Digit-increasing number test?

Question

A number is called digit-increasing if it is equal n + nn + nnn + ... for some digit n between 1 and 9. For example 24 is digit-increasing because it equals 2 + 22 (here n = 2). Actually, a friend of mine asked me this question and i am stuck thinking about it but couldn't find the exact solution so far. Can anyone help ? I needed the function that returns true if it is digit-increasing else false.

Answer 1

Interesting problem. Below is a non-standard (but C-like) pseudocode implementation for the solution for the function named isDigIncreasing().

bool isDigIncreasing(num)

for n = 1 thru 9

{

mynum = n;

m = 10*n +n;

while (mynum<num)

{

mynum = mynum + m;

m = m*10 +n;

if mynum == num, then return(true) // return value before nested looping ...

...finishes if the num is digit increasing.

}

}

return(false) // if all looping finishes without exiting early, then num is NOT digit increasing.

Answer 2

#include <stdio.h>

#include <stdlib.h>

#include <string.h>

long RepeatDigit( char digit, int n)

{

char * str;

str = (char *)malloc(n);

int N = 0;

memset(str,digit,n);

N = atoi(str);

free(str);

return(N);

}

int IsDigitIncreasing(int X )

{

int iReturn=1;

char chDigit;

int n;

long partial_sum;

int iNum;

if (X!=0)

{

for (chDigit='1'; chDigit<='9'; chDigit++)

{

n=0;

partial_sum=0;

while ( partial_sum<X)

{

n++;

iNum = RepeatDigit(chDigit,n);

partial_sum += iNum;

printf(" %d : partial sum = %ld \n",iNum,partial_sum);

}

iReturn = (partial_sum==X) ? 1 : 0;

if (iReturn==1)

{

break;

}

} //for

}//X is not zero

return(iReturn);

}

int main()

{

int input_integer;

printf(" input the integer :> "); //3702 is digit increasing since 3+33+333+3333 = 3702

scanf("%d",&input_integer);

if (input_integer==0)

{

printf(" ZERO is automatically digit increasing since 0 = 0 + 00 +000 +0000 + ... \n");

}

int iReturn = IsDigitIncreasing(input_integer);

if (iReturn==1)

{

printf(" It is digit increasing \n");

}

else

{

printf(" It is not digit increasing \n");

}

}

Answer 3

#include <stdio.h>

#include <string.h>

#include <stdlib.h>

#define MAX_NUM_BUFF_SIZE (255)

#define DIGIT_INCREASING_SUCCESS (0)

#define DIGIT_INCREASING_FAIL (-1)

void digitRepeat ( int digit, int count, char * zoutbuff)

{

memset(zoutbuff,digit+48,count);

}

void OutputDigitIncreasing(int x)

{

printf(" %d is digit increasing \n",x);

}

int IsDigitIncreasing(int inputVal)

{

int iLoop=0;

int iReturn = DIGIT_INCREASING_SUCCESS;

char numBuff[MAX_NUM_BUFF_SIZE]; // hope it's big enough;

/* zero is automatically digit increasing */

if (inputVal==0)

{

return iReturn;

}

int done=0;

for (iLoop=1; iLoop<10; iLoop++)

{

memset(numBuff,0,MAX_NUM_BUFF_SIZE);

int numDigits=1;

long sumSequence = iLoop;

while (sumSequence <= inputVal)

{

if (inputVal==sumSequence)

{

OutputDigitIncreasing(inputVal);

done=1;

break;

}

numDigits++;

digitRepeat(iLoop,numDigits,numBuff);

long longIntNum = atoi(numBuff);

sumSequence += longIntNum;

printf(" longIntNum = %ld : sumSequence = %ld \n",longIntNum,sumSequence);

}//while

if (done==1) { break; }

}// main for loop

iReturn = (done==1)? DIGIT_INCREASING_SUCCESS : DIGIT_INCREASING_FAIL;

return(iReturn);

}// IsDigitIncreasing

int main()

{

int inputValX= 102030405; //6170 = 5+55+555+5555

// 24 = 2 + 22

// 37035 = 3 +33 +333 +3333 +33333

if (IsDigitIncreasing(inputValX)==DIGIT_INCREASING_SUCCESS)

{

OutputDigitIncreasing(inputValX);

}

else

{

printf(" %ld is NOT DIGIT INCREASING \n");

}

}