Leetcode #2547: Minimum Cost to Split an Array
In this guide, we solve Leetcode #2547 Minimum Cost to Split an Array 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
You are given an integer array nums and an integer k. Split the array into some number of non-empty subarrays.
Quick Facts
- Difficulty: Hard
- Premium: No
- Tags: Array, Hash Table, Dynamic Programming, Counting
Intuition
Fast membership checks and value lookups are the heart of this problem, which makes a hash map the natural choice.
By storing what we have already seen (or counts/indexes), we can answer the question in one pass without backtracking.
Approach
Scan the input once, using the map to detect when the condition is satisfied and to update state as you go.
This keeps the solution linear while remaining easy to explain in an interview setting.
Steps:
- Initialize a hash map for seen items or counts.
- Iterate through the input, querying/updating the map.
- Return the first valid result or the final computed value.
Example
Input: nums = [1,2,1,2,1,3,3], k = 2
Output: 8
Explanation: We split nums to have two subarrays: [1,2], [1,2,1,3,3].
The importance value of [1,2] is 2 + (0) = 2.
The importance value of [1,2,1,3,3] is 2 + (2 + 2) = 6.
The cost of the split is 2 + 6 = 8. It can be shown that this is the minimum possible cost among all the possible splits.
Python Solution
class Solution:
def minCost(self, nums: List[int], k: int) -> int:
def dfs(i):
if i >= n:
return 0
cnt = Counter()
one = 0
ans = inf
for j in range(i, n):
cnt[nums[j]] += 1
if cnt[nums[j]] == 1:
one += 1
elif cnt[nums[j]] == 2:
one -= 1
ans = min(ans, k + j - i + 1 - one + dfs(j + 1))
return ans
n = len(nums)
return dfs(0)
Complexity
The time complexity is , and the space complexity is . 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.