Search Insert Position

Identifying Problem Isomorphism

“Search Insert Position” can be mapped to “First Bad Version”.

Reasoning: Both problems essentially involve finding a specific position within a sorted array (or a version history, in the case of “First Bad Version”) using a binary search approach.

In “Search Insert Position”, the task is to find the location where a given target should be inserted in a sorted array to maintain its sorted order. If the array contains the target, you return the index of the target.

In “First Bad Version”, you are tasked with finding the first ‘bad’ version given a sorted list of ‘versions’. Here, ‘bad’ versions follow all ‘good’ ones in order, just like a sorted array.

Both revolve around binary search, a well-understood algorithmic pattern. “First Bad Version” is simpler since it doesn’t require dealing with an edge case of inserting at the end of the array.

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class Solution:
    def searchInsert(self, nums: List[int], target: int) -> int:
        if not nums:
            return 0

        for i, num in enumerate(nums):
            if num >= target:
                return i

        return len(nums)

Problem Classification

Search Problem: It involves searching for a specific value in an array or a list.
Insertion Problem: The task is to find the position at which the target would be inserted to maintain sorted order of the list. It means it’s about identifying an insertion point.
Array/List Manipulation: It involves working with and manipulating an array or list to solve the problem.
Order and Comparison: The problem requires understanding the order of elements in the list and making comparisons with the target element.

Tt’s a combination of search, insertion, array manipulation, and comparison-based problem.

Language Agnostic Coding Drills

Handling Empty Input: The first step in the problem is handling the case where the input list nums is empty. If this is the case, we return 0 since the target would be inserted at index 0.
Traversal and Comparison: The second step involves traversing the list of numbers nums one by one. For each number num, we compare it with the target. This incorporates concepts of loops and conditional statements.
Early Return: If we find a number num which is equal to or larger than target, we return the index i immediately. This step involves understanding of flow control in a program and early return from a function.
Handling Not-Found Case: If we don’t find any such number in the entire traversal of nums, we return len(nums) as the target should be inserted at the end of the list. This requires understanding of list length calculation and handling of edge cases.

Here’s the sequence of drills based on the steps:

Write a function that takes a list and a target value, and returns 0 if the list is empty.
Write a function that can iterate through a list of integers. As a drill, you could write a function that returns the sum of all the numbers in the list.
Write a function that returns the index of the first element in a list which is equal to or greater than a given target number.
Write a function that, given a list of numbers and a target, returns the length of the list if the target is greater than all elements of the list.

In the final solution, these drills are combined. The function checks if the list is empty first, then iterates through the list, comparing each number to the target. If it finds a number equal to or larger than the target, it returns the index of that number. If no such number is found, it returns the length of the list.

Targeted Drills in Python

Handling Empty Input
Problem Statement: Write a function check_empty() that takes a list and a target value, and returns 0 if the list is empty.
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def check_empty(nums, target): if not nums: return 0
Traversal and Summation
Problem Statement: Write a function calculate_sum() that can iterate through a list of integers and return the sum of all the numbers in the list.
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def calculate_sum(nums): return sum(nums)
Index of First Element Equal or Larger than Target
Problem Statement: Write a function first_equal_or_larger() that returns the index of the first element in a list which is equal to or greater than a given target number.
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def first_equal_or_larger(nums, target): for i, num in enumerate(nums): if num >= target: return i
Length of List if Target is Greater than All Elements
Problem Statement: Write a function list_length_if_greater() that, given a list of numbers and a target, returns the length of the list if the target is greater than all elements of the list.
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def list_length_if_greater(nums, target): if all(num < target for num in nums): return len(nums)

The final integrated code would be the combination of all these small units of code which would form the final solution. Here is how it will look:

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class Solution:
    def searchInsert(self, nums: List[int], target: int) -> int:
        if not nums:  # Drill 1
            return 0
        for i, num in enumerate(nums):  # Drill 2 and 3
            if num >= target:
                return i
        return len(nums)  # Drill 4

Python Basics

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import bisect

class Solution:
    def searchInsert(self, nums: List[int], target: int) -> int:
        return bisect.bisect_left(nums, target)

This code is a Python solution for finding the position where a target value should be inserted in a sorted array to maintain the array’s sorted order.

Here is a detailed explanation of each part:

import bisect: The bisect module is a built-in Python library for handling bisections in sorted lists. The bisection method in mathematics is a root-finding method that applies to any continuous function for which one knows two values with opposite signs.
class Solution: In Python, a class is created by the keyword class. Here, Solution is an arbitrary name for the class.
def searchInsert(self, nums: List[int], target: int) -> int:: This is a function definition. The function is named searchInsert, and it’s a method of the Solution class. It takes two arguments: self (which is a reference to instances of the class), nums (a list of integers, representing the sorted array), and target (an integer, the value to be inserted).
return bisect.bisect_left(nums, target): Here, the function bisect_left from the bisect module is used. The bisect_left function locates the insertion point for target in nums to maintain sorted order. If target is already present in nums, the insertion point is before (to the left of) any existing entries. The returned value is the index position where the target should be inserted.

The entire code provides a class method to solve a common problem in computer science: determining where to insert an item in a sorted list to maintain the sorted order of the list. It utilizes Python’s built-in bisect module to efficiently solve this problem.