
}
static void heapSort()
// Sorts the values array using the heap sort algorithm.
{
int index;
// Convert the array of values into a heap.
for (index = SIZE/2 - 1; index >= 0; index--)
reheapDown(values.get(index), index, SIZE - 1);
// Sort the array.
for (index = SIZE - 1; index >=1; index--)
{
swap(0, index);
reheapDown(values.get(0), 0, index - 1);
}
}
/////////////////////////////////////////////////////////////////
//
// Main
public static void main(String[] args)
{
initValues();
printValues();
System.out.println("values is sorted: " + isSorted());
System.out.println();
// make call to sorting method here (just remove //)
selectionSort();
// bubbleSort();
// shortBubble();
// insertionSort();
// mergeSort(0, SIZE - 1);
// quickSort(0, SIZE - 1);
// heapSort();
printValues();
System.out.println("values is sorted: " + isSorted());
System.out.println();
}
}
Explanation / Answer
Hi, I have made a small change. Highlighted line is the change in code. it is working fine now.
P6.java
import java.util.*;
import java.text.DecimalFormat;
public class P6
{
static int SIZE = 10000;
static ArrayList<Integer> values = new ArrayList<Integer>();
//static int[] values = new int[SIZE]; // values to be sorted
static List<Integer> dup = new ArrayList<Integer>();
static void initValues()
// Initializes the values array with random integers from 0 to 99.
{
Random rand = new Random();
for (int index = 0; index < SIZE; index++)
values.add(Math.abs(rand.nextInt()) % 10000);
}
static public boolean isSorted()
// Returns true if the array values are sorted and false otherwise.
{
boolean sorted = true;
for (int index = 0; index < (SIZE - 1); index++)
if (values.get(index) > values.get(index+1))
sorted = false;
return sorted;
}
static public void deleteRepeats(ArrayList<Integer> values){
for(int index = 0; index <(values.size()-1); index++){
if(values.get(index)==values.get(index+1)){
dup.add(index);
values.remove(index);
System.out.print(dup);
SIZE--;
}
}
}
static public void swap(int index1, int index2)
// Precondition: index1 and index2 are >= 0 and < SIZE.
//
// Swaps the integers at locations index1 and index2 of the values array.
{
int temp = values.get(index1);
values.set(index1, values.get(index2));
values.set(index2,temp);
}
static public void printValues()
// Prints all the values integers.
{
int value;
DecimalFormat fmt = new DecimalFormat("00");
System.out.println("The values array is:");
for (int index = 0; index < SIZE; index++)
{
value = values.get(index);
if (((index + 1) % 10) == 0)
System.out.println(fmt.format(value));
else
System.out.print(fmt.format(value) + " ");
}
System.out.println();
}
/////////////////////////////////////////////////////////////////
//
// Selection Sort
static int minIndex(int startIndex, int endIndex)
// Returns the index of the smallest value in
// values[startIndex]..values[endIndex].
{
int indexOfMin = startIndex;
for (int index = startIndex + 1; index <= endIndex; index++)
if (values.get(index) < values.get(indexOfMin))
indexOfMin = index;
return indexOfMin;
}
static void selectionSort()
// Sorts the values array using the selection sort algorithm.
{
int endIndex = SIZE - 1;
for (int current = 0; current < endIndex; current++){
swap(current, minIndex(current, endIndex));
}
for (int current = 0; current < endIndex; current++){
deleteRepeats(values);
}
}
/////////////////////////////////////////////////////////////////
//
// Bubble Sort
static void bubbleUp(int startIndex, int endIndex)
// Switches adjacent pairs that are out of order
// between values[startIndex]..values[endIndex]
// beginning at values[endIndex].
{
for (int index = endIndex; index > startIndex; index--)
if (values.get(index) < values.get(index-1))
swap(index, index - 1);
}
static void bubbleSort()
// Sorts the values array using the bubble sort algorithm.
{
int current = 0;
while (current < (SIZE - 1))
{
bubbleUp(current, SIZE - 1);
current++;
}
}
/////////////////////////////////////////////////////////////////
//
// Short Bubble Sort
static boolean bubbleUp2(int startIndex, int endIndex)
// Switches adjacent pairs that are out of order
// between values[startIndex]..values[endIndex]
// beginning at values[endIndex].
