# Largest number less than N with digit sum greater than the digit sum of N

Last Updated : 09 May, 2023

Given an integer N, the task is to find the greatest number less than N such that the sum of its digits is greater than the sum of the digits of N. If the condition isn’t satisfied for any number then print -1.
Examples:

Input: N = 100
Output: 99
99 is the largest number less than 100 sum of whose digits is greater than the sum of the digits of 100

Input: N = 49
Output: -1

Brute Force Approach:

To solve this problem we can start iterating from N-1 down to 1, and for each number, compute the sum of its digits using a loop. Then, we can compare this sum to the sum of the digits of N, and if it is greater, we have found the answer and we can return the current number. If the loop completes without finding a suitable number, we can return -1.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach` `#include ` `using` `namespace` `std;`   `// Function to return the greatest` `// number less than n such that` `// the sum of its digits is greater` `// than the sum of the digits of n` `int` `findNumber(``int` `n)` `{` `    ``for` `(``int` `i = n - 1; i > 0; i--) {` `        ``int` `sum_i = 0, sum_n = 0;` `        ``int` `temp_i = i, temp_n = n;` `        ``while` `(temp_i > 0) {` `            ``sum_i += temp_i % 10;` `            ``temp_i /= 10;` `        ``}` `        ``while` `(temp_n > 0) {` `            ``sum_n += temp_n % 10;` `            ``temp_n /= 10;` `        ``}` `        ``if` `(sum_i > sum_n) {` `            ``return` `i;` `        ``}` `    ``}` `    ``return` `-1;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `n = 824;` `    ``cout << findNumber(n);`   `    ``return` `0;` `}`

## Java

 `// Java implementation of the approach` `import` `java.util.*;`   `class` `Main {` `    ``// Function to return the greatest` `    ``// number less than n such that` `    ``// the sum of its digits is greater` `    ``// than the sum of the digits of n` `    ``static` `int` `findNumber(``int` `n)` `    ``{` `        ``for` `(``int` `i = n - ``1``; i > ``0``; i--) {` `            ``int` `sum_i = ``0``, sum_n = ``0``;` `            ``int` `temp_i = i, temp_n = n;` `            ``while` `(temp_i > ``0``) {` `                ``sum_i += temp_i % ``10``;` `                ``temp_i /= ``10``;` `            ``}` `            ``while` `(temp_n > ``0``) {` `                ``sum_n += temp_n % ``10``;` `                ``temp_n /= ``10``;` `            ``}` `            ``if` `(sum_i > sum_n) {` `                ``return` `i;` `            ``}` `        ``}` `        ``return` `-``1``;` `    ``}`   `    ``// Driver code` `    ``public` `static` `void` `main(String[] args)` `    ``{` `        ``int` `n = ``824``;` `        ``System.out.println(findNumber(n));` `    ``}` `}`

## Python3

 `# Function to return the greatest` `# number less than n such that` `# the sum of its digits is greater` `# than the sum of the digits of n`     `def` `findNumber(n):` `    ``for` `i ``in` `range``(n``-``1``, ``0``, ``-``1``):` `        ``sum_i ``=` `0` `        ``sum_n ``=` `0` `        ``temp_i ``=` `i` `        ``temp_n ``=` `n` `        ``while` `temp_i > ``0``:` `            ``sum_i ``+``=` `temp_i ``%` `10` `            ``temp_i ``/``/``=` `10` `        ``while` `temp_n > ``0``:` `            ``sum_n ``+``=` `temp_n ``%` `10` `            ``temp_n ``/``/``=` `10` `        ``if` `sum_i > sum_n:` `            ``return` `i` `    ``return` `-``1`     `# Driver code` `n ``=` `824` `print``(findNumber(n))`

