Question

6174 is known as Kaprekar's constant after the Indian mathematician D. R. Kaprekar.

This number is notable for the following rule:
1. Take any four-digit number, using at least two different digits.
2. Arrange the digits in descending and then in ascending order to get two four-digit numbers, adding leading zeros if necessary.
3. Subtract the smaller number from the bigger number.
4. Go back to step 2 and repeat.

The above process, known as Kaprekar's routine, will always reach its fixed point, 6174, in at most 7 iterations.
Once 6174 is reached, the process will continue yielding 7641 – 1467 = 6174.

Example (8692)	number of steps counted
9862-2689=7173	Step 1
7731-1377=6354	Step 2
6543-3456=3087	Step 3
8730-378=8352	Step 4
8532-2358=6174	Step 5

Example (6174)	number of steps counted
7641-1467=6174	Step 1

The only four-digit numbers for which Kaprekar's routine does not reach 6174 are repdigits such as 1111, which give the result 0000 after a single subtraction.

Note: Kaprekar's constant is not unique. There are families of Kaprekar's constants for different bases or different number of digits. For example, the Kaprekar constant is 495 for 3-digit integer. In this program, we only consider Kaprekar's constant 6174 for 4-digit integer.

*Note:*
1. Add code ONLY in the correponding "TODO" area.
2. DO NOT change the function header of the given functions.
3. DO NOT add additional libraries.
4. DO NOT use array, otherwise ZERO marks for the assignment.
5. You can add helper function(s) if needed.

Function 1: int selectDigit(int number, int index)

• The function extracts one digit from a given index position of the positive integer
• The index starts from 0 at the rightmost digit
• The function return -1 if index is invalid
• The function should work on arbitrary positive integer

Example	Expected return value
selectDigit(4853,0)	3
selectDigit(4853,2)	8
selectDigit(18694,3)	8
selectDigit(18694,5)	-1
selectDigit(18694,-1)	-1

Function 2: bool isRepdigit(int number)

• The function checks whether all digits in a positive integer are the same
• It returns true if Yes, false otherwise
• The function should work on arbitrary positive integer

Example	Expected return value
isRepdigit(4855)	false
isRepdigit(5555)	true
isRepdigit(18642)	false
isRepdigit(1)	true

Function 3: int sortDigit(int number, bool order)

• The function takes a positive integer and returns a new integer with all digits in number arranged in ascending or descending order
• The function should work on number consists 0s
• The function should work on arbitrary positive integer

Example	Expected return value
sortDigit(4855,ASCENDING)	4558
sortDigit(4855,DESCENDING)	8554
sortDigit(89764,ASCENDING)	46789
sortDigit(89764,DESCENDING)	98764
sortDigit(20003,ASCENDING)	23
sortDigit(20003,DESCENDING)	32000

Function 4: int isKaprekar6174(int number, bool debug)

• The function takes an arbitrary positive integer and returns the number of steps needed to reach Kaprekar's constant 6174
• The function returns -1 if the number can't reach 6174
• when DEBUG is true, calculation details needs to be printed out
• Output format for the calculation details: each row represents a subtraction calculation. There is no space between the number and minus sign. There is no space between the number and equal sign

Example	Expected return value	Expected output
isKaprekar6174(8692,false)	5 (i.e. takes 5 steps to finish)
isKaprekar6174(8692,true)	5 (i.e. takes 5 steps to finish)	9862-2689=7173 7731-1377=6354 6543-3456=3087 8730-378=8352 8532-2358=6174
isKaprekar6174(865,false)	-1 (i.e. non 4-digit number)
isKaprekar6174(865,true)	-1 (i.e. non 4-digit number)	can't reach Kaprekar's constant 6174
isKaprekar6174(2222,false)	-1 (i.e. it is a repdigit)
isKaprekar6174(2222,true)	-1 (i.e. it is a repdigit)	can't reach Kaprekar's constant 6174

Function 5: void printStat(int m, int n)

