Overflow in intermediate arithmetic
Wrong move: Temporary multiplications exceed integer bounds.
Usually fails on: Large inputs wrap around unexpectedly.
Fix: Use wider types, modular arithmetic, or rearranged operations.
Move from brute-force thinking to an efficient approach using math strategy.
Given two integers num and k, consider a set of positive integers with the following properties:
k.num.Return the minimum possible size of such a set, or -1 if no such set exists.
Note:
0.Example 1:
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.
Example 2:
Input: num = 37, k = 2 Output: -1 Explanation: It is not possible to obtain a sum of 37 using only integers that have a units digit of 2.
Example 3:
Input: num = 0, k = 7 Output: 0 Explanation: The sum of an empty set is considered 0.
Constraints:
0 <= num <= 30000 <= k <= 9Problem summary: 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. Return the minimum possible size of such a set, or -1 if no such set exists. Note: The set can contain multiple instances of the same integer, and the sum of an empty set is considered 0. The units digit of a number is the rightmost digit of the number.
Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.
Pattern signal: Math · Dynamic Programming · Greedy
58 9
37 2
0 7
digit-count-in-range)count-integers-with-even-digit-sum)sum-of-number-and-its-reverse)Source-backed implementations are provided below for direct study and interview prep.
// Accepted solution for LeetCode #2310: Sum of Numbers With Units Digit K
class Solution {
public int minimumNumbers(int num, int k) {
if (num == 0) {
return 0;
}
for (int i = 1; i <= num; ++i) {
int t = num - k * i;
if (t >= 0 && t % 10 == 0) {
return i;
}
}
return -1;
}
}
// Accepted solution for LeetCode #2310: Sum of Numbers With Units Digit K
func minimumNumbers(num int, k int) int {
if num == 0 {
return 0
}
for i := 1; i <= num; i++ {
t := num - k*i
if t >= 0 && t%10 == 0 {
return i
}
}
return -1
}
# Accepted solution for LeetCode #2310: Sum of Numbers With Units Digit K
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
// Accepted solution for LeetCode #2310: Sum of Numbers With Units Digit K
/**
* [2310] Sum of Numbers With Units Digit K
*
* 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.
*
* Return the minimum possible size of such a set, or -1 if no such set exists.
* Note:
*
* The set can contain multiple instances of the same integer, and the sum of an empty set is considered 0.
* The units digit of a number is the rightmost digit of the number.
*
*
* Example 1:
*
* 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.
*
* Example 2:
*
* Input: num = 37, k = 2
* Output: -1
* Explanation: It is not possible to obtain a sum of 37 using only integers that have a units digit of 2.
*
* Example 3:
*
* Input: num = 0, k = 7
* Output: 0
* Explanation: The sum of an empty set is considered 0.
*
*
* Constraints:
*
* 0 <= num <= 3000
* 0 <= k <= 9
*
*/
pub struct Solution {}
// problem: https://leetcode.com/problems/sum-of-numbers-with-units-digit-k/
// discuss: https://leetcode.com/problems/sum-of-numbers-with-units-digit-k/discuss/?currentPage=1&orderBy=most_votes&query=
// submission codes start here
impl Solution {
pub fn minimum_numbers(num: i32, k: i32) -> i32 {
0
}
}
// submission codes end
#[cfg(test)]
mod tests {
use super::*;
#[test]
#[ignore]
fn test_2310_example_1() {
let num = 58;
let k = 9;
let result = 2;
assert_eq!(Solution::minimum_numbers(num, k), result);
}
#[test]
#[ignore]
fn test_2310_example_2() {
let num = 37;
let k = 2;
let result = -1;
assert_eq!(Solution::minimum_numbers(num, k), result);
}
#[test]
#[ignore]
fn test_2310_example_3() {
let num = 0;
let k = 7;
let result = 0;
assert_eq!(Solution::minimum_numbers(num, k), result);
}
}
// Accepted solution for LeetCode #2310: Sum of Numbers With Units Digit K
function minimumNumbers(num: number, k: number): number {
if (!num) return 0;
let digit = num % 10;
for (let i = 1; i < 11; i++) {
let target = i * k;
if (target <= num && target % 10 == digit) return i;
}
return -1;
}
Use this to step through a reusable interview workflow for this problem.
Pure recursion explores every possible choice at each step. With two choices per state (take or skip), the decision tree has 2ⁿ leaves. The recursion stack uses O(n) space. Many subproblems are recomputed exponentially many times.
Each cell in the DP table is computed exactly once from previously solved subproblems. The table dimensions determine both time and space. Look for the state variables — each unique combination of state values is one cell. Often a rolling array can reduce space by one dimension.
Review these before coding to avoid predictable interview regressions.
Wrong move: Temporary multiplications exceed integer bounds.
Usually fails on: Large inputs wrap around unexpectedly.
Fix: Use wider types, modular arithmetic, or rearranged operations.
Wrong move: An incomplete state merges distinct subproblems and caches incorrect answers.
Usually fails on: Correctness breaks on cases that differ only in hidden state.
Fix: Define state so each unique subproblem maps to one DP cell.
Wrong move: Locally optimal choices may fail globally.
Usually fails on: Counterexamples appear on crafted input orderings.
Fix: Verify with exchange argument or monotonic objective before committing.