//
// Returns false if a swap was made; otherwise, returns true.
{
boolean sorted = true;
for (int index = endIndex; index > startIndex; index--)
if (values.get(index) < values.get(index-1))
{
swap(index, index - 1);
sorted = false;
}
return sorted;
}
static void shortBubble()
// Sorts the values array using the bubble sort algorithm.
// The process stops as soon as values is sorted.
{
int current = 0;
boolean sorted = false;
while ((current < (SIZE - 1)) && !sorted)
{
sorted = bubbleUp2(current, SIZE - 1);
current++;
}
}
/////////////////////////////////////////////////////////////////
//
// Insertion Sort
static void insertItem(int startIndex, int endIndex)
// Upon completion, values[0]..values[endIndex] are sorted.
{
boolean finished = false;
int current = endIndex;
boolean moreToSearch = true;
while (moreToSearch && !finished)
{
if (values.get(current) < values.get(current-1))
{
swap(current, current - 1);
current--;
moreToSearch = (current != startIndex);
}
else
finished = true;
}
}
static void insertionSort()
// Sorts the values array using the insertion sort algorithm.
{
for (int count = 1; count < SIZE; count++)
insertItem(0, count);
}
/////////////////////////////////////////////////////////////////
//
// Merge Sort
static void merge (int leftFirst, int leftLast, int rightFirst, int rightLast)
// Preconditions: values[leftFirst]..values[leftLast] are sorted.
// values[rightFirst]..values[rightLast] are sorted.
//
// Sorts values[leftFirst]..values[rightLast] by merging the two subarrays.
{
List<Integer> tempArray = new ArrayList<Integer>(SIZE);
int index = leftFirst;
int saveFirst = leftFirst; // to remember where to copy back
while ((leftFirst <= leftLast) && (rightFirst <= rightLast))
{
if (values.get(leftFirst) < values.get(rightFirst))
{
tempArray.set(index, values.get(leftFirst));
leftFirst++;
}
else
{
tempArray.set(index,values.get(rightFirst));
rightFirst++;
}
index++;
}
while (leftFirst <= leftLast)
// Copy remaining items from left half.
{
tempArray.set(index,values.get(leftFirst));
leftFirst++;
index++;
}
while (rightFirst <= rightLast)
// Copy remaining items from right half.
{
tempArray.set(index,values.get(rightFirst));
rightFirst++;
index++;
}
for (index = saveFirst; index <= rightLast; index++)
values.set(index,tempArray.get(index));
}
static void mergeSort(int first, int last)
// Sorts the values array using the merge sort algorithm.
{
if (first < last)
{
int middle = (first + last) / 2;
mergeSort(first, middle);
mergeSort(middle + 1, last);
merge(first, middle, middle + 1, last);
}
}
/////////////////////////////////////////////////////////////////
//
// Quick Sort
static int split(int first, int last)
{
int splitVal = values.get(first);
int saveF = first;
boolean onCorrectSide;
first++;
do
{
> while (onCorrectSide) // move first toward last
if (values.get(first) > splitVal)
> else
{
first++;
<= last);
}
<= last);
while (onCorrectSide) // move last toward first
if (values.get(last) <= splitVal)
> else
{
last--;
<= last);
}
if (first < last)
{
swap(first, last);
first++;
last--;
}
} while (first <= last);
swap(saveF, last);
return last;
}
static void quickSort(int first, int last)
{
if (first < last)
{
int splitPoint;
splitPoint = split(first, last);
// values[first]..values[splitPoint - 1] <= splitVal
// values[splitPoint] = splitVal
// values[splitPoint+1]..values[last] > splitVal
quickSort(first, splitPoint - 1);
quickSort(splitPoint + 1, last);
}
}
/////////////////////////////////////////////////////////////////
//
// Heap Sort
static int newHole(int hole, int lastIndex, int item)
// If either child of hole is larger than item this returns the index
// of the larger child; otherwise it returns the index of hole.
