Which algorithmic approach guarantees an optimal solution efficiently?
easy🔍 Pattern Recognition Q11 of Q15
Greedy Algorithms - Monotone Increasing Digits
You are given a positive integer n. The task is to find the largest integer less than or equal to n such that its digits are in non-decreasing order from left to right. Which algorithmic approach guarantees an optimal solution efficiently?
ADivide and conquer splitting the number into halves and solving recursively
BDynamic Programming that tries all digit combinations to build the largest monotone number
CBrute force decrementing from <code>n</code> downwards checking monotonicity for each number
DGreedy algorithm scanning digits from right to left, adjusting digits and setting trailing digits to 9
Step-by-Step Solution
Solution:
Step 1: Understand the problem constraints
The problem requires the largest number ≤ n with digits in non-decreasing order, which suggests a digit-wise adjustment rather than enumerating all numbers.
Step 2: Identify the approach that efficiently fixes digits from right to left
The greedy right-to-left scan decreases digits when a violation is found and sets subsequent digits to 9, ensuring the largest monotone number ≤ n.
Final Answer:
Option D -> Option D
Quick Check:
Greedy right-to-left fix is optimal and efficient [OK]
Quick Trick:Greedy right-to-left digit fix ensures optimal monotone number [OK]
Common Mistakes:
MISTAKES
Thinking brute force is efficient enough
Assuming DP is needed for digit monotonicity
Believing divide and conquer applies here
Trap Explanation:
PITFALL
Brute force and DP seem plausible but are inefficient or overcomplicated; greedy digit adjustment is the key insight.
Interviewer Note:
CONTEXT
Tests if candidate can recognize the greedy pattern for digit monotonicity problems.
Master "Monotone Increasing Digits" in Greedy Algorithms
3 interactive learning modes - each teaches the same concept differently
