#97Hard~60 min
Interleaving String
Time O(m * n) · Space O(m + n) · Official statement on LeetCode
Solutions
# Time: O(m * n)
# Space: O(m + n)
class Solution(object):
# @return a boolean
def isInterleave(self, s1, s2, s3):
if len(s1) + len(s2) != len(s3):
return False
if len(s1) > len(s2):
return self.isInterleave(s2, s1, s3)
match = [False for i in xrange(len(s1) + 1)]
match[0] = True
for i in xrange(1, len(s1) + 1):
match[i] = match[i -1] and s1[i - 1] == s3[i - 1]
for j in xrange(1, len(s2) + 1):
match[0] = match[0] and s2[j - 1] == s3[j - 1]
for i in xrange(1, len(s1) + 1):
match[i] = (match[i - 1] and s1[i - 1] == s3[i + j - 1]) \
or (match[i] and s2[j - 1] == s3[i + j - 1])
return match[-1]
# Time: O(m * n)
# Space: O(m * n)
# Dynamic Programming
class Solution2(object):
# @return a boolean
def isInterleave(self, s1, s2, s3):
if len(s1) + len(s2) != len(s3):
return False
match = [[False for i in xrange(len(s2) + 1)] for j in xrange(len(s1) + 1)]
match[0][0] = True
for i in xrange(1, len(s1) + 1):
match[i][0] = match[i - 1][0] and s1[i - 1] == s3[i - 1]
for j in xrange(1, len(s2) + 1):
match[0][j] = match[0][j - 1] and s2[j - 1] == s3[j - 1]
for i in xrange(1, len(s1) + 1):
for j in xrange(1, len(s2) + 1):
match[i][j] = (match[i - 1][j] and s1[i - 1] == s3[i + j - 1]) \
or (match[i][j - 1] and s2[j - 1] == s3[i + j - 1])
return match[-1][-1]
# Time: O(m * n)
# Space: O(m * n)
# Recursive + Hash
class Solution3(object):
# @return a boolean
def isInterleave(self, s1, s2, s3):
self.match = {}
if len(s1) + len(s2) != len(s3):
return False
return self.isInterleaveRecu(s1, s2, s3, 0, 0, 0)
def isInterleaveRecu(self, s1, s2, s3, a, b, c):
if repr([a, b]) in self.match.keys():
return self.match[repr([a, b])]
if c == len(s3):
return True
result = False
if a < len(s1) and s1[a] == s3[c]:
result = result or self.isInterleaveRecu(s1, s2, s3, a + 1, b, c + 1)
if b < len(s2) and s2[b] == s3[c]:
result = result or self.isInterleaveRecu(s1, s2, s3, a, b + 1, c + 1)
self.match[repr([a, b])] = result
return result
Beginner Explanation
What is Interleaving String?
Interleaving String (LeetCode #97) is a Hard problem that primarily trains dynamic programming.
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 dynamic programming.
- Only then translate the idea into code.
Why this problem matters
Hard problems force you to combine patterns and prove complexity carefully — interview gold.
AlgoForge explanations are original teaching notes. Always open the official problem statement on LeetCode for constraints and examples.
Interview Walkthrough
Interview approach for Interleaving String
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 dynamic programming.
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(m * n)) and space (O(m + n)) 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(m * n) time and O(m + n) space.
Pattern focus: dynamic programming
Use the pattern as a checklist:
- dynamic programming — 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(m * n) |
| Space | O(m + n) |
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 Interleaving String
- Skipping edge cases — empty collections, single-element inputs, max constraints.
- Wrong invariant for dynamic programming — 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 dynamic programming:
- 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: dynamic programming.
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 Interleaving String in a second language (python).
- Drill 3–5 more problems tagged dynamic programming.
- Teach the solution out loud in under 5 minutes.
- Add this problem to your revision calendar in 3 days and 14 days.
Visualization
Conceptual diagram for Interleaving String: show input structure (dynamic programming), highlight the moving parts of the dynamic programming approach, and annotate each step with the maintained invariant and complexity.
Study checklist
- Read the official problem statement on LeetCode
- Solve on paper / whiteboard first
- Implement the dynamic programming 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
Interleaving String (#97) — Hard. Pattern: dynamic programming. Complexity: O(m * n) time / O(m + n) space. Re-derive the invariant before coding.
FAQs
What is the time complexity of Interleaving String?+
The reference solutions aim for O(m * n) time and O(m + n) space. Always re-derive complexity from the code you write in the interview.
What pattern does Interleaving String use?+
It primarily maps to dynamic programming, within the broader topic of dynamic programming.
Is Interleaving String good for interviews?+
Yes — as a Hard 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/interleaving-string/