• the function shows the bincounts #steps to reach Kaprekar's constant 6174 for numbers in a given range from m to n (both m and n inclusive), then print the bar chart (*)
• For simplicity, you can assume that m and n are positive integers and there is always a valid range
• 8 bins are used, which count the numbers with 1 to 7 steps to reach Kaprekar's constant 6174, or fail to do so
• Output format: For each row, starts with the bin number (i.e. 1 to 7) and immediately followed by the star. Do not leave any spaces between them
• Output format: The last row (eighth row) of the output represents the failure case (started with -1 and immediately followed by the star, do not leave any spaces between them)
• A * is printed for every 50 counted, also print a * star if there is a remainder
• For example if bincount = 350, print 7 stars; bincount = 351, print 8 stars

Example	Expected output
printStat(1000,2000)	1* 2** 3***** 4*** 5**** 6**** 7**** -1*
printStat(1000,9999)	1******** 2*********** 3******************************************* 4*********************** 5**************************** 6******************************* 7**************************************** -1*

Down below is the skeleton code for this program:

#include <iostream>
#include <math.h>
using namespace std;

const bool ASCENDING = 0;
const bool DESCENDING = 1;
const bool DEBUG = true;

/**
 *  Task 1: selectDigit() returns one digit from a given index location of an arbitrary positive integer
 *  The index starts from 0 at the rightmost digit
 *  The function return -1 if index is invalid
 *  Examples: selectDigit(123, 0) = 3, selectDigit(1234, 3) = 1, selectDigit(123, 3) = -1, selectDigit(123, -1) = -1
 */
int selectDigit(int number, int index){

//TODO: start your coding here

}

/**
 *  Task 2: isRepdigit() checks whether all digits in a positive integer are the same
 *  It returns true if Yes, false otherwise
 *  Examples: isRepdigit(222) = true, isRepdigit(212) = false, isRepdigit(2) = true
 */
bool isRepdigit(int number){

//TODO: start your coding here

}

/**
 *  Task 3: sortDigit() takes an arbitrary positive integer number,
 *  and returns a new integer with all digits in number arranged in ascending or descending order
 *  Examples: sortDigit(16845, ASCENDING) = 14568, sortDigit(16845, DESCENDING) = 86541
 *  The function should be able to handle number consists 0s
 *  Examples: sortDigit(500, ASCENDING) = 5, sortDigit(100250, DESCENDING) = 521000, sortDigit(100250, ASCENDING) = 125
 */
int sortDigit(int number, bool order){

//TODO: start your coding here

}

/**
 * Task 4: isKaprekar6174() takes an arbitrary positive integer,
 * and returns the number of steps needed to reach Kaprekar's constant 6174
 * The function returns -1 if the number can't reach 6174
 * when DEBUG is true, calculation details needs to be printed out
 * Output format for the calculation details: Each row represents a subtraction calculation
 * There is no space between the number and minus sign. There is no space between the number and equal sign
 */
int isKaprekar6174(int number, bool debug){

//TODO: start your coding here

}

/**
 * Task 5: printStat() bincounts #steps to reach Kaprekar's constant 6174 for numbers in a given range from m to n (both inclusive)
 * Then print the bar chart (*)
 * For simplicity, you can assume that m and n are positive integers and there is always a valid range
 * 8 bins are used, which count the numbers with 1 to 7 steps to reach Kaprekar's constant 6174, or fail to do so
 * A * is printed for every 50 counted
 * Print a * if there is remainder
 * For example if bincount = 350, print 7 stars; bincount = 351, print 8 stars
 * Output format: For each row, starts with the bin number (i.e. 1 to 7) and immediately followed by the star. Do not leave any spaces between them
 * Output format: The last row (eighth row) of the output represents the failure case (started with -1 and immediately followed by the star, do not leave any spaces between them)
 */
void printStat(int m, int n){

//TODO: start your coding here

}

// This is the main function. It is already done. Please DO NOT make any modification.
int main()
{
cout << "Task 1:" << endl;
cout << "selectDigit(896543,0) = " << selectDigit(896543,0) << endl;
cout << "selectDigit(896543,5) = " << selectDigit(896543,5) << endl;
cout << "selectDigit(896543,-1) = " << selectDigit(896543,-1) << endl;
cout << "selectDigit(896543,6) = " << selectDigit(896543,6) << endl;

cout << endl << "Task 2:" << endl;
cout << "isRepdigit(2999) " << boolalpha << isRepdigit(2999) << endl;
cout << "isRepdigit(888888) " << boolalpha << isRepdigit(888888) << endl;
cout << "isRepdigit(1) " << boolalpha << isRepdigit(1) << endl;

