Monotone Increasing Digits

Monotone Increasing Digits - Problem

Math Greedy Medium

An integer has monotone increasing digits if and only if each pair of adjacent digits x and y satisfy x ≤ y.

Given an integer n, return the largest number that is less than or equal to n with monotone increasing digits.

Example: For n = 10, the answer is 9 because 10 has digits 1, 0 where 1 > 0, so it's not monotone increasing. The largest monotone increasing number ≤ 10 is 9.

Input & Output

Example 1 — Basic Violation

$ Input: n = 10

› Output: 9

💡 Note: 10 has digits [1,0] where 1 > 0, violating monotone property. The largest monotone number ≤ 10 is 9.

Example 2 — Already Monotone

$ Input: n = 1234

› Output: 1234

💡 Note: 1234 has digits [1,2,3,4] where 1 ≤ 2 ≤ 3 ≤ 4, so it's already monotone increasing.

Example 3 — Multiple Violations

$ Input: n = 54321

› Output: 49999

💡 Note: 54321 violates at position 0 (5>4). Reduce 5→4 and set rest to 9s: 49999.

Constraints

0 ≤ n ≤ 10⁹

Visualization

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Asked in

G Google 25 a Amazon 18 M Microsoft 15

The greedy approach is optimal: scan digits right to left, fix violations by reducing the violating digit and setting following digits to 9. This ensures the largest possible monotone number. Time: O(d), Space: O(d) where d is number of digits.

Common Approaches

✓ Brute Force - Check Every Number

⏱️ Time: O(n × d) Space: O(d)

Start from n and decrement by 1 each time. For each number, convert to string and check if digits are non-decreasing. Return the first valid number found.

Greedy - Right to Left Fix

⏱️ Time: O(d) Space: O(d)

Convert number to string. Scan from right to left looking for violations (digit > next digit). When found, reduce the violating digit by 1 and set all digits to its right to 9. This ensures we get the largest possible monotone number.

Brute Force - Check Every Number — Algorithm Steps

Start from n and go down
For each number, check if digits are monotone increasing
Return first valid number

Visualization

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Step-by-Step Walkthrough

Start from n

Begin checking from the given number

Check monotone

Verify if digits are non-decreasing

Return first valid

First number with monotone digits is the answer

Code -

solution.c — C

#include <stdio.h>
#include <string.h>
#include <stdlib.h>

int isMonotone(int num) {
    char s[20];
    sprintf(s, "%d", num);
    int len = strlen(s);
    for (int i = 1; i < len; i++) {
        if (s[i-1] > s[i]) {
            return 0;
        }
    }
    return 1;
}

int solution(int n) {
    for (int i = n; i > 0; i--) {
        if (isMonotone(i)) {
            return i;
        }
    }
    return 0;
}

int main() {
    int n;
    scanf("%d", &n);
    printf("%d\n", solution(n));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n × d)

In worst case, check n numbers, each taking O(d) time to verify digits

✓ Linear Growth

Space Complexity

O(d)

String conversion requires O(d) space where d is number of digits

✓ Linear Space

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Related Problems

Common Approaches

Brute Force - Check Every Number — Algorithm Steps

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Code -

Time & Space Complexity

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