Partition Labels
A medium Greedy problem included in Love Babbar 450, Striver A2Z. Below: the roles whose interviews prioritise this topic, and how to practise it.
- Topic
- Greedy
- Sheets
- 2
- Core for
- 3 roles
- Platform
- LeetCode
The problem
Given a string, partition it into as many parts as possible so that each letter appears in at most one part. Return a list of the sizes of these parts.
Example 1
- Input
- s = "ababcbacadefegdehijhklij"
- Output
- [9,7,8]
- Why
- Partition is "ababcbaca", "defegde", "hijhklij". Each letter appears in only one part.
Example 2
- Input
- s = "eccbbbbdec"
- Output
- [10]
- Why
- All characters appear in a single partition.
Constraints
- 1 <= s.length <= 500
- s consists of lowercase English letters
How to think about it
Updated 2026-09-09The first time a character appears, its final appearance sets the minimum ending boundary for the current segment. As you scan forward, any newly encountered character can only push this boundary further right, never shrink it.
Approaches, worst first
Interval merge
time O(n log k) · space O(k)
Record the first and last occurrence for every distinct character to form intervals, then merge overlapping intervals. Correct, but constructing and sorting intervals involves unnecessary overhead.
Greedy boundary expansionWrite this one
time O(n) · space O(1)
Precompute the last occurrence index of each character in a 26-element array. Iterate through the string, stretching the partition boundary to max(boundary, last[c]). When current index reaches boundary, seal the chunk and begin a new one.
Where people lose marks · 2
- Off-by-one in partition size: the length of a segment from start to end inclusive is `end - start + 1`, not `end - start`.
- Forgetting to update the start pointer to `i + 1` after closing a partition causes subsequent lengths to accumulate previous slices.
The theory behind it
Greedy — the ground this problem stands on. All Greedy problems
What Greedy is
A greedy algorithm makes the best-looking choice available right now, at every step, without ever looking back or second-guessing its decision. Think of a cashier making change by handing over the largest possible coin first, repeatedly, until the total is reached. Unlike dynamic programming, which saves and compares answers to multiple overlapping paths, a greedy strategy commits to one immediate option and keeps moving forward.
When to reach for it
Reach for greedy when problems ask for minimum jumps, interval scheduling, assigning resources to maximize satisfaction, or finding fractional values. Key signals include sorted orders where greedily taking the next item never hurts future options, or gas station round trips where running balances prove reachability. If you can prove that taking the immediate best choice never leaves you worse off than any alternative, greedy gives the fastest answer.
How the pattern works
Start by sorting the input to bring the most promising candidates to the front. At each position, evaluate your local rule, take the best available piece, and update your running state. The crucial mental step is proving the greedy choice property: demonstrate that picking this immediate winner cannot block a better global solution down the road. If choosing an item now forces you to reconsider past decisions when conditions change later, greedy fails and you must switch to dynamic programming instead.
What each operation costs
| Operation | Time |
|---|---|
| sort elements to enable greedy selection | O(n log n) |
| greedy single-pass scan through sorted input | O(n) |
| greedy choice using a priority queue | O(n log n) |
What usually goes wrong with Greedy
- Applying a greedy choice without proving it yields the global optimum, such as picking the largest coin first for arbitrary denominations where dynamic programming was required.
- Forgetting to sort the input before running the greedy loop, making local decisions on unordered elements that produce invalid answers.
- Picking items based on only one attribute when the optimal decision depends on a ratio or combination of multiple attributes.
Which roles need this problem
Greedy is a core topic for these 3 roles — if you're targeting one of them, this problem is early in your path, not optional.
Secondary for 4 more roles, including Site Reliability Engineer, Search Engineer, Quant Developer.
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