{
int left = (hole * 2) + 1;
int right = (hole * 2) + 2;
if (left > lastIndex)
// hole has no children
return hole;
else
if (left == lastIndex)
// hole has left child only
if (item < values.get(left))
// item < left child
return left;
else
// item >= left child
return hole;
else
// hole has two children
if (values.get(left) < values.get(right))
// left child < right child
if (values.get(right) <= item)
// right child <= item
return hole;
else
// item < right child
return right;
else
// left child >= right child
if (values.get(left) <= item)
// left child <= item
return hole;
else
// item < left child
return left;
}
static void reheapDown(int item, int root, int lastIndex)
// Precondition: Current root position is "empty".
//
// Inserts item into the tree and ensures shape and order properties.
{
int hole = root; // current index of hole
int newhole; // index where hole should move to
newhole = newHole(hole, lastIndex, item); // find next hole
while (newhole != hole)
{
values.set(hole, values.get(newhole)); // move value up
hole = newhole; // move hole down
newhole = newHole(hole, lastIndex, item); // find next hole
}
values.set(hole,item); // fill in the final hole
}
static void heapSort()
// Sorts the values array using the heap sort algorithm.
{
int index;
// Convert the array of values into a heap.
for (index = SIZE/2 - 1; index >= 0; index--)
reheapDown(values.get(index), index, SIZE - 1);
// Sort the array.
for (index = SIZE - 1; index >=1; index--)
{
swap(0, index);
reheapDown(values.get(0), 0, index - 1);
}
}
/////////////////////////////////////////////////////////////////
//
// Main
public static void main(String[] args)
{
initValues();
printValues();
System.out.println("values is sorted: " + isSorted());
System.out.println();
// make call to sorting method here (just remove //)
selectionSort();
// bubbleSort();
// shortBubble();
// insertionSort();
// mergeSort(0, SIZE - 1);
// quickSort(0, SIZE - 1);
// heapSort();
System.out.println(" ------------------------------------------------------------ ");
printValues();
System.out.println("values is sorted: " + isSorted());
System.out.println();
}
}
Output:
5669 4945 9685 1831 2135 1703 3620 4415 7526 9351
3293 5961 9295 1007 1120 7965 5188 5502 8450 4774
7461 5853 5107 3334 9485 3635 5755 1589 17 5957
8584 7904 3353 5687 2955 2726 7770 7516 8124 3628
8685 4414 9862 8857 6180 8219 7805 5094 3619 8945
4061 896 7329 8418 7856 3485 8190 9076 6076 6161
2741 2238 2224 8371 5585 6480 2564 7637 9153 6734
9992 9899 3735 4498 3909 7686 87 5690 7998 2938
374 278 4046 5334 7525 5564 4211 611 1982 981
8668 6025 1704 1606 3674 883 4939 2812 3033 8736
9634 1184 3552 2077 1818 6235 5868 8652 3992 5176
2120 879 3512 9507 6346 2689 6189 8849 9951 2642
9709 9272 6117 5357 8672 9792 3037 3628 4916 2987
6546 3409 7984 7986 9789 4621 2704 6879 8888 176
7224 1252 1349 5362 2391 1842 7168 5875 7426 8359
3957 9967 9769 5173 2550 6087 8613 3400 2942 2992
6352 7180 1486 5630 5843 5860 4279 4939 5823 7003
3936 5659 5712 8162 8372 1858 3570 1632 3049 1419
5627 6350 4080 8968 2496 5641 1368 9311 9199 5350
