Can Place Flowers

The problem of planting flowers in a flowerbed without violating the no-adjacent-flowers rule can be approached by iterating through the flowerbed and looking for eligible spots to plant the flowers. Let’s break down the process:

Algorithm

  1. Initialize Counter: Create a counter variable to track the number of flowers that can be planted.
  2. Iterate Through Flowerbed: Use a loop to iterate through the given flowerbed.
    • Check Eligible Spot: For each spot, check if it’s empty (value is 0), and if both its adjacent spots are also empty or out of bounds. The adjacent spots are the previous and next elements in the array.
    • Plant Flower: If the spot is eligible, increment the counter by 1 and mark the spot as planted by setting its value to 1.
  3. Compare with Required Flowers: After the loop, compare the counter with the required number of flowers n.
  4. Return Result: Return true if the counter is greater than or equal to n, else return false.

Code

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class Solution:
    def canPlaceFlowers(self, flowerbed: List[int], n: int) -> bool:
        count = 0

        for i in range(len(flowerbed)):
            if flowerbed[i] == 0 and (i == 0 or flowerbed[i - 1] == 0) and (i == len(flowerbed) - 1 or flowerbed[i + 1] == 0):
                count += 1
                flowerbed[i] = 1

        return count >= n

Explanation

  • The loop iterates through the flowerbed, checking each spot for eligibility.
  • The eligibility is determined by checking the current spot and its adjacent spots (using boundary checks).
  • If a spot is found, the counter is incremented, and the spot is marked as planted.

Insights

  • Time Complexity: The time complexity of this approach is (O(m)), where (m) is the length of the flowerbed.
  • Space Complexity: The space complexity is (O(1)), as only a constant amount of extra space is used.

This solution is efficient and meets the constraints and requirements of the problem, providing a simple and straightforward way to determine if the specified number of flowers can be planted.

Identifying Problem Isomorphism

“Can Place Flowers” can be mapped to “Non-decreasing Array”.

In “Can Place Flowers”, you’re given an array representing a flowerbed and you have to decide if you can place a certain number of flowers without any two flowers being adjacent. In “Non-decreasing Array”, you’re also given an array and have to decide if you can make at most one change to ensure that the whole array is non-decreasing.

Both involve traversing an array and making decisions based on the current and future elements. In both cases, you can modify the array once and need to check if the modification results in the desired outcome (a flowerbed where flowers can be planted without violating the rule or an array that is non-decreasing).

It’s an approximate mapping based on the structure of the problems. “Can Place Flowers” is simpler, as it only requires checking if two adjacent places are available for planting, whereas “Non-decreasing Array” requires more sophisticated checking and decisions.

“Can Place Flowers” is an array problem that requires understanding of how to iterate over an array and apply certain conditions. Simpler problems to solve before this one:

  1. Two Sum (LeetCode 1): This is a basic problem which helps to understand the concept of iterating over an array and looking up values.

  2. Best Time to Buy and Sell Stock II (LeetCode 122): This problem involves figuring out the optimal times to buy and sell stocks, which is a somewhat similar concept to figuring out where to plant flowers.

  3. Rotate Array (LeetCode 189): This problem deals with manipulating an array, which can help with understanding how to work with arrays in general.

  4. Contains Duplicate (LeetCode 217): This problem involves looking for duplicates in an array, which is a useful basic skill for array problems.

  5. Single Number (LeetCode 136): In this problem, you have to find a single number in an array where all other numbers exist twice. It introduces bit manipulation but is quite straightforward.

  6. Plus One (LeetCode 66): This is another simple problem that involves manipulation of an array.

  7. Remove Duplicates from Sorted Array (LeetCode 26): This problem can help with understanding how to handle arrays and how to deal with the removal of elements.

  8. Maximum Subarray (LeetCode 53): This problem helps in understanding how to find maximum/minimum in an array.

  9. Find All Numbers Disappeared in an Array (LeetCode 448): This problem is a bit more complex, but it also helps to learn how to work with arrays.

  10. Move Zeroes (LeetCode 283): This problem is about re-arranging an array based on certain conditions which is somewhat similar to the “Can Place Flowers” problem.

These cover array related problems.

