#1689

Medium

auto_awesomeGreedy choice plus invariant validation

LeetCode Problem Workspace

Partitioning Into Minimum Number Of Deci-Binary Numbers

This problem asks to find the minimum number of deci-binary numbers needed to sum to a given number represented as a string.

string greedy

Problem Statement

A decimal number is called deci-binary if each of its digits is either 0 or 1 without any leading zeros. For example, 101 and 1100 are deci-binary, while 112 and 3001 are not.

Given a string n representing a positive decimal integer, return the minimum number of positive deci-binary numbers required to sum up to n.

Examples

Example 1

Input: n = "32"

Output: 3

10 + 11 + 11 = 32

Example 2

Input: n = "82734"

Output: 8

Example details omitted.

Example 3

Input: n = "27346209830709182346"

Output: 9

Example details omitted.

Constraints

1 <= n.length <= 105
n consists of only digits.
n does not contain any leading zeros and represents a positive integer.

Solution Approach

Greedy Approach

Start with the largest possible deci-binary number for each digit of n, reducing the remaining value iteratively until n is completely decomposed.

Invariant Validation

Each time a deci-binary number is chosen, ensure the sum of all previously selected deci-binary numbers remains valid and contributes correctly towards the total.

Optimized Iteration

Iterate through the digits, constructing deci-binary numbers one by one. Track the maximum number of deci-binary numbers necessary by determining the highest digit in each pass.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity depends on iterating through each digit of n. Space complexity involves tracking values through each iteration but remains manageable within the input constraints.

What Interviewers Usually Probe

Ability to apply greedy algorithms effectively.
Understanding how to reduce a problem to simpler subproblems.
Proficiency in validating constraints and invariants in problem-solving.

Common Pitfalls or Variants

Common pitfalls

Forgetting to handle multiple digits efficiently while maintaining a greedy approach.
Not ensuring that deci-binary numbers are constructed correctly according to the problem's rules.
Misunderstanding the greedy choice strategy and missing edge cases.

Follow-up variants

Handling very large input sizes efficiently.
Modifying the problem to use other number systems.
Optimizing space complexity while maintaining time efficiency.

FAQ

What is a deci-binary number?

A deci-binary number is a decimal number where each digit is either 0 or 1, and there are no leading zeros.

How do I apply a greedy strategy to this problem?

A greedy strategy involves selecting the largest possible deci-binary number at each step and reducing the number until the sum equals the given number.

How does the problem pattern relate to greedy algorithms?

The greedy choice is evident in picking the largest valid deci-binary number at each iteration, minimizing the total count of numbers needed to sum to the target.

What if the input number is very large?

The problem can still be solved efficiently by iterating over the digits, and the algorithm should handle input sizes up to 10^5 digits.

What is the time complexity of this problem?

The time complexity is O(n), where n is the length of the input string, as we process each digit once.

terminal

Solution

Solution 1: Quick Thinking

The problem is equivalent to finding the maximum number in the string.

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class Solution:
    def minPartitions(self, n: str) -> int:
        return int(max(n))

Continue Practicing

#1702 maximum binary string after change #1663 smallest string with a given numeric value #1717 maximum score from removing substrings