8241 9659 4727 6447 703 7638 8685 9867 4699 1163
6481 6846 3603 7285 6650 262 9098 4455 6652 3452
88 6542 1156 6950 3819 4128 7129 8515 9250 5569
2118 9806 97 8331 6341 576 5487 3842 2888 5001
2607 748 4364 4975 2231 8309 5836 9517 5974 12
8131 3192 6746 8164 2873 6635 5885 2369 7813 3673
2733 315 3134 9219 4422 4473 2414 5714 4431 5857
9462 4664 6914 6993 8409 6615 645 6540 3601 8265
4673 8294 8945 5986 1765 7819 74 2643 4943 512
1968 463 5233 7989 8437 115 1413 6164 8378 3727
5066 2335 2079 9233 8857 8258 4832 9829 64 6666
6764 828 494 911 9800 3508 2130 2426 3529 7817
7079 3624 2927 2174 2597 2791 7513 3624 2854 3619
8701 3182 1928 6500 8405 1414 2647 8698 6647 5216
111 8850 7191 1259 4758 9838 6306 2660 4152 790
3077 4158 7650 8655 1856 1774 8255 9204 1971 8747
336 9020 5104 6807 9952 1177 4961 8166 4091 2038
148 4735 587 9959 1905 1260 1404 2155 1772 9850
4928 8654 5084 4434 9939 9298 4939 5287 4382 2019
9933 1821 7280 3160 7800 4838 2810 3333 2379 5915
1046 9097 2625 3013 4348 3331 6138 5254 5740 3729
1430 5360 5855 7005 8100 1207 2115 5428 9688 1871
7252 3443 8704 5062 4481 9645 1605 1778 8319 3487
6369 9923 371 9785 4256 3540 8809 3460 5670 45
2897 4015 7040 6539 812 7631 8181 508 4139 3726
2401 4653 3099 982 4769 1670 5644 6666 8302 3895
8025 8580 41 7637 4836 8844 6273 6342 9462 3987
887 999 3212 183 3814 2704 1792 1116 3559 1133
7410 8952 3961 7270 8985 5138 2880 3040 9767 4072
37 8575 343 7498 5959 5771 9342 3947 6244 803
7657 9847 8255 6127 5716 9120 9084 7014 5885 3437
9102 3658 5329 1178 5668 6350 8841 1868 4723 8128
4081 7731 4340 2185 5522 9999 8001 4934 9956 5069
6200 7444 5067 893 3020 643 9218 2013 4498 933
9780 1687 5682 2940 5744 7389 6305 2655 9087 6801
5795 9998 2342 9620 47 1238 6770 952 5391 5426
9197 4005 2047 1025 7754 3735 9616 522 5891 424
8280 6363 1388 1160 6717 1057 3110 3160 2559 9451
6489 3064 9527 161 5576 1683 2330 2288 7711 2232
9570 8217 5430 8893 3417 1294 5022 7197 7141 12
5974 6281 3454 8609 7550 4669 6743 8037 4997 1843
5422 8363 826 6555 1189 7219 310 7303 9240 6703
8116 5127 5007 2728 4886 1942 3350 5913 8273 5709
6978 1757 4197 1609 4924 790 4287 5617 9111 7897
7768 5657 9358 8037 8180 9473 8978 2310 5975 9591
785 3515 437 4114 5698 5367 9962 7605 5314 4214
4700 6690 4097 6940 1039 2257 8695 6435 1906 8378
999 8285 9147 4117 3701 5493 886 2065 6006 8689
3125 4143 4510 5396 7723 979 7618 9710 3418 4360
6957 8482 5083 2344 7687 5607 5523 388 9553 3437
6044 4585 7405 3106 297 5127 8877 396 8625 1583
6175 6346 8436 4698 168 2491 5855 817 627 9780
8223 2615 7891 7286 235 3299 7697 2532 5010 561
9659 6305 3916 6351 1949 2988 77 1684 5965 1507
2949 1554 6875 9603 5131 7279 4843 6689 3080 2211
1353 6883 2911 1909 8311 415 3138 1577 4333 3645
5095 616 3374 1696 989 9914 9743 7083 7655 2329
3536 9248 4696 1986 5808 1281 3768 5398 2721 6176
161 8047 4956 8799 3610 6933 9140 1109 4101 3411
827 1091 713 6105 1809 729 6623 9536 2133 6330
4292 8686 3738 1379 7349 8585 8824 1955 4604 3176
2140 6058 3461 9996 7701 9191 2391 5231 7366 2960
2953 7507 4912 3701 881 7445 9819 573 8621 7654
179 5963 122 1084 9850 2719 7406 2182 3259 6369
