Count Prefix and Suffix Pairs I
Time O(n * l) · Space O(t) · Official statement on LeetCode
Solutions
// Time: O(n * l)
// Space: O(t)
// trie
class Solution {
private:
class Trie {
public:
Trie()
: nodes_() {
new_node();
}
int add(const string& w) {
int result = 0, curr = 0;
for (int i = 0; i < size(w); ++i) {
const int k = (w[i] - 'a') * 26 + (w[size(w) - 1 - i] - 'a');
if (!nodes_[curr].count(k)) {
nodes_[curr][k] = new_node();
}
curr = nodes_[curr][k];
result += cnts_[curr];
}
++cnts_[curr];
return result;
}
private:
int new_node() {
nodes_.emplace_back();
cnts_.emplace_back(0);
return size(nodes_) - 1;
}
vector<unordered_map<int, int>> nodes_;
vector<int> cnts_;
};
public:
long long countPrefixSuffixPairs(vector<string>& words) {
int64_t result = 0;
Trie trie;
for (const auto& w : words) {
result += trie.add(w);
}
return result;
}
};
// Time: O(n^2 * l)
// Space: O(1)
// brute force
class Solution2 {
public:
long long countPrefixSuffixPairs(vector<string>& words) {
const auto& check = [&](int i, int j) {
return words[j].starts_with(words[i]) && words[j].ends_with(words[i]);
};
int64_t result = 0;
for (int i = 0; i < size(words); ++i) {
for (int j = i + 1; j < size(words); ++j) {
if (check(i, j)) {
++result;
}
}
}
return result;
}
};
Beginner Explanation
What is Count Prefix and Suffix Pairs I?
Count Prefix and Suffix Pairs I (LeetCode #3042) is a Easy problem that primarily trains string.
How to think about it
- Restate the goal in your own words before coding.
- Work a tiny example by hand so the invariant becomes obvious.
- Identify the pattern — this problem aligns with trie.
- Only then translate the idea into code.
Why this problem matters
It builds core muscle memory you will reuse on harder variants. Official solution notes mention: Trie, Brute Force.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Count Prefix and Suffix Pairs I
Opening (30–60 seconds)
- Clarify inputs/outputs and edge cases (empty input, single element, duplicates, overflow).
- State a brute force so the interviewer knows you can solve it naively.
- Propose the optimal direction tied to trie.
Core solution narrative
- Define the state you track (pointers, DP cell, set membership, stack top, etc.).
- Explain the transition when you process the next element.
- Call out time (O(n * l)) and space (O(t)) before coding.
- Code cleanly; narrate variable names.
What interviewers listen for
- Correctness on edge cases
- Complexity honesty
- Ability to discuss trade-offs (e.g., hash map space vs. sort + two pointers)
Follow-up questions they may ask
- Can you solve it with less memory?
- What if the input stream is infinite / doesn't fit in RAM?
- How would tests look for adversarial inputs?
Optimized Approach
Optimized solution notes
The reference solutions on AlgoForge target O(n * l) time and O(t) space.
Pattern focus: trie
Use the pattern as a checklist:
- trie — confirm the invariant holds after each step
Multiple methods appear in the source solutions — compare them and explain when each is preferable.
Implementation tips
- Prefer readable names over micro-optimizations in interviews.
- Extract helpers only when they clarify (e.g., expand-around-center, DFS visit).
- After AC-level logic, re-scan for off-by-one and null checks.
Complexity Analysis
Complexity
| Measure | Bound |
|---|---|
| Time | O(n * l) |
| Space | O(t) |
How to justify this in an interview
- Time: count loops, map/set operations, and recursive branching; state average vs worst case if relevant.
- Space: include hash maps, recursion stack, and output allocation when the problem asks for it.
If your implementation differs from the reference, re-derive big-O from your code — never memorize a complexity you cannot defend.
Common Mistakes
Common mistakes on Count Prefix and Suffix Pairs I
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for trie — updating state too early or too late.
- Mutating input unexpectedly when the problem forbids it.
- Off-by-one in windows, ranges, or binary search bounds.
- Ignoring overflow / precision for integer arithmetic problems.
- Overengineering — jumping to an advanced structure when a simpler approach works.
Alternative Approaches
Alternatives
The source file includes more than one method. Compare:
- Primary optimized path — best complexity for typical interviews.
- Secondary approach — often brute force, sorting-based, or space-optimized variant.
Practice articulating when you would pick each (constraints, readability, follow-ups).
Edge Cases
Edge cases checklist
- Minimum input size
- Maximum input size / time limits
- Duplicates and already-sorted input
- Negative numbers / zeros (if applicable)
- Disconnected structures (graphs/trees)
- Single path vs branching recursion depth
Pattern Recognition
Spotting this pattern
Signal phrases that point to trie:
- Sorted input or ability to sort without changing the answer class
- Need for contiguous subarray / substring → consider sliding window
- Need for O(1) membership → hash set/map
- Optimal substructure + overlapping subproblems → DP
- Connectivity / components → graph DFS/BFS or Union-Find
Primary topics: string.
Follow-up Interview Questions
Follow-ups
- How does the solution change if the input is a stream?
- Can you solve it in-place?
- What if duplicates must be handled differently?
- How would you parallelize the approach?
- Design tests that would break a buggy implementation.
Practice Recommendations
What to practice next
- Re-solve Count Prefix and Suffix Pairs I in a second language (cpp, python).
- Drill 3–5 more problems tagged string.
- Teach the solution out loud in under 5 minutes.
- Add this problem to your revision calendar in 3 days and 14 days.
Visualization
Study checklist
- Read the official problem statement on LeetCode
- Solve on paper / whiteboard first
- Implement the trie approach
- Verify edge cases from the checklist
- State time and space complexity aloud
- Compare with the AlgoForge reference solution
- Schedule a revision session
Revision notes
Count Prefix and Suffix Pairs I (#3042) — Easy. Pattern: trie. Complexity: O(n * l) time / O(t) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Count Prefix and Suffix Pairs I?+
The reference solutions aim for O(n * l) time and O(t) space. Always re-derive complexity from the code you write in the interview.
What pattern does Count Prefix and Suffix Pairs I use?+
It primarily maps to trie, within the broader topic of string.
Is Count Prefix and Suffix Pairs I good for interviews?+
Yes — as a Easy problem it is a solid practice target. Pair it with related problems in the same pattern family for spaced repetition.
Where can I read the official statement?+
Open the official LeetCode page for constraints and examples: https://leetcode.com/problems/count-prefix-and-suffix-pairs-i/