Pascal's Triangle
Hard Problems: N-Sum & Hashing DSA practice problem on Onlearn.
Difficulty: medium.
Topics: Variations and efficient approaches to generating and querying Pascal's Triangle, Mathematical Algorithms, Combinatorics, Loops, Time Complexity, Space Complexity, Big O Notation, Arrays, Two-dimensional Array Traversal, Basic Arithmetic, combinatorics, iterative algorithms, complexity analysis, dynamic programming, Combinatorics & Binomial Coefficients, Subset & Permutation Problems, Dynamic Programming (DP).
Pascal's Triangle Pascal's triangle is a triangular array of the binomial coefficients. In Pascal's triangle, each number is the sum of the two numbers directly above it. You are tasked with solving three variations related to Pascal's Triangle: Variation 1: Find the Element Given a row number r and a column number c (1 indexed), print the element at position (r, c) in Pascal’s triangle. Variation 2: Generate a Specific Row Given a row number N (1 indexed), print the N th row of Pascal’s triangle. Variation 3: Generate the Entire Triangle Given the total number of rows N, print the first N rows of Pascal’s triangle. Input Specification The input will consist of three integers: N, r, c. N: Represents the total number of rows for Variation 2 and Variation 3, and the context for r and c in Variation 1. r: Row number for Variation 1. c: Column number for Variation 1. Output Specification For each variation, output the result as follows: Variation 1: A single integer representing the element at (r, c). Variation 2: The elements of the N th row, space separated. Variation 3: The first N rows of Pascal's triangle, with elements in each row space separated and each row on a new line. Constraints 1 <= c <= r <= N <= 30 Sample Test Cases Example 1: Input: Output: Example 2: Input: Output: