# Monotone Increasing Digits

**Objective:** Given a number N, find the largest number which is less than equal to N and has monotone increasing digits.

**Monotone Increasing Digits** – If all the pairs (x, y) of adjacent digits satisfy the property, x<=y. In other words if all digits are in ascending order (can have duplicates) then digits are called monotone increasing digits.

**Example:**

N = 324 Output: 299 N = 4321 Output: 3999 N = 12345 Output: 12345

**Approach:**

- Iterate the number from right to left (in reverse order).
- Find the last pair of adjacent digits (x, y) where x > y and store the index of x.
- In original number, put x-1 at the stored index and put 9 all the indexes at the right of the array.
- See the example below for more understanding.

N = 7384 pair 8, 4 8 > 4, stored index= 2 pair 3, 8 3 < 8, no change, stored index = 2 pair 7, 3 7 > 3, stored index = 0 Output = 7 – 1 at the index 0 and put 9 at all the places at right => 6999 ___________________________________________________________ N = 391 pair 9, 1 9 > 1, stored index = 1 pair 3, 9 3 < 9, no change in stored index Output: 9 – 1 at the index 1 and put 9 at all the places at right => 389

**Complete Code:**

**Output:**

N = 7384 monotone increasing: 6999 N = 1234 monotone increasing: 1234 N = 1111 monotone increasing: 1111 N = 4321 monotone increasing: 3999

Reference: here