## C#

 `using` `System;`   `public` `class` `Program ` `{`   `  ``// Function to return the greatest` `  ``// number less than n such that` `  ``// the sum of its digits is greater` `  ``// than the sum of the digits of n` `  ``public` `static` `int` `FindNumber(``int` `n)` `  ``{` `    ``for` `(``int` `i = n - 1; i > 0; i--) {` `      ``int` `sum_i = 0, sum_n = 0;` `      ``int` `temp_i = i, temp_n = n;` `      ``while` `(temp_i > 0) {` `        ``sum_i += temp_i % 10;` `        ``temp_i /= 10;` `      ``}` `      ``while` `(temp_n > 0) {` `        ``sum_n += temp_n % 10;` `        ``temp_n /= 10;` `      ``}` `      ``if` `(sum_i > sum_n) {` `        ``return` `i;` `      ``}` `    ``}` `    ``return` `-1;` `  ``}`   `  ``// Driver code` `  ``public` `static` `void` `Main()` `  ``{` `    ``int` `n = 824;` `    ``Console.WriteLine(FindNumber(n));` `  ``}` `}`

## Javascript

 `function` `FindNumber(n) {` `  ``for` `(let i = n - 1; i > 0; i--) {` `    ``let sum_i = 0, sum_n = 0;` `    ``let temp_i = i, temp_n = n;` `    ``while` `(temp_i > 0) {` `      ``sum_i += temp_i % 10;` `      ``temp_i = Math.floor(temp_i / 10);` `    ``}` `    ``while` `(temp_n > 0) {` `      ``sum_n += temp_n % 10;` `      ``temp_n = Math.floor(temp_n / 10);` `    ``}` `    ``if` `(sum_i > sum_n) {` `      ``return` `i;` `    ``}` `  ``}` `  ``return` `-1;` `}`   `function` `Main() {` `  ``let n = 824;` `  ``console.log(FindNumber(n));` `}`   `Main();`

Output

`819`

Time Complexity: O(N^2)
Auxiliary Space: O(1)

Approach: Start a loop from N-1 to 1 and check whether the sum of the digits of any number is greater than the sum of the digits of N. The first number that satisfies the condition is the required number.
Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach` `#include ` `using` `namespace` `std;`   `// Function to return the sum of the digits of n` `int` `sumOfDigits(``int` `n)` `{` `    ``int` `res = 0;`   `    ``// Loop for each digit of the number` `    ``while` `(n > 0) {` `        ``res += n % 10;` `        ``n /= 10;` `    ``}`   `    ``return` `res;` `}`   `// Function to return the greatest` `// number less than n such that` `// the sum of its digits is greater` `// than the sum of the digits of n` `int` `findNumber(``int` `n)` `{`   `    ``// Starting from n-1` `    ``int` `i = n - 1;`   `    ``// Check until 1` `    ``while` `(i > 0) {`   `        ``// If i satisfies the given condition` `        ``if` `(sumOfDigits(i) > sumOfDigits(n))` `            ``return` `i;` `        ``i--;` `    ``}`   `    ``// If the condition is not satisfied` `    ``return` `-1;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `n = 824;` `    ``cout << findNumber(n);`   `    ``return` `0;` `}`

## Java

 `//Java implementation of the approach`   `import` `java.io.*;`   `class` `GFG {` `    ``// Function to return the sum of the digits of n` `static` `int` `sumOfDigits(``int` `n)` `{` `    ``int` `res = ``0``;`   `    ``// Loop for each digit of the number` `    ``while` `(n > ``0``) {` `        ``res += n % ``10``;` `        ``n /= ``10``;` `    ``}`   `    ``return` `res;` `}`   `// Function to return the greatest` `// number less than n such that` `// the sum of its digits is greater` `// than the sum of the digits of n` `static` `int` `findNumber(``int` `n)` `{`   `    ``// Starting from n-1` `    ``int` `i = n - ``1``;`   `    ``// Check until 1` `    ``while` `(i > ``0``) {`   `        ``// If i satisfies the given condition` `        ``if` `(sumOfDigits(i) > sumOfDigits(n))` `            ``return` `i;` `        ``i--;` `    ``}`   `    ``// If the condition is not satisfied` `    ``return` `-``1``;` `}`   `// Driver code` `    ``public` `static` `void` `main (String[] args) {`   `    ``int` `n = ``824``;` `    ``System.out.println (findNumber(n));` `    ``}` `//This code is contributed by akt_mit    ` `}`