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class Solution:
    def canPlaceFlowers(self, flowerbed: List[int], n: int) -> bool:
        if n == 0:
            return True

        for i in range(len(flowerbed)):
            if flowerbed[i] == 0 and (i == 0 or flowerbed[i-1] == 0) and (i == len(flowerbed)-1 or flowerbed[i+1] == 0):
                flowerbed[i] = 1
                n -= 1
                if n == 0:
                    return True

        return False

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def empty_position?(element)
    element == 0
end

def adjacent_positions_empty?(flowerbed, i)
   (i==0 || flowerbed[i-1] == 0) && (i == flowerbed.size - 1 || flowerbed[i+1] == 0) 
end
# @param {Integer[]} flowerbed
# @param {Integer} n
# @return {Boolean}
def can_place_flowers(flowerbed, n)
    i = 0
    count = 0
    while i < flowerbed.size
       if empty_position?(flowerbed[i]) && adjacent_positions_empty?(flowerbed, i) 
          flowerbed[i] = 1
          count += 1
       end
        if count >= n
            return true
        end
        i += 1
    end
    return false
end

Problem Classification

This problem falls into the category of Combinatorial Optimization problems within the domain of Array Manipulation and Greedy Algorithms.

The ‘What’ components of the problem are as follows:

  1. An integer array flowerbed (a series of 0s and 1s where 0 means empty and 1 means not empty).
  2. An integer n representing the number of new flowers to be planted.
  3. The rule that no two flowers can be planted in adjacent plots.
  4. The output, which is a boolean value indicating whether it’s possible to plant n new flowers in the flowerbed without violating the given rule.

We can further classify this problem as a Boolean Validation problem where the task is to determine the feasibility of a certain condition - in this case, whether it’s possible to plant n new flowers in the flowerbed without breaking the given rule.

The problem relies on the concept of space availability and optimal placement, requiring an understanding of how to best utilize available spaces (0s) in the flowerbed array such that the maximum number of new flowers can be planted without violating the adjacency rule. This involves a greedy approach to always make the locally optimal choice at each step in the hope of finding a global optimum.

Language Agnostic Coding Drills

  1. Distinct Coding Concepts

This piece of code contains several distinct coding concepts:

a. Data Types: Understanding basic data types such as integers, boolean, and lists.

b. Conditional Statements: The use of if conditions to control the flow of the code based on certain criteria.

c. Looping Constructs: The use of a for loop to iterate over elements in a list.

d. Indexing in Lists: Accessing elements in a list using their indices. This includes accessing the previous and next elements relative to the current element.

e. In-place Modification of a List: The code modifies the list flowerbed during iteration.

f. Return Statement: The use of return to exit a function and return a value.

g. Greedy Algorithm: A problem-solving approach where the optimal solution is built incrementally by making a locally optimal choice at each step.

  1. Coding Drills in Order of Increasing Difficulty

a. Data Types: Understanding and using basic data types is the most basic concept. Python’s dynamic typing makes it easier for beginners.

b. Conditional Statements: Conditional statements are slightly more complex, requiring understanding of Boolean expressions and control flow.

c. Looping Constructs: Looping over data structures is a fundamental concept in programming but it’s a step up in complexity because it requires thinking in terms of iteration and understanding when and how the loop ends.

d. Indexing in Lists: Indexing is an essential part of working with lists. This code also uses indexing to access previous and next elements which adds an extra layer of complexity.

e. Return Statement: While the return statement itself is simple, understanding when to return and what value to return is part of the larger problem-solving process.

f. In-place Modification of a List: Changing the content of a list while iterating over it can be tricky because it affects the subsequent iterations.

g. Greedy Algorithm: Implementing a greedy algorithm is the most complex concept in this code as it requires not just knowledge of Python syntax but also a deeper understanding of algorithm design and problem-solving strategies.

  1. Problem-Solving Approach

This code solves the problem by iteratively scanning through the flowerbed list and trying to plant a flower at each plot (represented by ‘0’s in the list) if it can (i.e., if the previous and next plots are not already planted). This is a greedy approach because it tries to plant a flower whenever it can, assuming this will lead to the maximum number of flowers planted.

The coding drills play different roles in this problem-solving process:

a. Understanding of Data Types and Indexing in Lists allows us to work with the flowerbed list and access each plot.

b. Looping Constructs let us iterate over the list and try to plant a flower at each plot.

c. Conditional Statements are used to check whether a flower can be planted at a certain plot and whether we have reached the required number of flowers.

d. In-place Modification of a List enables us to update the flowerbed list as we go, reflecting the flowers we have planted.

e. Return Statement allows us to end the function once we’ve found a solution or if we determine that it’s impossible to plant the required number of flowers.

f. The Greedy Algorithm concept guides the overall approach to the problem, dictating how we make decisions at each step.