7975 4580 9354 2343 6507 7729 3798 4444 1441 2384
9822 5625 5569 4653 7476 2385 6630 3001 1126 1130
3248 4289 7010 1712 2376 8458 296 5588 2696 8259
8274 7729 6041 2502 6436 8398 1508 9703 5860 2742
3218 8901 1812 668 6854 455 4414 8161 6847 5141
2505 170 9937 6872 4522 2912 6786 3936 8420 1006
6946 104 3501 2235 7775 2422 1262 5528 9232 8630
8091 8743 9734 425 3784 6269 6256 1902 2632 4362
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528 3249 2947 1885 1755 2672 9165 7894 495 3485
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287 4334 6211 3724 3667 8042 7090 6378 20 9666
8320 7831 4516 3111 3650 7247 304 3272 9670 97
9771 6043 8568 8114 2786 580 2104 6787 8368 2814
1801 8334 6269 7059 7541 9617 8823 1082 7675 6828
3852 193 7946 3178 8937 1876 124 5259 7503 3650
690 9747 7226 9452 4155 2873 8191 5655 777 6944
4353 5831 6787 9700 5946 4444 3486 4167 914 2274
4407 1344 1869 4627 3265 8920 425 8730 3348 4411
8108 7391 798 9128 5132 2478 233 3630 5549 5992
9496 2355 1401 7995 5444 2296 7932 4046 2779 1485
1156 4029 2844 5644 4582 3036 1522 1578 5924 4926
8028 855 4975 6584 3746 1093 6744 8952 6254 6981
8784 7646 4925 8484 7288 8050 2211 4980 1377 8520
9241 5963 792 3023 7699 4026 6784 460 3544 8143
5586 5314 5713 8601 7620 4714 4613 4034 9418 7644
3065 8440 7649 8355 2273 5482 1454 5692 551 3471
values is sorted: false
[7][7, 13][7, 13, 14][7, 13, 14, 15][7, 13, 14, 15, 16][7, 13, 14, 15, 16, 20][7, 13, 14, 15, 16, 20, 22][7, 13, 14, 15, 16, 20, 22, 29][7, 13, 14, 15, 16, 20, 22, 29, 31][7, 13, 14, 15, 16, 20, 22, 29, 31, 34][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98, 20][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98, 20, 28][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98, 20, 28, 29][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98, 20, 28, 29, 31][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98, 20, 28, 29, 31, 55][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98, 20, 28, 29, 31, 55, 57][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98, 20, 28, 29, 31, 55, 57, 60][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98, 20, 28, 29, 31, 55, 57, 60, 62][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98, 20, 28, 29, 31, 55, 57, 60, 62, 67][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98, 20, 28, 29, 31, 55, 57, 60, 62, 67, 68][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98, 20, 28, 29, 31, 55, 57, 60, 62, 67, 68, 72][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98, 20, 28, 29, 31, 55, 57, 60, 62, 67, 68, 72, 74][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98, 20, 28, 29, 31, 55, 57, 60, 62, 67, 68, 72, 74, 79][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98, 20, 28, 29, 31, 55, 57, 60, 62, 67, 68, 72, 74, 79, 60][7, 13, 14, 15, 16, 20, 22, 29, 31, 34, 36, 45, 46, 50, 52, 57, 58, 59, 61, 62, 66, 67, 69, 70, 73, 75, 77, 82, 83, 84, 85, 86, 91, 92, 93, 95, 96, 98, 20, 28, 29, 31, 55, 57, 60, 62, 67, 68, 72, 74, 79, 60, 61]
------------------------------------------------------------
The values array is:
00 02 04 05 07 08 09 12 13 14
15 16 17 18 20 22 23 24 26 28
