# Number of times a number can be replaced by the sum of its digits until it only contains one digit

Count the number of times a number can be replaced by the sum of its digits until it only contains one digit and number can be very large.

**Examples:**

Input : 10 Output : 1 1 + 0 = 1, so only one times an number can be replaced by its sum . Input : 991 Output : 3 9 + 9 + 1 = 19, 1 + 9 = 10, 1 + 0 = 1 hence 3 times the number can be replaced by its sum.

We have discussed Finding sum of digits of a number until sum becomes single digit.

The problem here is just extension of the above previous problem. Here, we just want to count number of times a number can be replaced by its sum until it only contains one digit. As number can be very much large so to avoid overflow, we input the number as string. **So, to compute this we take one variable named as temporary_sum in which we repeatedly calculate the sum of digits of string and convert this temporary_sum into string again. This process repeats till the string length becomes 1 .** To explain this in a more clear way consider number 991

9 + 9 + 1 = 19, Now 19 is a string

1 + 9 = 10, again 10 is a string

1 + 0 = 1 . again 1 is a string but here string length is 1 so, loop breaks .

**The number of sum operations is the final answer .**

Below is implementation of this approach .

## C/C++

`// C++ program to count number of times we ` `// need to add digits to get a single digit. ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `int` `NumberofTimes(string str) ` `{ ` ` ` `// Here the count variable store ` ` ` `// how many times we do sum of ` ` ` `// digits and temporary_sum ` ` ` `// always store the temporary sum ` ` ` `// we get at each iteration . ` ` ` `int` `temporary_sum = 0, count = 0; ` ` ` ` ` `// In this loop we always compute ` ` ` `// the sum of digits in temporary_ ` ` ` `// sum variable and convert it ` ` ` `// into string str till its length ` ` ` `// become 1 and increase the count ` ` ` `// in each iteration. ` ` ` `while` `(str.length() > 1) ` ` ` `{ ` ` ` `temporary_sum = 0; ` ` ` ` ` `// computing sum of its digits ` ` ` `for` `(` `int` `i = 0; i < str.length(); i++) ` ` ` `temporary_sum += ( str[ i ] - ` `'0'` `) ; ` ` ` ` ` `// converting temporary_sum into string ` ` ` `// str again . ` ` ` `str = to_string(temporary_sum) ; ` ` ` ` ` `// increase the count ` ` ` `count++; ` ` ` `} ` ` ` ` ` `return` `count; ` `} ` ` ` `// Driver program to test the above function ` `int` `main() ` `{ ` ` ` `string s = ` `"991"` `; ` ` ` `cout << NumberofTimes(s); ` ` ` `return` `0; ` `} ` |

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## Java

`// Java program to count number of times we ` `// need to add digits to get a single digit. ` ` ` `public` `class` `GFG ` `{ ` ` ` `static` `int` `NumberofTimes(String str) ` ` ` `{ ` ` ` `// Here the count variable store ` ` ` `// how many times we do sum of ` ` ` `// digits and temporary_sum ` ` ` `// always store the temporary sum ` ` ` `// we get at each iteration . ` ` ` `int` `temporary_sum = ` `0` `, count = ` `0` `; ` ` ` ` ` `// In this loop we always compute ` ` ` `// the sum of digits in temporary_ ` ` ` `// sum variable and convert it ` ` ` `// into string str till its length ` ` ` `// become 1 and increase the count ` ` ` `// in each iteration. ` ` ` `while` `(str.length() > ` `1` `) ` ` ` `{ ` ` ` `temporary_sum = ` `0` `; ` ` ` ` ` `// computing sum of its digits ` ` ` `for` `(` `int` `i = ` `0` `; i < str.length(); i++) ` ` ` `temporary_sum += ( str.charAt(i) - ` `'0'` `) ; ` ` ` ` ` `// converting temporary_sum into string ` ` ` `// str again . ` ` ` `str = temporary_sum + ` `""` `; ` ` ` ` ` `// increase the count ` ` ` `count++; ` ` ` `} ` ` ` ` ` `return` `count; ` ` ` `} ` ` ` ` ` `// Driver program to test above functions ` ` ` `public` `static` `void` `main(String[] args) ` ` ` `{ ` ` ` `String s = ` `"991"` `; ` ` ` `System.out.println(NumberofTimes(s)); ` ` ` `} ` ` ` `} ` `/* This code is contributed by Mr. Somesh Awasthi */` |

