Leetcode #2310: Sum of Numbers With Units Digit K
In this guide, we solve Leetcode #2310 Sum of Numbers With Units Digit K in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
Given two integers num and k, consider a set of positive integers with the following properties: The units digit of each integer is k. The sum of the integers is num.
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Math, Dynamic Programming, Enumeration
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: num = 58, k = 9
Output: 2
Explanation:
One valid set is [9,49], as the sum is 58 and each integer has a units digit of 9.
Another valid set is [19,39].
It can be shown that 2 is the minimum possible size of a valid set.
Python Solution
class Solution:
def minimumNumbers(self, num: int, k: int) -> int:
if num == 0:
return 0
for i in range(1, num + 1):
if (t := num - k * i) >= 0 and t % 10 == 0:
return i
return -1
Complexity
The time complexity is , where is the size of . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.