String Algorithms Overview

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Questions and Answers

What is the time complexity to calculate the prefix sum array for an array of size 'n'?

  • O(1)
  • O(n) (correct)
  • O(log n)
  • O(n^2)

Which of the following is the main advantage of using a frequency array?

  • It reduces the size of the input array.
  • It helps in sorting an array efficiently.
  • It ensures the array is sorted.
  • It helps in counting occurrences of elements. (correct)

In the two-pointer technique, what is a typical use case of moving the pointers inward from the ends of a sorted array?

  • Sorting an array.
  • Finding subarrays with a given sum in an unsorted array.
  • Solving problems related to finding pairs with a specific sum. (correct)
  • Counting distinct elements in an array.

How can you efficiently find if a subarray exists with a given sum using a prefix sum array?

<p>By using a hashmap to store prefix sums and checking for <code>prefixSum[i] - targetSum</code>. (B)</p>
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What is the space complexity of the two-pointer approach in its most basic form, assuming no additional data structures are used?

<p>O(1) (D)</p>
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What is the time complexity of the Knuth-Morris-Pratt (KMP) algorithm for pattern matching?

<p>O(m+n) (A)</p>
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Which algorithm is known for finding the longest palindromic substring in O(n) time?

<p>Manacher’s Algorithm (D)</p>
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What is the primary purpose of the Z-Algorithm in string processing?

<p>Efficient pattern matching. (A)</p>
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In the Rabin-Karp algorithm, what is the main advantage of using a rolling hash function?

<p>To achieve a rolling hash for efficient comparison of substrings. (B)</p>
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How does a suffix array improve upon a naive approach for finding repeated substrings in a string?

<p>By sorting all suffixes lexicographically to bring repeated substrings together. (C)</p>
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What is the time complexity of the naive recursive Fibonacci function for an input 'n'?

<p>O(2^n) (B)</p>
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How many moves are required to solve the Tower of Hanoi problem for n=5 disks?

<p>31 (B)</p>
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What will be the output of the following recursive function for n=5? int fun(int n){if(n==0) return 0; return n + fun(n-1);}

<p>15 (B)</p>
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Which of the following conditions is the correct base case to check for a palindrome string recursively, where start and end are the starting and ending indices of the string, respectively?

<p>start &gt;= end (A)</p>
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How many subsets (including the empty set) can be generated for a set of size 'n' using recursion?

<p>2^n (D)</p>
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What is the time complexity of calculating all possible subsets of a set containing 'n' elements?

<p>O(2^n) (A)</p>
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In backtracking, what is the purpose of the 'unchoose' step after exploring a potential solution?

<p>To reset the state to explore alternative solutions. (C)</p>
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Which problem is most efficiently solved using backtracking?

<p>Generating all possible Sudoku solutions. (A)</p>
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What is a primary advantage of using dynamic programming over recursion for optimization problems?

<p>Dynamic programming avoids recomputation by storing intermediate results. (C)</p>
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When should dynamic programming (DP) typically be considered as an approach to solve a problem?

<p>When the problem exhibits overlapping subproblems and optimal substructure. (A)</p>
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Flashcards

Time complexity to calculate prefix sum array?

Iterating through the array once to compute the prefix sum, where each element is the sum of all preceding elements.

Advantage of using a frequency array?

It enables counting the number of times each element occurs in the array by using array indices as elements and array values as counts.

Typical use case of two-pointer technique?

Finding pairs or ranges that meet certain conditions, such as finding subarrays with a specific sum.

Find subarray with a given sum using prefix sum?

Check if the difference between two prefix sum values equals the target sum. Use a hashmap to store prefix sums encountered so far.

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Space complexity of the two-pointer approach?

The two-pointer approach typically uses a constant amount of extra space, regardless of the input size.

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Time complexity of the KMP algorithm?

The KMP algorithm preprocesses the pattern to build a table that helps to avoid redundant comparisons during the search.

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Algorithm finds longest palindromic substring in O(n) time?

Manacher’s Algorithm

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Purpose of the Z-Algorithm?

The Z-Algorithm computes the Z array, where Z[i] is the length of the longest substring starting from i which is also a prefix of the string.

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Advantage of using hashing in Rabin-Karp?

Hashing allows constant-time comparisons of substrings, significantly speeding up the search for patterns.

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How does a suffix array improve finding repeated substrings?

By sorting all suffixes, similar substrings are grouped together, making it easier to find repeated sequences.

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Time complexity of recursive Fibonacci function?

Due to the overlapping subproblems, the function recalculates values, leading to exponential time complexity.

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Moves to solve Tower of Hanoi for n=5 disks?

The number of moves for n disks is given by 2^n - 1. For n=5, it is 2^5 - 1 = 31.

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Output of recursive function for n=5?

The function calculates the sum of integers from 1 to n. For n=5, the result is 1 + 2 + 3 + 4 + 5 = 15.

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Base condition for palindrome check?

When the start index is greater than or equal to the end index, it means the string is a palindrome up to that point.

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Subsets generated for a set of size n using recursion?

Each element can either be in the subset or not, leading to 2 options for each element, resulting in 2^n possible subsets.

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Study Notes

  • Calculating the prefix sum array for an array of size n has a time complexity of O(n).
  • The main advantage of using a frequency array is that it helps in counting occurrences of elements.
  • In the two-pointer technique, moving the pointers inward from the ends is commonly used for solving problems related to palindromes.
  • You can efficiently find if a subarray exists with a given sum using a prefix sum array by utilizing a hashmap to store prefix sums.
  • The space complexity of the two-pointer approach, assuming no additional data structures are used, is O(1).
  • The time complexity of the Knuth-Morris-Pratt (KMP) algorithm for pattern matching is O(m+n).
  • Manacher's Algorithm is used to find the longest palindromic substring in O(n) time.
  • The purpose of the Z-Algorithm in string processing is efficient pattern matching.
  • In the Rabin-Karp algorithm, the main advantage of using hashing is to achieve a rolling hash for efficient comparison.
  • A suffix array improves upon a naive approach for finding repeated substrings in a string by enabling efficient search operations.
  • The time complexity of the recursive Fibonacci function for input n is O(2^n).
  • It requires 31 moves to solve the Tower of Hanoi problem for n=5 disks.
  • The recursive function int fun(int n){if(n==0) return 0; return n + fun(n-1);} will output 15 for n=5.
  • The base condition to check for a palindrome string recursively is start >= end.
  • The number of subsets (including empty) that can be generated for a set of size n using recursion is 2^n.

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