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## Python 3

`# Python 3 program to count number of times we ` `# need to add digits to get a single digit. ` `def` `NumberofTimes(s): ` ` ` ` ` `# Here the count variable store ` ` ` `# how many times we do sum of ` ` ` `# digits and temporary_sum ` ` ` `# always store the temporary sum ` ` ` `# we get at each iteration . ` ` ` `temporary_sum ` `=` `0` ` ` `count ` `=` `0` ` ` ` ` `# In this loop we always compute ` ` ` `# the sum of digits in temporary_ ` ` ` `# sum variable and convert it ` ` ` `# into string str till its length ` ` ` `# become 1 and increase the count ` ` ` `# in each iteration. ` ` ` `while` `(` `len` `(s) > ` `1` `): ` ` ` ` ` `temporary_sum ` `=` `0` ` ` ` ` `# computing sum of its digits ` ` ` `for` `i ` `in` `range` `(` `len` `(s)): ` ` ` `temporary_sum ` `+` `=` `(` `ord` `(s[ i ]) ` `-` ` ` `ord` `(` `'0'` `)) ` ` ` ` ` `# converting temporary_sum into ` ` ` `# string str again . ` ` ` `s ` `=` `str` `(temporary_sum) ` ` ` ` ` `# increase the count ` ` ` `count ` `+` `=` `1` ` ` ` ` `return` `count ` ` ` `# Driver Code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` ` ` `s ` `=` `"991"` ` ` `print` `(NumberofTimes(s)) ` ` ` `# This code is contributed by Ita_c ` |

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## C#

`// C# program to count number of ` `// times we need to add digits to ` `// get a single digit. ` `using` `System; ` ` ` `class` `GFG { ` ` ` ` ` `// Function to count number of ` ` ` `// times we need to add digits ` ` ` `// to get a single digit ` ` ` `static` `int` `NumberofTimes(String str) ` ` ` `{ ` ` ` ` ` `// Here the count variable store ` ` ` `// how many times we do sum of ` ` ` `// digits and temporary_sum ` ` ` `// always store the temporary sum ` ` ` `// we get at each iteration . ` ` ` `int` `temporary_sum = 0, count = 0; ` ` ` ` ` `// In this loop we always compute ` ` ` `// the sum of digits in temporary_ ` ` ` `// sum variable and convert it ` ` ` `// into string str till its length ` ` ` `// become 1 and increase the count ` ` ` `// in each iteration. ` ` ` `while` `(str.Length > 1) ` ` ` `{ ` ` ` `temporary_sum = 0; ` ` ` ` ` `// computing sum of its digits ` ` ` `for` `(` `int` `i = 0; i < str.Length; i++) ` ` ` `temporary_sum += (str[i] - ` `'0'` `); ` ` ` ` ` `// converting temporary_sum ` ` ` `// into string str again . ` ` ` `str = temporary_sum + ` `""` `; ` ` ` ` ` `// increase the count ` ` ` `count++; ` ` ` `} ` ` ` ` ` `return` `count; ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `String s = ` `"991"` `; ` ` ` `Console.Write(NumberofTimes(s)); ` ` ` `} ` ` ` `} ` ` ` `// This code is contributed by Nitin Mittal. ` |

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## PHP

`<?php ` `// PHP program to count number of times we ` `// need to add digits to get a single digit. ` ` ` `function` `NumberofTimes(` `$str` `) ` `{ ` ` ` `// Here the count variable store ` ` ` `// how many times we do sum of ` ` ` `// digits and temporary_sum ` ` ` `// always store the temporary sum ` ` ` `// we get at each iteration . ` ` ` `$temporary_sum` `= 0; ` `$count` `= 0; ` ` ` ` ` `// In this loop we always compute ` ` ` `// the sum of digits in temporary_ ` ` ` `// sum variable and convert it ` ` ` `// into string str till its length ` ` ` `// become 1 and increase the count ` ` ` `// in each iteration. ` ` ` `while` `(` `strlen` `(` `$str` `) > 1) ` ` ` `{ ` ` ` `$temporary_sum` `= 0; ` ` ` ` ` `// computing sum of its digits ` ` ` `for` `(` `$i` `= 0; ` `$i` `< ` `strlen` `(` `$str` `); ` `$i` `++) ` ` ` `$temporary_sum` `+= (` `$str` `[ ` `$i` `] - ` `'0'` `); ` ` ` ` ` `// converting temporary_sum into ` ` ` `// string str again . ` ` ` `$str` `= (string)(` `$temporary_sum` `); ` ` ` ` ` `// increase the count ` ` ` `$count` `++; ` ` ` `} ` ` ` ` ` `return` `$count` `; ` `} ` ` ` `// Driver Code ` `$s` `= ` `"991"` `; ` `echo` `NumberofTimes(` `$s` `); ` ` ` `// This code is contributed ` `// by Akanksha Rai ` `?> ` |

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**Output:**

3

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