30 33 34 35 36 37 38 39 41 42
43 45 47 48 49 51 53 56 58 59
61 62 63 64 65 67 71 73 74 76
77 78 81 82 84 87 88 89 93 94
95 97 99 100 101 102 104 105 107 109
111 112 115 116 117 118 119 120 121 122
123 124 125 126 127 128 129 130 132 133
134 136 136 139 139 140 142 143 144 145
145 145 146 147 148 148 149 149 149 149
154 154 156 158 161 161 164 166 166 168
168 170 170 170 173 175 176 177 177 178
178 178 178 179 179 179 179 181 181 182
182 183 183 185 185 186 188 188 191 191
191 193 194 195 196 196 198 198 199 201
202 203 204 205 207 208 208 210 212 213
213 213 215 216 218 220 222 223 224 226
226 227 230 232 232 233 235 235 237 237
237 237 238 238 239 240 240 243 243 246
246 247 248 248 248 251 251 252 253 257
258 260 261 261 261 262 264 265 266 270
271 272 273 274 278 279 279 280 281 283
284 285 286 286 286 287 287 287 288 289
289 289 290 290 291 291 291 291 292 293
293 294 296 296 297 298 299 300 300 304
304 305 308 309 310 310 315 317 321 322
322 324 326 327 328 329 329 330 332 333
333 335 336 336 336 338 338 338 340 341
341 343 343 343 343 343 344 344 350 351
351 351 351 355 355 355 356 356 356 357
357 358 362 362 362 362 364 364 365 367
368 369 369 370 370 371 371 374 374 374
375 375 375 375 375 377 378 380 381 381
383 386 387 387 388 388 391 391 391 392
393 393 393 395 395 396 397 397 399 401
401 404 408 409 412 412 412 413 413 414
414 415 415 415 415 417 421 421 422 422
422 422 422 424 424 424 425 425 427 428
429 429 430 430 431 431 433 434 434 435
436 437 440 443 443 447 450 451 452 453
455 455 457 457 458 458 460 460 460 460
463 463 463 466 470 471 473 477 477 478
479 479 481 482 484 485 486 487 487 488
488 488 490 491 491 492 494 495 497 498
498 501 501 502 502 504 506 506 506 506
506 506 507 508 509 510 512 513 515 520
520 522 523 523 525 528 532 533 533 533
535 535 536 536 537 537 539 539 541 542
542 543 545 546 546 546 547 548 549 550
550 550 551 552 552 553 554 556 558 558
559 560 560 561 561 561 562 567 568 569
571 571 572 572 573 573 573 573 574 574
576 576 579 579 579 580 580 580 583 586
587 587 587 589 593 595 595 599 599 599
601 601 606 608 608 610 611 611 613 614
616 616 617 618 618 627 627 629 630 630
631 632 633 636 636 638 640 641 642 642
642 643 645 646 647 648 648 648 651 652
652 653 653 655 657 658 659 660 661 661
662 663 664 668 668 672 674 676 676 677
677 681 682 683 685 687 689 689 690 690
690 690 690 690 693 694 696 696 697 698
699 699 700 700 700 700 701 701 703 703
704 704 705 707 707 708 708 709 710 710
711 712 713 714 714 716 717 718 719 721
722 725 725 726 726 727 727 728 729 732
736 736 738 740 741 742 742 745 745 746
746 748 748 748 753 754 755 755 757 759
760 760 761 763 763 764 765 766 767 767
769 770 771 772 776 777 777 778 780 780
780 781 781 782 783 783 785 785 786 788
789 789 790 790 792 795 798 798 799 800
801 803 803 805 807 808 808 809 810 810
810 812 812 812 813 814 814 814 814 816
817 817 818 818 820 820 820 820 824 825
826 826 827 828 828 828 829 829 829 830
830 830 831 831 831 832 833 834 835 835
836 838 839 841 843 843 844 849 850 851
852 853 855 855 855 855 855 857 858 858
858 859 860 862 863 864 865 866 866 870
