LeetCode #763 — MEDIUM

Partition Labels

Move from brute-force thinking to an efficient approach using hash map strategy.

The Problem

Problem Statement

You are given a string s. We want to partition the string into as many parts as possible so that each letter appears in at most one part. For example, the string "ababcc" can be partitioned into ["abab", "cc"], but partitions such as ["aba", "bcc"] or ["ab", "ab", "cc"] are invalid.

Note that the partition is done so that after concatenating all the parts in order, the resultant string should be s.

Return a list of integers representing the size of these parts.

Example 1:

Input: s = "ababcbacadefegdehijhklij"
Output: [9,7,8]
Explanation:
The partition is "ababcbaca", "defegde", "hijhklij".
This is a partition so that each letter appears in at most one part.
A partition like "ababcbacadefegde", "hijhklij" is incorrect, because it splits s into less parts.

Example 2:

Input: s = "eccbbbbdec"
Output: [10]

Constraints:

1 <= s.length <= 500
s consists of lowercase English letters.

Step 01

Brute Force Baseline

Problem summary: You are given a string s. We want to partition the string into as many parts as possible so that each letter appears in at most one part. For example, the string "ababcc" can be partitioned into ["abab", "cc"], but partitions such as ["aba", "bcc"] or ["ab", "ab", "cc"] are invalid. Note that the partition is done so that after concatenating all the parts in order, the resultant string should be s. Return a list of integers representing the size of these parts.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Hash Map · Two Pointers · Greedy

Example 1

"ababcbacadefegdehijhklij"

Example 2

"eccbbbbdec"

Core Insight

What unlocks the optimal approach

Try to greedily choose the smallest partition that includes the first letter. If you have something like "abaccbdeffed", then you might need to add b. You can use an map like "last['b'] = 5" to help you expand the width of your partition.

Interview move: turn each hint into an invariant you can check after every iteration/recursion step.

Step 03

Algorithm Walkthrough

Iteration Checklist

Define state (indices, window, stack, map, DP cell, or recursion frame).
Apply one transition step and update the invariant.
Record answer candidate when condition is met.
Continue until all input is consumed.

Use the first example testcase as your mental trace to verify each transition.

Step 04

Edge Cases

Minimum Input

Single element / shortest valid input

Validate boundary behavior before entering the main loop or recursion.

Duplicates & Repeats

Repeated values / repeated states

Decide whether duplicates should be merged, skipped, or counted explicitly.

Extreme Constraints

Upper-end input sizes

Re-check complexity target against constraints to avoid time-limit issues.

Invalid / Corner Shape

Empty collections, zeros, or disconnected structures

Handle special-case structure before the core algorithm path.

Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #763: Partition Labels
class Solution {
    public List<Integer> partitionLabels(String s) {
        int[] last = new int[26];
        int n = s.length();
        for (int i = 0; i < n; ++i) {
            last[s.charAt(i) - 'a'] = i;
        }
        List<Integer> ans = new ArrayList<>();
        int mx = 0, j = 0;
        for (int i = 0; i < n; ++i) {
            mx = Math.max(mx, last[s.charAt(i) - 'a']);
            if (mx == i) {
                ans.add(i - j + 1);
                j = i + 1;
            }
        }
        return ans;
    }
}

// Accepted solution for LeetCode #763: Partition Labels
func partitionLabels(s string) (ans []int) {
	last := [26]int{}
	for i, c := range s {
		last[c-'a'] = i
	}
	var mx, j int
	for i, c := range s {
		mx = max(mx, last[c-'a'])
		if mx == i {
			ans = append(ans, i-j+1)
			j = i + 1
		}
	}
	return
}

# Accepted solution for LeetCode #763: Partition Labels
class Solution:
    def partitionLabels(self, s: str) -> List[int]:
        last = {c: i for i, c in enumerate(s)}
        mx = j = 0
        ans = []
        for i, c in enumerate(s):
            mx = max(mx, last[c])
            if mx == i:
                ans.append(i - j + 1)
                j = i + 1
        return ans

// Accepted solution for LeetCode #763: Partition Labels
impl Solution {
    pub fn partition_labels(s: String) -> Vec<i32> {
        let n = s.len();
        let bytes = s.as_bytes();
        let mut last = [0; 26];
        for i in 0..n {
            last[(bytes[i] - b'a') as usize] = i;
        }
        let mut ans = vec![];
        let mut j = 0;
        let mut mx = 0;
        for i in 0..n {
            mx = mx.max(last[(bytes[i] - b'a') as usize]);
            if mx == i {
                ans.push((i - j + 1) as i32);
                j = i + 1;
            }
        }
        ans
    }
}

// Accepted solution for LeetCode #763: Partition Labels
function partitionLabels(s: string): number[] {
    const last: number[] = Array(26).fill(0);
    const idx = (c: string) => c.charCodeAt(0) - 'a'.charCodeAt(0);
    const n = s.length;
    for (let i = 0; i < n; ++i) {
        last[idx(s[i])] = i;
    }
    const ans: number[] = [];
    for (let i = 0, j = 0, mx = 0; i < n; ++i) {
        mx = Math.max(mx, last[idx(s[i])]);
        if (mx === i) {
            ans.push(i - j + 1);
            j = i + 1;
        }
    }
    return ans;
}

Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Custom checkpoints (one per line)

Press Step or Run All to begin.

Step 07

Complexity Analysis

Time

O(n)

Space

O(|\Sigma|)

Approach Breakdown

BRUTE FORCE

O(n²) time

O(1) space

Two nested loops check every pair of elements. The outer loop picks one element, the inner loop scans the rest. For n elements that is n × (n−1)/2 comparisons = O(n²). No extra memory — just two loop variables.

TWO POINTERS

O(n) time

O(1) space

Each pointer traverses the array at most once. With two pointers moving inward (or both moving right), the total number of steps is bounded by n. Each comparison is O(1), giving O(n) overall. No auxiliary data structures are needed — just two index variables.

Shortcut: Two converging pointers on sorted data → O(n) time, O(1) space.

Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Mutating counts without cleanup

Wrong move: Zero-count keys stay in map and break distinct/count constraints.

Usually fails on: Window/map size checks are consistently off by one.

Fix: Delete keys when count reaches zero.

Moving both pointers on every comparison

Wrong move: Advancing both pointers shrinks the search space too aggressively and skips candidates.

Usually fails on: A valid pair can be skipped when only one side should move.

Fix: Move exactly one pointer per decision branch based on invariant.

Using greedy without proof

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.