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Print a Centered Pascal Triangle | Faire Coding Question

Print a Centered Pascal Triangle

Company: Faire

Role: Software Engineer

Category: Coding & Algorithms

Difficulty: medium

Interview Round: Technical Screen

Given a positive integer `height`, generate the first `height` rows of Pascal's triangle and print them as a centered text triangle. Formatting requirements: - Let `max_value` be the largest number that appears in the triangle. - Let `w` be the number of decimal digits in `max_value`. - Print each number right-aligned in a field of width `w`. - Use consistent spacing between values so the output looks visually symmetric. - Add leading spaces so each row is centered relative to the last row. Example: if the largest value is `121`, then `w = 3`, so the value `1` should be printed as `" 1"`.

Quick Answer: This question evaluates the ability to generate combinatorial structures (Pascal's triangle) and apply precise numeric formatting, alignment, and string-layout skills, reflecting algorithmic thinking and attention to presentation details.

Given a positive integer `height`, generate the first `height` rows of Pascal's triangle and return them as a list of strings representing a centered text triangle. If the returned strings are printed line by line, they should form a visually symmetric Pascal triangle. Formatting rules: - Let `max_value` be the largest number anywhere in the generated triangle. - Let `w` be the number of decimal digits in `max_value`. - Format every number right-aligned in a field of width `w`. - Separate adjacent formatted numbers with exactly one space. - Let `last_width` be the length of the formatted last row. - For each row, add `floor((last_width - current_row_width) / 2)` leading spaces so it is centered relative to the last row. - Do not include trailing spaces in the returned strings. Example: if `max_value = 121`, then `w = 3`, so the value `1` should be formatted as `' 1'`.

Constraints

1 <= height <= 30
Each interior value in Pascal's triangle is the sum of the two values directly above it

Examples

Input: (1,)

Expected Output: ['1']

Explanation: The triangle has only one row, so the result is just ['1'].

Input: (2,)

Expected Output: [' 1', '1 1']

Explanation: With height 2, the last row is '1 1' and the first row is centered above it with one leading space.

Input: (5,)

Expected Output: [' 1', ' 1 1', ' 1 2 1', ' 1 3 3 1', '1 4 6 4 1']

Explanation: The largest value is 6, so each number uses width 1. Rows are centered relative to the last row '1 4 6 4 1'.

Input: (6,)

Expected Output: [' 1', ' 1 1', ' 1 2 1', ' 1 3 3 1', ' 1 4 6 4 1', ' 1 5 10 10 5 1']

Explanation: The largest value is 10, so each number uses width 2. This adds internal padding to every row, including the last one.

Hints

Build Pascal's triangle row by row: every row starts and ends with 1, and each middle value comes from two adjacent values in the previous row.
Because the spacing depends on the largest value and the width of the last row, generate all rows first and format them in a second pass.

Quick Overview

This question evaluates the ability to generate combinatorial structures (Pascal's triangle) and apply precise numeric formatting, alignment, and string-layout skills, reflecting algorithmic thinking and attention to presentation details.