874 876 877 877 877 877 879 879 879 880
881 881 882 883 883 884 884 884 885 886
886 887 887 893 893 895 896 896 896 897
898 899 899 900 903 904 906 907 911 911
912 914 914 915 916 916 917 918 919 920
929 933 933 934 934 934 935 938 939 939
945 945 946 946 947 948 948 949 951 951
952 952 954 954 955 955 956 959 960 961
962 963 966 967 976 976 977 978 979 979
979 980 981 982 982 982 983 985 986 987
989 990 992 992 993 994 996 998 999 999
1002 1003 1003 1004 1006 1006 1007 1008 1008 1009
1010 1010 1010 1012 1012 1013 1015 1015 1018 1019
1020 1021 1022 1024 1025 1025 1027 1027 1029 1033
1033 1033 1035 1036 1036 1037 1038 1038 1039 1040
1040 1041 1042 1043 1044 1044 1044 1045 1046 1046
1047 1049 1049 1050 1050 1052 1053 1054 1057 1057
1058 1060 1061 1061 1061 1062 1064 1065 1066 1067
1068 1068 1068 1069 1073 1074 1074 1075 1077 1077
1079 1080 1082 1082 1083 1083 1084 1084 1084 1085
1085 1088 1089 1089 1090 1091 1091 1091 1091 1092
1092 1093 1093 1095 1096 1100 1101 1101 1102 1104
1105 1107 1107 1108 1109 1109 1111 1111 1114 1114
1114 1115 1116 1117 1119 1120 1124 1125 1125 1126
1126 1128 1129 1130 1131 1131 1132 1132 1133 1136
1138 1139 1140 1140 1141 1142 1142 1142 1144 1146
1148 1149 1149 1150 1150 1151 1153 1154 1154 1154
1154 1156 1156 1156 1157 1157 1158 1158 1160 1162
1163 1164 1165 1165 1167 1167 1168 1168 1172 1174
1174 1175 1175 1176 1177 1177 1177 1177 1177 1178
1178 1179 1180 1180 1184 1185 1185 1185 1186 1186
1187 1188 1189 1189 1190 1190 1191 1193 1194 1194
1194 1198 1203 1203 1205 1207 1210 1211 1214 1215
1216 1216 1218 1218 1218 1222 1222 1223 1224 1228
1228 1229 1231 1231 1232 1234 1235 1236 1236 1236
1238 1238 1240 1241 1242 1243 1244 1247 1250 1251
1252 1252 1252 1253 1254 1255 1255 1255 1256 1256
1256 1259 1260 1262 1262 1264 1265 1266 1268 1270
1270 1271 1271 1271 1271 1272 1272 1273 1274 1274
1275 1276 1277 1277 1278 1281 1281 1281 1282 1283
1284 1289 1290 1292 1293 1293 1294 1295 1296 1296
1297 1297 1300 1303 1303 1303 1307 1307 1307 1308
1309 1309 1311 1311 1312 1314 1314 1314 1315 1317
1317 1318 1324 1324 1327 1333 1338 1339 1340 1340
1341 1341 1341 1342 1342 1342 1344 1344 1345 1345
1345 1348 1349 1351 1353 1355 1358 1360 1363 1363
1365 1365 1367 1368 1368 1369 1369 1370 1372 1372
1373 1373 1373 1374 1375 1375 1376 1377 1379 1381
1384 1385 1388 1388 1388 1391 1391 1391 1393 1393
1393 1394 1394 1395 1396 1397 1398 1398 1399 1400
1400 1400 1401 1403 1403 1404 1404 1404 1405 1405
1409 1410 1411 1412 1413 1414 1414 1414 1417 1418
1419 1419 1419 1419 1421 1422 1422 1422 1423 1427
1429 1430 1431 1432 1433 1433 1437 1438 1438 1439
1439 1440 1441 1441 1441 1441 1443 1443 1445 1446
1446 1447 1448 1450 1452 1452 1453 1453 1453 1454
1454 1454 1455 1459 1461 1464 1469 1470 1471 1474
1474 1475 1475 1482 1483 1485 1486 1486 1487 1487
1488 1489 1492 1493 1496 1504 1505 1506 1507 1507
1508 1510 1513 1514 1515 1516 1518 1518 1520 1521
1522 1522 1522 1524 1525 1527 1532 1532 1535 1536
1538 1539 1540 1540 1541 1541 1543 1545 1547 1550
1552 1553 1553 1554 1556 1557 1557 1557 1558 1559
1560 1561 1561 1561 1562 1563 1563 1563 1564 1564