cout << endl << "Task 3:" << endl;
cout << "sortDigit(54321, ASCENDING) = " << sortDigit(54321, ASCENDING) << endl;
cout << "sortDigit(794621, ASCENDING) = " << sortDigit(794621, ASCENDING) << endl;
cout << "sortDigit(794621, DESCENDING) = " << sortDigit(794621, DESCENDING) << endl;
cout << "sortDigit(100250, ASCENDING) = " << sortDigit(100250, ASCENDING) << endl;
cout << "sortDigit(100250, DESCENDING) = " << sortDigit(100250, DESCENDING) << endl;
cout << "sortDigit(500, ASCENDING) = " << sortDigit(500, ASCENDING) << endl;

cout << endl << "Task 4:" << endl;
cout << "isKaprekar6174(546, DEBUG) = " << isKaprekar6174(546, !DEBUG) << endl;
isKaprekar6174(546, DEBUG);
cout << "isKaprekar6174(18604, DEBUG) = " << isKaprekar6174(18604, !DEBUG)<< endl;
isKaprekar6174(18604, DEBUG);
cout << "isKaprekar6174(8888, DEBUG) = " << isKaprekar6174(8888, !DEBUG) << endl;
isKaprekar6174(8888, DEBUG);
cout << "isKaprekar6174(2894, DEBUG) = " << isKaprekar6174(2894, !DEBUG)<< endl;
isKaprekar6174(2894, DEBUG);
cout << "isKaprekar6174(6174, DEBUG) = " << isKaprekar6174(6174, !DEBUG)<< endl;
isKaprekar6174(6174, DEBUG);

cout << endl << "Task 5: " << endl;
cout << "Statistic for range from 1000 to 9999" << endl;
printStat(1000,9999);
cout << "Statistic for range from 500 to 10500" << endl;
printStat(500,10500);

return 0;
}

Answer 1

SOLUTION:-

Given that code

#include <iostream>
#include <math.h>
#include <cmath>
using namespace std;
const bool ASCENDING = 0;
const bool DESCENDING = 1;
const bool DEBUG = true;

/** Task 1: selectDigit() returns one digit from a given index location of an arbitrary positive integer
*/
int selectDigit(int number, int index)
{
int d, currentIndex = 0;
while(number > 0) {
d = number % 10;
if(currentIndex == index){
return d;
}
currentIndex ++;
number = number / 10;
}
return -1;
}

/** Task 2: isRepdigit() checks whether all digits in a positive integer are the same
*/
bool isRepdigit(int number)
{
int d=0,d1=0, flag = 0;
if(number <= 10) {
return true;
}
else{
while(number > 10) {
d = number % 10;
d1 = ((number % 100) - d)/ 10;
if(d != d1){
return false;
}
number = number/10;
}
return true;
}

}
/** Task 3: sortDigit() takes an arbitrary positive integer number,
*/
int sortDigit(int number, bool order)
{ int i, p, n = 0, r;
if(order) {
//Descending
for(i=9;i>=0;i--)
{
p=number;
while(p!=0)
{
r = p%10;
if(r==i)
{
n = n * 10 + r;
}
p=p/10;
}
}
}
else
{
//Ascending
for(i=0;i<10;i++)
{
p=number;
while(p!=0)
{
r = p%10;
if(r==i)
{
n = n * 10 + r;
}
p=p/10;
}
}
}
return n;
}
/** Task 4: isKaprekar6174() takes an arbitrary positive integer,
*/
int isKaprekar6174(int number, bool debug)
{ int maxCount = 7,i = 0, count = 0;
int n = number;
if(isRepdigit(number) || number < 1000 || number >9999){
if(debug == true)
printf("Can't reach Kaprekar's constant 6174\n");
return -1;
}
else{
while(count <= maxCount)
{
count ++;
if(debug == true) {
cout<<n<<" = "<<sortDigit(n, true)<<" - "<<sortDigit(n, false)<<endl;
}
n = sortDigit(n, true) - sortDigit(n, false);
if(n == 6174){
return count;
}
}
return count;
}