## Python3

 `# Python3 implementation of the approach`   `# Function to return the sum ` `# of the digits of n` `def` `sumOfDigits(n) :`   `    ``res ``=` `0``;`   `    ``# Loop for each digit of the number` `    ``while` `(n > ``0``) :` `        ``res ``+``=` `n ``%` `10` `        ``n ``/``=` `10`   `    ``return` `res;`   `# Function to return the greatest` `# number less than n such that` `# the sum of its digits is greater` `# than the sum of the digits of n` `def` `findNumber(n) :`   `    ``# Starting from n-1` `    ``i ``=` `n ``-` `1``;`   `    ``# Check until 1` `    ``while` `(i > ``0``) :`   `        ``# If i satisfies the given condition` `        ``if` `(sumOfDigits(i) > sumOfDigits(n)) :` `            ``return` `i` `            `  `        ``i ``-``=` `1`   `    ``# If the condition is not satisfied` `    ``return` `-``1``;`   `# Driver code` `if` `__name__ ``=``=` `"__main__"` `:` `    `  `    ``n ``=` `824``;` `    ``print``(findNumber(n))`   `# This code is contributed by Ryuga`

## C#

 `// C# implementation of the approach` `using` `System;`   `class` `GFG` `{` `// Function to return the sum ` `// of the digits of n` `static` `int` `sumOfDigits(``int` `n)` `{` `    ``int` `res = 0;`   `    ``// Loop for each digit of ` `    ``// the number` `    ``while` `(n > 0) ` `    ``{` `        ``res += n % 10;` `        ``n /= 10;` `    ``}`   `    ``return` `res;` `}`   `// Function to return the greatest` `// number less than n such that` `// the sum of its digits is greater` `// than the sum of the digits of n` `static` `int` `findNumber(``int` `n)` `{`   `    ``// Starting from n-1` `    ``int` `i = n - 1;`   `    ``// Check until 1` `    ``while` `(i > 0)` `    ``{`   `        ``// If i satisfies the given condition` `        ``if` `(sumOfDigits(i) > sumOfDigits(n))` `            ``return` `i;` `        ``i--;` `    ``}`   `    ``// If the condition is` `    ``// not satisfied` `    ``return` `-1;` `}`   `// Driver code` `static` `public` `void` `Main ()` `{` `    ``int` `n = 824;` `    ``Console.WriteLine (findNumber(n));` `}` `}`   `// This code is contributed by @Tushil`

## PHP

 ` 0) ` `    ``{` `        ``\$res` `+= ``\$n` `% 10;` `        ``\$n` `/= 10;` `    ``}`   `    ``return` `\$res``;` `}`   `// Function to return the greatest` `// number less than n such that` `// the sum of its digits is greater` `// than the sum of the digits of n` `function` `findNumber(``\$n``)` `{`   `    ``// Starting from n-1` `    ``\$i` `= ``\$n` `- 1;`   `    ``// Check until 1` `    ``while` `(``\$i` `> 0) ` `    ``{`   `        ``// If i satisfies the given condition` `        ``if` `(sumOfDigits(``\$i``) > sumOfDigits(``\$n``))` `            ``return` `\$i``;` `        ``\$i``--;` `    ``}`   `    ``// If the condition is not satisfied` `    ``return` `-1;` `}`   `// Driver code` `\$n` `= 824;`   `echo` `findNumber(``\$n``);` `    `  `// This code is contributed by Mukul singh` `?>`

## Javascript

 ``

Output

`819`

Time Complexity: O(N * log10N)
Auxiliary Space: O(1)