Clarification Questions

Here are some questions that can provide better understanding:

  1. What happens at the boundaries of the flowerbed? Are we allowed to consider an extra empty plot at the beginning and end of the flowerbed? This may affect how we count available spaces.

  2. Is the input array always valid? The problem statement mentions that there are no two adjacent flowers in the flowerbed. Can we assume that the input will always adhere to this rule, or should our solution account for the possibility of invalid input?

  3. What should the output be if n is zero? If no new flowers need to be planted, should the output always be true, or does it depend on the specific situation?

  4. Is there any maximum or minimum constraint on the length of the flowerbed? Understanding size constraints can influence the algorithm’s design and optimization.

  5. What does “adjacent” specifically mean in this context? Presumably, it refers to consecutive plots in the flowerbed, but it may be good to confirm that “adjacent” doesn’t include any other form of proximity, such as diagonally adjacent in a grid (if the flowerbed were represented in another way).

These questions can help ensure that the problem is understood in depth and that the solution takes into account all possible edge cases and constraints.

Identifying Problem Isomorphism

Isomorphic problems share the same core structure and can often be transformed into each other by renaming variables and reinterpreting the context. While the problem “Can Place Flowers” (LeetCode 605) is distinct in its context and presentation, we can identify problems that have the same underlying structure.

A general problem that is isomorphic to “Can Place Flowers” is Placing Objects with Restrictions:

Given an array of 0’s and 1’s, where 0 represents an available slot and 1 represents an occupied slot, and an integer n, determine if n new objects can be placed in the available slots without placing two objects in adjacent slots.

This problem statement removes the specific context of planting flowers and instead refers to placing objects with the same constraints about adjacency. You can think of many real-world scenarios that fit this structure, such as allocating resources in a network, arranging seats with social distancing measures, or scheduling tasks with constraints.

The isomorphism here lies in the constraint that objects (or flowers) cannot be placed adjacently, and the task of determining if a certain number can be placed given these constraints. By understanding this core structure, solutions can be developed or adapted across different contexts that fit this pattern.

Targeted Drills in Python

  1. Python Coding Drills for Identified Concepts

Here are Python coding drills for each concept identified:

a. Data Types

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# Integer
x = 5
print(x)

# Boolean
y = True
print(y)

# List of integers
z = [1, 2, 3, 4, 5]
print(z)

b. Conditional Statements

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x = 10
if x > 5:
    print("x is greater than 5")
else:
    print("x is less than or equal to 5")

c. Looping Constructs

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nums = [1, 2, 3, 4, 5]
for num in nums:
    print(num)

d. Indexing in Lists

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nums = [1, 2, 3, 4, 5]
print(nums[0])  # prints 1
print(nums[1])  # prints 2

e. Return Statement

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def square(x):
    return x ** 2

print(square(5))  # prints 25

f. In-place Modification of a List

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nums = [1, 2, 3, 4, 5]
for i in range(len(nums)):
    nums[i] = nums[i] ** 2
print(nums)  # prints [1, 4, 9, 16, 25]

g. Greedy Algorithm

A simple example of a greedy algorithm would be finding change using the least number of coins. In Python, it would look something like this:

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def find_change(n):
    coins = [25, 10, 5, 1]
    change = []
    for coin in coins:
        while n >= coin:
            change.append(coin)
            n -= coin
    return change

print(find_change(63))  # prints [25, 25, 10, 1, 1, 1]
  1. Problem-specific drills

The main problem-specific concept here is the use of the Greedy Algorithm concept, which we have already covered in the general concepts. The drill is essentially the same; the idea is to make the locally optimal choice at each step with the hope that these local optimal choices will lead to a global optimum. This concept is crucial for the given problem because it dictates the decision-making process at each step of the iteration.

  1. Integration of Drills

First, the problem solver should understand and be able to use the basic Python data types, which form the foundation of everything else. They will then learn to control the flow of the code using conditional statements. After that, they should learn about looping constructs, which allow the code to perform repeated actions. They should also understand list indexing to access individual elements in the list.

Once they have a handle on these foundational skills, they can move on to the more complex concepts. They can learn about the return statement, which controls what the function outputs. They can also practice modifying lists in-place, which is a key part of how the given solution works.

Finally, they should understand and be able to implement the greedy algorithm, which is the overarching strategy that the solution uses to solve the problem. With all these skills and concepts under their belt, they will be able to understand and recreate the given solution.