}
/** Task 5: printStat() bincounts
*/
void printStat(int m, int n)
{
int c0=0, c1=0, c2=0, c3=0, c4=0, c5=0, c6=0, c7=0, i;
int star;
for (i = m; i <= n; i ++) {
if(isKaprekar6174(i,0) == 1) {
c1++;
}
else if(isKaprekar6174(i,0) == 2) {
c2++;
}
else if(isKaprekar6174(i,0) == 3) {
c3++;
}
else if(isKaprekar6174(i,0) == 4) {
c4++;
}
else if(isKaprekar6174(i,0) == 5) {
c5++;
}
else if(isKaprekar6174(i,0) == 6) {
c6++;
}
else if(isKaprekar6174(i,0) == 7) {
c7++;
}
else if(isKaprekar6174(i,0) == -1){
c0++;
}
}
for(i = 1; i <= 7; i ++){
if(i == 1) {
star = c1 / 50;
if(c1 % 50 != 0) {
star ++;
}
}
else if(i ==2) {
star = c2 / 50;
if(c2 % 50 != 0) {
star ++;
}
}
else if(i == 3) {
star = c3 / 50;
if(c3 % 50 != 0) {
star ++;
}
}
else if(i == 4) {
star = c4 / 50;
if(c4 % 50 != 0) {
star ++;
}
}
else if(i == 5) {
star = c5 / 50;
if(c5 % 50 != 0) {
star ++;
}
}
else if(i == 6) {
star = c6 / 50;
if(c6 % 50 != 0) {
star ++;
}
}
else if(i == 7) {
star = c7 / 50;
if(c7 % 50 != 0) {
star ++;
}
}
cout<<i;
for(int j = 1; j <= star; j ++) {
cout<<"*";
}
cout<<endl;
}
star = c0/50;
if(c0 % 50 != 0) {
star ++;
}
cout<<"-1";
for(int j = 1; j <= star; j ++) {
cout<<"*";
}
cout<<endl;
}
// This is the main function. It is already done. Please DO NOT make any modification.
int main()
{
cout << "Task 1:" << endl;
cout << "selectDigit(896543,0) = " << selectDigit(896543,0) << endl;
cout << "selectDigit(896543,5) = " << selectDigit(896543,5) << endl;
cout << "selectDigit(896543,-1) = " << selectDigit(896543,-1) << endl;
cout << "selectDigit(896543,6) = " << selectDigit(896543,6) << endl;
cout << endl << "Task 2:" << endl;
cout << "isRepdigit(2999) " << boolalpha << isRepdigit(2999) << endl;
cout << "isRepdigit(888888) " << boolalpha << isRepdigit(888888) << endl;
cout << "isRepdigit(1) " << boolalpha << isRepdigit(1) << endl;
cout << endl << "Task 3:" << endl; cout << "sortDigit(54321, ASCENDING) = " << sortDigit(54321, ASCENDING) << endl;
cout << "sortDigit(794621, ASCENDING) = " << sortDigit(794621, ASCENDING) << endl;
cout << "sortDigit(794621, DESCENDING) = " << sortDigit(794621, DESCENDING) << endl;
cout << "sortDigit(100250, ASCENDING) = " << sortDigit(100250, ASCENDING) << endl;
cout << "sortDigit(100250, DESCENDING) = " << sortDigit(100250, DESCENDING) << endl;
cout << "sortDigit(500, ASCENDING) = " << sortDigit(500, ASCENDING) << endl;
cout << endl << "Task 4:" << endl;
cout << "isKaprekar6174(546, DEBUG) = " << isKaprekar6174(546, !DEBUG) << endl;
isKaprekar6174(546, DEBUG);
cout << "isKaprekar6174(18604, DEBUG) = " << isKaprekar6174(18604, !DEBUG)<< endl;
isKaprekar6174(18604, DEBUG);
cout << "isKaprekar6174(8888, DEBUG) = " << isKaprekar6174(8888, !DEBUG) << endl;
isKaprekar6174(8888, DEBUG);
cout << "isKaprekar6174(2894, DEBUG) = " << isKaprekar6174(2894, !DEBUG)<< endl;
isKaprekar6174(2894, DEBUG);
cout << "isKaprekar6174(6174, DEBUG) = " << isKaprekar6174(6174, !DEBUG)<< endl;
isKaprekar6174(6174, DEBUG);
cout << endl << "Task 5: " << endl;
cout << "Statistic for range from 1000 to 9999" << endl;
printStat(1000,9999);
cout << "Statistic for range from 500 to 10500" << endl;
printStat(500,10500);
return 0;
}

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