Distributed task allocation in Drone Programming - Time & Space Complexity

Time Complexity: Distributed task allocation

O(d * t)

Understanding Time Complexity

When drones share tasks, we want to know how the time to assign tasks grows as more drones or tasks appear.

We ask: How does the work needed to allocate tasks change when the number of drones or tasks increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

for drone in drones:
    for task in tasks:
        if drone.can_perform(task):
            drone.assign(task)
            break

This code tries to assign each drone the first task it can perform from a list of tasks.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Nested loops over drones and tasks.
• How many times: For each drone, it checks tasks until it finds one it can do.

How Execution Grows With Input

As the number of drones and tasks grows, the checks increase roughly by multiplying their counts.

Input Size (drones x tasks)	Approx. Operations
10 x 10	Up to 100 checks
100 x 100	Up to 10,000 checks
1000 x 1000	Up to 1,000,000 checks

Pattern observation: The total work grows quickly as both drones and tasks increase, multiplying together.

Final Time Complexity

Time Complexity: O(d * t)

This means the time to assign tasks grows proportionally to the number of drones times the number of tasks.

Common Mistake

[X] Wrong: "The time only depends on the number of drones or only on tasks, not both."

[OK] Correct: Each drone may check many tasks, so both counts multiply to affect total time.

Interview Connect

Understanding how nested loops affect time helps you explain how systems handle many drones and tasks efficiently.

Self-Check

"What if each drone could perform multiple tasks instead of just one? How would the time complexity change?"

Practice

1. What is the main goal of distributed task allocation in drone programming?

easy

A. To share work fairly among drones without a central controller

B. To make one drone do all the tasks quickly

C. To randomly assign tasks without any order

D. To stop drones from communicating with each other

Solution

1. Step 1: Understand distributed task allocation

   It means dividing tasks so all drones get work fairly.

2. Step 2: Identify the goal in drone programming

   The goal is to avoid a single controller and let drones share tasks efficiently.

3. Final Answer:

   To share work fairly among drones without a central controller -> Option A

4. Quick Check:

   Distributed task allocation = fair work sharing [OK]

Hint: Remember: share tasks fairly, no single boss drone [OK]

Common Mistakes:

• Thinking one drone does all tasks
• Assuming tasks are assigned randomly
• Believing drones don't communicate

2. Which of the following is the correct way to assign tasks to drones in a round-robin style using Python?

easy

A. task_index * len(drones)

B. len(drones) % task_index

C. task_index + len(drones)

D. task_index % len(drones)

Solution

1. Step 1: Understand round-robin assignment

   Round-robin cycles through drones by using modulo with drone count.

2. Step 2: Apply modulo operator correctly

   Using task_index % len(drones) cycles task indices over drone list indices.

3. Final Answer:

   task_index % len(drones) -> Option D

4. Quick Check:

   Modulo with drone count cycles tasks [OK]

Hint: Use modulo (%) with drone count to cycle tasks [OK]

Common Mistakes:

• Reversing modulo operands
• Adding or multiplying instead of modulo
• Using modulo with wrong variable

3. What will be the output of this code snippet?

tasks = ['scan', 'deliver', 'map', 'charge']
drones = ['droneA', 'droneB']
assignments = {}
for i, task in enumerate(tasks):
    drone = drones[i % len(drones)]
    assignments.setdefault(drone, []).append(task)
print(assignments)

medium

A. {'droneA': ['scan', 'map'], 'droneB': ['deliver', 'charge']}

B. {'droneA': ['scan', 'deliver'], 'droneB': ['map', 'charge']}

C. {'droneA': ['scan'], 'droneB': ['deliver', 'map', 'charge']}

D. {'droneA': ['charge'], 'droneB': ['scan', 'deliver', 'map']}

Solution

1. Step 1: Assign tasks using modulo

   Tasks are assigned to drones cycling through drones list by i % 2.

2. Step 2: Map tasks to drones

   Index 0: 'scan' -> droneA, 1: 'deliver' -> droneB, 2: 'map' -> droneA, 3: 'charge' -> droneB.

3. Final Answer:

   {'droneA': ['scan', 'map'], 'droneB': ['deliver', 'charge']} -> Option A

4. Quick Check:

   Modulo cycles tasks evenly [OK]

Hint: Match task index modulo drone count to assign tasks [OK]

Common Mistakes:

• Mixing task order in assignments
• Ignoring modulo cycling
• Appending tasks to wrong drone

4. Identify the error in this drone task allocation code:

drones = ['D1', 'D2', 'D3']
tasks = ['photo', 'survey', 'deliver']
assignments = {}
for i in range(len(tasks)):
    drone = drones[i // len(drones)]
    assignments.setdefault(drone, []).append(tasks[i])
print(assignments)

medium

A. assignments.setdefault is used incorrectly

B. Using range(len(tasks)) is incorrect for looping

C. Using integer division (//) instead of modulo (%) assigns all tasks to the first drone

D. The drones list should be empty

Solution

1. Step 1: Check drone index calculation

   Using i // len(drones) results in index 0 for i=0,1,2 (len(drones)=3), assigning all tasks to 'D1' instead of cycling round-robin.

2. Step 2: Identify correct operator

   Modulo (%) should be used to cycle through drone indices safely.

3. Final Answer:

   Using integer division (//) instead of modulo (%) assigns all tasks to the first drone -> Option C

4. Quick Check:

   Use modulo (%) to cycle indices [OK]

Hint: Use % not // to cycle through drone indices [OK]

Common Mistakes:

• Confusing // with %
• Thinking range(len(tasks)) is wrong
• Misusing setdefault method

5. You have 3 drones and 7 tasks. You want to assign tasks so each drone gets tasks in a round-robin way but skip any task named 'wait'. Which code snippet correctly implements this?

hard

A. assignments = {}
for i, task in enumerate(tasks):
if task == 'wait':
continue
drone = drones[len(drones) % i]
assignments.setdefault(drone, []).append(task)

B. assignments = {}
for i, task in enumerate(tasks):
drone = drones[i % len(drones)]
if task != 'wait':
assignments.setdefault(drone, []).append(task)

C. assignments = {}
for task in tasks:
if task == 'wait':
continue
drone = drones[tasks.index(task) % len(drones)]
assignments.setdefault(drone, []).append(task)

D. assignments = {}
for i in range(len(tasks)):
if tasks[i] == 'wait':
continue
drone = drones[i // len(drones)]
assignments.setdefault(drone, []).append(tasks[i])

Solution

1. Step 1: Filter out 'wait' tasks correctly

   Check task != 'wait' before assigning to drones.

2. Step 2: Assign tasks using modulo for round-robin

   Use i % len(drones) to cycle drones correctly.

3. Step 3: Avoid using index() inside loop to prevent errors with duplicates

   Using tasks.index(task) can cause wrong drone assignment if tasks repeat.

4. Final Answer:

   assignments = {} for i, task in enumerate(tasks): drone = drones[i % len(drones)] if task != 'wait': assignments.setdefault(drone, []).append(task) -> Option B

5. Quick Check:

   Filter first, then assign with modulo [OK]

Hint: Check task before assign; use modulo for drone cycling [OK]

Common Mistakes:

• Using integer division instead of modulo
• Using tasks.index() causing wrong assignments
• Not skipping 'wait' tasks properly