Below is a comprehensive study guide that analyzes the collection of array and string problems, summarizes their common characteristics, and organizes the key techniques—from the most frequently used to those seen less often—in a way that you can reference as you practice and prepare.
1. Identifying Array/String Problems
Array and string problems have several typical traits that help you quickly recognize them:
- Input Type and Structure:
- Arrays: Usually, you are given a list (or sequence) of numbers or objects. The problem may involve operations like searching, sorting, filtering, or in-place modifications. For example, problems like Remove Element and Merge Sorted Array work directly with arrays.
- Strings: The input is a sequence of characters. These problems often focus on manipulating or parsing the string (e.g., splitting, reversing, or pattern matching). Examples include Longest Common Prefix and Reverse Words in a String.
- Common Operations and Patterns:
- Traversal: Many problems require iterating through each element (or character) to check conditions, update counters, or perform operations such as two‐pointer techniques.
- In-Place Modification: Several problems ask you to modify the input without extra memory. For example, Remove Duplicates from Sorted Array and Rotate Array must update the array in place.
- Comparisons and Searches: You often compare adjacent elements (e.g., for duplicates or sorted order) or search for patterns (as in the Find the Index of the First Occurrence in a String using KMP).
- Problem Statements and Constraints:
- Look for phrases such as “in-place,” “minimum number of operations,” “cumulative,” “reverse,” or “find the first/last.”
- The constraints sometimes guide you toward linear or constant-space solutions—for instance, many problems specify that you must use O(1) extra space, nudging you toward in-place two-pointer or greedy approaches.
- Domain-Specific Hints:
By paying attention to the type of data (array vs. string), the operation (traversal, in-place edit, transformation), and the specific instructions (e.g., “return the number of unique elements” or “reverse the order”), you can quickly classify a problem into these categories.
2. Most Common to Least Common Techniques and Approaches to Solving Array/String Problems
When approaching these problems, many techniques overlap. Below is a ranked guide—starting with the most commonly encountered—to help you choose an efficient strategy for any given problem.
A. Two-Pointer Techniques
Why it’s common:
The two-pointer method is a natural fit when dealing with sorted arrays, filtering elements, or reversing parts of a structure. It minimizes extra space and often leads to an O(n) solution.
- Applications & Examples:
- Filtering/In-Place Removal:
- Remove Element: Iterates through the array and writes non-target elements to a new position.
- Remove Duplicates from Sorted Array and Remove Duplicates from Sorted Array II: Use one pointer to read and one to write, ensuring that each element appears only a specified number of times.
- Reversal and Rotation:
- Rotate Array: Uses a helper reversal function to reverse segments of the array in place.
- Reverse Words in a String: Although this problem can be solved via built-in functions, a two-pointer approach can be used to reverse segments manually.
- Technique Summary:
Maintain two indices—a slow (write) pointer and a fast (read) pointer—to process elements and rewrite the array or string in place.
B. Greedy Approaches
Why it’s common:
Greedy strategies are particularly effective in problems where local decisions (like selecting the best jump or capturing all immediate profit opportunities) lead to a globally optimal solution.
- Applications & Examples:
- Best Time to Buy and Sell Stock:
- Iterates once while tracking the minimum price seen so far to compute maximum profit.
- Best Time to Buy and Sell Stock II:
- Accumulates profit by summing all positive price differences between consecutive days.
- Jump Game & Jump Game II:
- Track the farthest reachable index (or the next interval) to determine the minimum number of jumps.
- Trapping Rain Water:
- A two-pointer greedy approach updating the maximum boundaries from both ends to compute trapped water.
- Technique Summary:
At each step, choose the locally optimal decision (whether it is a jump length or a profit opportunity) without re-evaluating past decisions. This avoids unnecessary recomputation and often leads to a linear-time algorithm.
C. In-Place Manipulation and Simulation
Why it’s common:
Many problems require modifying the input without allocating extra memory. Simulation often comes into play when you must mimic a real-world process (like balancing candies based on ratings).
- Applications & Examples:
- Merge Sorted Array:
- Uses reverse iteration to merge two arrays in place without extra space.
- Rotate Array:
- Involves reversing segments to achieve the desired rotation.
- Candy:
- Uses two passes (left-to-right and right-to-left) to distribute candies by simulating rating comparisons with neighbors.
- Text Justification:
- Simulates the process of word packing and space distribution across lines.
- Technique Summary:
Apply simulation—often through multiple passes over the data—to gradually enforce the problem constraints (e.g., ensuring higher-rated elements receive more resources, or that the array remains sorted after merging).
D. Pattern Matching and String Parsing
Why it’s common:
Problems that involve transforming or converting strings often rely on identifying patterns, mapping characters, or simulating state transitions based on rules.
- Applications & Examples:
- Longest Common Prefix:
- Iteratively reduce a candidate prefix until it fits all strings.
- Find the Index of the First Occurrence in a String:
- Implements the KMP (Knuth-Morris-Pratt) algorithm, which preprocesses the pattern (needle) and then uses that information to efficiently search through the text (haystack).
- Roman to Integer and Integer to Roman:
- Use mappings (dictionaries) to convert between number and symbol representations, handling special cases like subtractive notation.
- Zigzag Conversion:
- Simulates writing the string in a zigzag pattern by toggling direction based on the current row.
- Technique Summary:
Focus on parsing the string either by tokenizing (using split methods) or by simulating state transitions (using direction flags or lookup tables) to reconstruct the desired output.
E. Multi-Pass and Auxiliary Array Techniques
Why it’s somewhat less common:
While many problems can be solved in one pass, sometimes a two-pass solution is more intuitive and still efficient. This is especially true when forward and backward dependencies exist.
- Applications & Examples:
- Product of Array Except Self:
- Uses a left pass to compute cumulative products and a right pass to combine them, all while maintaining O(1) additional space (ignoring the output).
- Candy:
- Requires one pass from left-to-right and a second pass from right-to-left to ensure that each child’s candy count obeys both neighbor constraints.
- Technique Summary:
Break the problem into independent passes that each enforce a part of the constraint. Combine the results from these passes (often using an auxiliary array or by directly modifying the original array) to get the final answer.
Quick Reference: Examples from the Collection
- Two-Pointer Techniques:
- Greedy Approaches:
- In-Place Manipulation/Simulation:
- Pattern Matching and String Parsing:
- Multi-Pass Techniques:
By recognizing these patterns and techniques—and noting which problems use which approach—you can better decide how to tackle new array and string problems. As you practice, try to map the problem’s requirements to one of these categories and choose the technique that minimizes time and space complexity while addressing all edge cases. Happy coding!