Teemo Attacking

The problem asks for the total duration that Ashe is poisoned. This can be calculated by iterating over the list of attack times, adding the duration to a total, and adjusting for any overlap in poisoning times.

Python solution:

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class Solution:
    def findPoisonedDuration(self, timeSeries: List[int], duration: int) -> int:
        if not timeSeries:  # If timeSeries is empty, return 0
            return 0

        total_duration = 0
        for i in range(1, len(timeSeries)):
            # Check if the next attack happened during the duration of the current attack
            if timeSeries[i] < timeSeries[i-1] + duration:
                # The overlap duration is subtracted from the total duration
                total_duration += timeSeries[i] - timeSeries[i-1]
            else:
                # If there's no overlap, simply add the full duration
                total_duration += duration

        # Finally, add the duration of the last attack
        total_duration += duration

        return total_duration

This solution iterates over each attack time in timeSeries (except the first), checking if the next attack is within the poisoning duration of the current attack. If it is, we add the time difference between the current and next attack to total_duration to account for the overlap. If there’s no overlap, we simply add the entire duration. After the loop, we add the duration of the last attack to total_duration and return the result.

Identifying Problem Isomorphism

“Teemo Attacking” can be approximately mapped to “Merge Intervals”.

In “Teemo Attacking”, you’re given an array of time points at which attacks happen, and each attack causes damage over an interval of time. The task is to calculate the total time of damage.

In “Merge Intervals”, you’re given a collection of intervals and need to merge any overlapping intervals to create a new list of distinct intervals.

The reason is that both problems require handling overlapping intervals. In “Teemo Attacking”, the intervals are the time periods of the attacks, and you need to calculate the total damage time considering the overlapping intervals. In “Merge Intervals”, the task is to find and merge the overlapping intervals.

“Merge Intervals” is simpler because it involves a simple sorting and merging of intervals. On the other hand, “Teemo Attacking” adds extra complexity as it involves calculating the total damage time, which is a specific application of merging intervals.

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class Solution(object):
    def findPoisonedDuration(self, timeSeries, duration):
        repeat = 0
        for i in range(len(timeSeries)-1):
            diff = timeSeries[i+1] - timeSeries[i]
            if diff < duration:
                repeat += duration - diff
        return len(timeSeries)*duration - repeat

Problem Classification

This problem falls under the domain of Time Series Analysis and Array Manipulation.

What Components:

  1. There’s a non-decreasing integer array timeSeries, each of which denotes the second when Teemo attacks Ashe.
  2. An integer duration represents the duration of each poison effect.
  3. Need to calculate the total number of seconds that Ashe is poisoned.

This problem can be further classified as a Sequential Processing and Overlap Interval Calculation problem.

  • Time Series Analysis: We are given a sequence of points in time at which events (attacks) occur. This is a classic time series scenario.
  • Array Manipulation: We need to traverse and manipulate the given array to determine the total duration of poison effects.
  • Sequential Processing: The order of the attacks matters because each attack resets the duration of the poison effect. This introduces a sequential aspect to the problem, as we must process the times in order.
  • Overlap Interval Calculation: When an attack happens before the previous poison effect has ended, the poison effect duration is reset. So, the problem involves determining overlapping intervals (an attack happening during another poison effect) and calculating the total time for which poison effects are active.

Language Agnostic Coding Drills

  1. Identified Concepts:

    • Variable Initialization: The variables repeat is initialized to keep track of overlapping poison durations.

    • Array/ List Traversal: The list timeSeries is traversed using a loop.

    • Condition Checking: An if statement is used to check if the time difference between two attacks is less than the poison duration.

    • Arithmetic Operations: Basic arithmetic operations are performed to calculate the time difference and update the repeat variable.

    • Returning the Result: The final result, the total duration that Ashe is poisoned, is calculated and returned.

  2. Difficulty Level:

    • Easy: Variable Initialization, Arithmetic Operations, Returning the Result

    • Medium: Array/ List Traversal, Condition Checking

  3. Problem-Solving Approach:

    • Initialize a variable repeat to zero. This will be used to track the overlap in the poison durations.

    • Loop through the timeSeries array, and for each pair of consecutive attacks, calculate the time difference diff.

    • If diff is less than the duration, it means the poison effect of the current attack overlapped with the next attack. We then calculate the overlap by subtracting diff from duration and add this to repeat.

    • At the end, the total poison duration is calculated by multiplying the total number of attacks by the duration and subtracting the total overlap repeat.

    • Each drill contributes to the overall solution by gradually building up the logic required to calculate the total poison duration considering the overlaps. This step-by-step approach is critical in solving the problem without getting overwhelmed by the whole complexity at once.

Targeted Drills in Python

  1. Python Drills for Each Concept:

    • Variable Initialization: A beginner-friendly drill could be to initialize variables of different types and print their values.
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    x = 0
print(x)
y = "Hello, World!"
print(y)
    • List Traversal Using Index: A simple drill could be to traverse a list of integers and print each one.
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    nums = [1, 2, 3, 4, 5]
for i in range(len(nums)):
    print(nums[i])
    • Arithmetic Operations: A good starting drill might involve performing basic arithmetic operations like addition, subtraction, multiplication, and division.
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    x = 10
y = 2
print(x + y)
print(x - y)
print(x * y)
print(x / y)
    • Conditional Statements: A drill for this concept could involve writing a simple program that checks if a number is even or odd.
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    x = 10
if x % 2 == 0:
    print("Even")
else:
    print("Odd")
    • Returning Values: A simple function that takes an input and returns a value could be used as a drill for this concept.
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    def square(x):
    return x**2
print(square(5))

  2. Additional Drills for Specific Needs of the Problem:

    • Calculating Difference Between Consecutive Elements in a List: This concept is essential to calculate the time difference between consecutive attacks.
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    times = [2, 4, 7, 10]
for i in range(len(times) - 1):
    print(times[i+1] - times[i])
    • Accumulating Value Based on Condition: This drill can help in understanding how to keep track of overlapping durations.
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    nums = [1, 2, 3, 4, 5]
sum = 0
for num in nums:
    if num % 2 == 0:
        sum += num
print(sum)

  3. How to Merge these Drills for the Final Solution:

    • Begin by initializing repeat to 0.

    • Traverse through the timeSeries list. In each iteration, calculate the difference between the current attack time and the next attack time.

    • Check if this difference is less than duration. If it is, update repeat by adding the overlapping time (duration - diff).

    • After the loop ends, calculate the total poison time as len(timeSeries)*duration - repeat and return this value.

    By following these steps and integrating the drills, one can obtain the final solution for the problem.