This article covers several dynamic programming problems, including finding the maximum subarray sum, the longest increasing subsequence, the longest common subsequence, the longest palindromic substring, and finding the longest path in a Directed Acyclic Graph (DAG). Maximum Subarray Sum This probl...
Hash tables provide O(1) average-time complexity for insertion, deletion, and lookup operations. They are the optimal choice when the primary requirement is rapidly verifying the existence of an element within a collection or tracking frequency counts. The core mechanism relies on a hash function th...
Stack and Queue Fundamentals A queue follows the First-In-First-Out (FIFO) principle, while a stack follows the Last-In-First-Out (LIFO) principle. Understanding Stack Implementation in C++ Is the C++ stack considered a container? Which STL version does our stack implementation belong to? How is the...
Implementing a Queue Using Two Stacks A queue follows FIFO (First-In-First-Out) semantics, while a stack follows LIFO (Last-In-First-Out). To simulate queue behavior using only stacks, two stacks are employed: one for input (inStack) and another for output (outStack). Push: Elements are always pushe...
Basic Element Manipulation push_back() Adds an element to the end of the vector. std::vector<int> numbers; numbers.push_back(10); numbers.push_back(20); pop_back() Removes the last element from the vector. numbers.pop_back(); insert() Inserts elements at a specified position. std::vector<in...
Prime FactorizationDecomposing an integer into its prime components operates with a time complexity of O(√n). The following implementation accepts an integer val and a boolean flag uniqueOnly. If uniqueOnly is true, the result contains distinct primes only; otherwise, all prime factors includi...
Problem A: Minimum Function Summation Given the function f(x) = min_{i∈ℕ⁺}, compute the sum Σ_{i=1}^{n} f(i) modulo 10^9+7 across multiple test cases. Constraints: n ≤ 10^16, T ≤ 10^4. Solution Approach: Analyze the frequency of each value in the sequence f(i). For a particular value x, we need to c...
This problem requires the implementation of a standard Last-In-First-Out (LIFO) stack capable of processing a high volume of operations efficiently. The solution must handle multiple independent test cases. Core Functional Requirements The data structure must support the following commands: push(x):...
Simple arithmetic expressions like 1 + 2 are straightforward to compute. However, evaluating more complex infix expressions such as 1 + (2 ^ 2) / 3 * 4 requires a systematic approach accounting for operator precedence and parentheses. A standard solution uses two stacks: one for numeric operands and...
Approach 1: Monotonic Stack The monotonic stack method offers a linear time complexity solution, O(n), with O(n) space complexity. While it may appear more complex to implement than a recursive approach, it provides superior performance in large-scale scenarios. The algorithm iterates through the in...