Unit 2: Sorting, Searching, and Algorithm Efficiency

Given a monotonic condition over integer values, find the smallest value where the condition becomes true.

Given a sorted array with duplicates, return the first and last index of a target without scanning the whole range.

Find a target in a rotated sorted array by identifying which half is ordered at each step.

Return the index where a target should be inserted to keep a sorted array ordered, including duplicates.

Sort meeting intervals by start time and merge any intervals that overlap or touch.

Choose the largest number of tasks that can fit without overlap by sorting by ending time.

Given logs where each item is at most k positions away from its correct spot, choose and justify an efficient sorting approach.

Compare sorting the whole array, using a heap, and partition-based selection for finding the kth smallest value.

Sort values, then scan adjacent pairs to identify duplicates and explain the runtime tradeoff.

Sort records by score descending, then name ascending, then submission time ascending, and explain tie handling.

Given a sorted array, count unique pairs that add to a target while skipping duplicate values correctly.

Given a sorted array, find the pair whose sum is closest to a target and explain how the pointers move.

Find the smallest value in a rotated sorted array and state the invariant maintained by the search.

Given student records with equal grades, explain when preserving original order matters and how to test it.

Count occurrences of values, then sort values by decreasing frequency and increasing numeric value.

Find an index whose value is not smaller than its neighbors using a logarithmic search strategy.

Given code that compares every pair of values, identify the runtime and propose a faster method using sorting or a set.

Design an experiment comparing random, sorted, and reverse-sorted input for insertion sort and merge sort.

Given sorted unique values from a consecutive range with one missing value, find the missing number in logarithmic time.

Given job lengths and worker count, find the smallest maximum workload that allows all jobs to be assigned in order.

Explain how sorted order can be used to find a median without merging every value.

For each value in an array, report how many values are smaller using a sorted copy and binary search.

Given a custom alphabet order, sort words by mapping each character to its rank.

Scan an array to find the longest contiguous increasing run and explain why sorting would change the problem.

Given input sizes and time limits, choose between O(n), O(n log n), and O(n squared) approaches and justify the choice.

Given several intermediate arrays, determine which one could occur after a pass of insertion sort or selection sort.

Find a target in a matrix where rows and columns are sorted by starting from a strategic corner.

Given versions where all builds after the first failure also fail, find the first failing version with minimum checks.

Given many lookup queries, decide whether sorting plus binary search or a HashSet gives the better long-term plan.

Create a short written analysis comparing two correct solutions by runtime, memory, readability, and input constraints.