81. Explain the concept of memoization and its applications.
82. What is the role of dynamic programming in solving optimization problems?
83. Describe the significance of the Knapsack problem in resource allocation.
84. How does the Maximum Subarray problem relate to dynamic programming?
85. What is a directed acyclic graph (DAG), and what are its properties?
86. Explain how to use dynamic programming to solve the edit distance problem.
87. What is a mixed-integer linear programming (MILP) problem?
88. Describe the significance of Schur's lemma in combinatorial optimization.
89. How does the concept of a heuristic function improve search algorithms?
90. What is a context-free grammar, and how is it used in parsing algorithms?
91. Discuss the significance of regular expressions in string processing.
92. What is a syntax tree, and how is it constructed?
93. Explain the concept of a hash collision and its implications in hashing.
94. Describe the role of a Monte Carlo simulation in decision-making processes.
95. How do you compute the shortest path using Dijkstra’s algorithm?
96. What is a range query, and how do segment trees handle it?
97. Explain how a priority queue is implemented using a heap.
98. What are the advantages of using a suffix array over a suffix tree?
99. Discuss the concept of a non-deterministic finite automaton (NFA).
100. What is a deterministic finite automaton (DFA), and how does it differ from NFA?
101. Explain the role of finite state transducers in string processing.
102. Describe how to implement a topological sort algorithm.
103. What is the significance of a non-linear data structure in algorithm design?
104. Explain how to use Kahn's algorithm for topological sorting.
105. What are the properties of a complete binary tree?
106. Describe the significance of Johnson's algorithm in graph theory.
107. How does the concept of duality relate to linear programming?
108. What is the significance of Fulkerson's theorem in flow networks?
109. Discuss the use of randomization in the QuickSelect algorithm.
110. How does the FFT (Fast Fourier Transform) algorithm work, and what are its applications?
111. Explain the concept of a heap sort and its time complexity.
112. What is the significance of the birthday paradox in hash functions?
113. How do you implement a simple gradient descent algorithm?
114. What is the significance of a kernel in machine learning algorithms?
115. Describe the process of training a decision tree classifier.
116. Explain how to compute the convex hull of a set of points.
117. What is the difference between supervised and unsupervised learning in algorithms?
118. Describe how to use a backtracking algorithm to solve Sudoku puzzles.
119. What is a Lagrangian relaxation, and how is it used in optimization problems?
120. Explain the concept of a dual graph and its properties.