1565 1567 1568 1569 1569 1569 1570 1573 1574 1576
1576 1577 1577 1577 1578 1580 1580 1583 1583 1583
1584 1584 1585 1586 1588 1589 1589 1592 1592 1593
1593 1593 1593 1594 1594 1595 1600 1600 1601 1601
1602 1602 1603 1603 1604 1604 1605 1605 1605 1606
1606 1606 1607 1608 1609 1609 1609 1610 1611 1612
1614 1614 1615 1615 1616 1618 1619 1621 1621 1621
1621 1622 1622 1622 1624 1624 1625 1626 1626 1627
1628 1629 1629 1629 1629 1630 1631 1632 1634 1635
1635 1637 1638 1639 1639 1639 1640 1641 1642 1644
1645 1645 1645 1646 1646 1647 1648 1648 1648 1649
1649 1651 1651 1652 1652 1653 1654 1656 1656 1657
1658 1658 1659 1660 1661 1662 1663 1663 1664 1667
1667 1668 1668 1669 1670 1670 1674 1676 1676 1676
1678 1678 1680 1680 1682 1683 1683 1684 1684 1686
1687 1687 1690 1692 1692 1692 1695 1696 1697 1698
1700 1701 1703 1703 1704 1705 1706 1706 1707 1708
1709 1710 1712 1712 1715 1717 1718 1719 1719 1719
1720 1721 1723 1723 1724 1724 1724 1725 1725 1725
1726 1728 1729 1731 1732 1732 1733 1734 1735 1735
1735 1736 1736 1737 1737 1740 1740 1741 1741 1743
1743 1747 1747 1750 1750 1753 1753 1754 1755 1755
1757 1758 1758 1759 1760 1760 1761 1762 1763 1763
1763 1764 1764 1764 1765 1766 1767 1767 1768 1771
1771 1771 1771 1772 1772 1772 1773 1774 1774 1776
1776 1776 1776 1777 1778 1778 1779 1782 1782 1783
1783 1783 1784 1784 1785 1787 1789 1790 1791 1792
1792 1793 1793 1797 1798 1799 1801 1807 1809 1812
1813 1814 1814 1814 1814 1814 1815 1816 1818 1818
1818 1818 1819 1821 1821 1822 1822 1823 1824 1824
1824 1827 1828 1828 1829 1830 1830 1831 1831 1832
1832 1833 1835 1836 1837 1838 1838 1839 1839 1839
1839 1841 1842 1842 1843 1843 1845 1845 1846 1846
1847 1849 1849 1853 1855 1856 1856 1858 1858 1859
1861 1863 1863 1866 1868 1868 1869 1870 1871 1871
1871 1872 1873 1874 1876 1876 1878 1878 1878 1880
1880 1881 1881 1883 1884 1885 1886 1887 1887 1888
1889 1890 1890 1890 1891 1894 1895 1896 1897 1898
1899 1900 1901 1902 1902 1903 1904 1905 1905 1905
1906 1906 1906 1907 1908 1909 1910 1910 1913 1916
1917 1918 1918 1920 1920 1920 1920 1922 1923 1924
1926 1926 1927 1927 1927 1928 1928 1928 1929 1931
1932 1932 1935 1935 1936 1936 1937 1939 1940 1941
1942 1944 1945 1945 1946 1946 1946 1947 1947 1948
1949 1950 1950 1950 1950 1952 1952 1953 1954 1955
1955 1958 1958 1960 1963 1965 1965 1966 1967 1967
1967 1968 1969 1969 1969 1971 1971 1971 1974 1975
1975 1978 1979 1979 1979 1980 1981 1982 1982 1982
1983 1984 1986 1987 1987 1988 1989 1989 1990 1990
1992 1993 1994 1994 1995 1996 1996 1997 1997 2000
2005 2005 2005 2006 2008 2011 2012 2012 2013 2013
2016 2019 2019 2020 2026 2026 2026 2026 2026 2027
2027 2029 2030 2031 2032 2032 2032 2033 2034 2036
2037 2038 2038 2042 2043 2044 2047 2048 2049 2049
2049 2051 2052 2052 2054 2058 2058 2059 2061 2061
2062 2064 2065 2065 2065 2066 2067 2068 2069 2070
2071 2071 2072 2073 2073 2075 2075 2076 2077 2077
2078 2078 2079 2081 2082 2083 2083 2084 2084 2084
2085 2087 2089 2091 2092 2092 2093 2093 2096 2096
2097 2098 2098 2099 2099 2100 2101 2101 2102 2102
2102 2103 2104 2107 2108 2108 2109 2111 2113 2115
values is sorted: true
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