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46 changes: 46 additions & 0 deletions partition-labels.py
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Original file line number Diff line number Diff line change
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class Solution:
def partitionLabels(self, s: str) -> List[int]:
# last positions
last = {}
for i,c in enumerate(s):
last[c]=i
# {c:i for i,c in enumerate(s)}
# {'a': 8, 'b': 5, 'c': 7, 'd': 14, 'e': 15, 'f': 11, 'g': 13, 'h': 19, 'i': 22, 'j': 23, 'k': 20, 'l': 21}
start = 0 #16
end = 0 #23
output = [] #9,7,8
# end = 8
# 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
# "a b a b c b a c a d e f e g d e h i j h k l i j"
# i
for i,c in enumerate(s):
end = max(end,last[c])
if i == end:
output.append(end-start+1)
start = i+1
return output


# 3. Visualizing the Guarantee: "ababcc"
# Let's see why it's mathematically impossible for a letter to leak out, using the example s = "ababcc" where last = {'a': 2, 'b': 3, 'c': 5}.

# i = 0, c = 'a': last['a'] is 2. end becomes max(0, 2) = 2. The partition must go to at least index 2.

# i = 1, c = 'b': last['b'] is 3. end becomes max(2, 3) = 3. Because 'b' sneaked in, our boundary is forced to stretch further out to index 3.

# i = 2, c = 'a': last['a'] is 2. end becomes max(3, 2) = 3. No expansion needed.

# i = 3, c = 'b': last['b'] is 3. end becomes max(3, 3) = 3.

# At this exact moment, i == end (3 == 3).

# Why is this the perfect moment to snap the partition?
# Think about what it means when i finally catches up to end:

# We have successfully examined every single character from start to i.

# For every single one of those characters, we checked where its final duplicate lives.

# None of them had a final duplicate living anywhere past index i (otherwise, end would have been pushed past i, and i == end wouldn't be true).

# Because no character inside our current window has a twin waiting for it down the line, we can safely snap the partition shut knowing it is a completely isolated island. We log the size, reset start = i + 1, and begin building the next island.
167 changes: 167 additions & 0 deletions task-scheduler.py
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class Solution:
def leastInterval(self, tasks: List[str], n: int) -> int:
count = Counter(tasks)
# Counter({'A': 3, 'B': 3})
maxHeap=[]
for cnt in count.values():
maxHeap.append(-cnt)
# maxHeap = [-2,-3]
heapq.heapify(maxHeap)
time = 0 # 1
q = collections.deque()
# q=[[-2,3]]
while maxHeap or q:
time += 1
if maxHeap:
cnt = 1 + heapq.heappop(maxHeap)
# cnt = -2
if cnt:
q.append([cnt,time+n])
if q and q[0][1] == time:
heapq.heappush(maxHeap, q.popleft()[0])

return time



--- SIMULATION START ---

⏰ [Time = 1] Loop condition evaluated: 'while maxHeap or q' is TRUE because:
-> Elements in Heap? True (Frequencies: [3, 3])
-> Elements in Queue? False (Queue: [])

❓ Checking condition: 'if maxHeap:'
✅ TRUE: There is at least one task type available to run.
👉 Action: Popped task from heap (had 3 remaining). It is now executing.
❓ Checking sub-condition: 'if cnt:' (Are there more copies of this task left? New count = 2)
✅ TRUE: 2 copies remain. Sending task to cooldown queue.
👉 Calculation: Current Time (1) + Cooldown (2) = Available again at Time 3

❓ Checking condition: 'if q and q[0][1] == time:'
... Queue has items. Checking if the front task's ready time (3) matches Current Time (1)...
❌ FALSE: The front task isn't ready yet. It needs to wait until Time = 3.

📊 End of Tick 1 Status -> Heap: [3] | Queue: [[2, 3]]
------------------------------------------------------------

⏰ [Time = 2] Loop condition evaluated: 'while maxHeap or q' is TRUE because:
-> Elements in Heap? True (Frequencies: [3])
-> Elements in Queue? True (Queue: [[2, 3]])

❓ Checking condition: 'if maxHeap:'
✅ TRUE: There is at least one task type available to run.
👉 Action: Popped task from heap (had 3 remaining). It is now executing.
❓ Checking sub-condition: 'if cnt:' (Are there more copies of this task left? New count = 2)
✅ TRUE: 2 copies remain. Sending task to cooldown queue.
👉 Calculation: Current Time (2) + Cooldown (2) = Available again at Time 4

❓ Checking condition: 'if q and q[0][1] == time:'
... Queue has items. Checking if the front task's ready time (3) matches Current Time (2)...
❌ FALSE: The front task isn't ready yet. It needs to wait until Time = 3.

📊 End of Tick 2 Status -> Heap: [] | Queue: [[2, 3], [2, 4]]
------------------------------------------------------------

⏰ [Time = 3] Loop condition evaluated: 'while maxHeap or q' is TRUE because:
-> Elements in Heap? False (Frequencies: [])
-> Elements in Queue? True (Queue: [[2, 3], [2, 4]])

❓ Checking condition: 'if maxHeap:'
❌ FALSE: The heap is completely empty. The CPU has no choice but to sit IDLE this turn.

❓ Checking condition: 'if q and q[0][1] == time:'
... Queue has items. Checking if the front task's ready time (3) matches Current Time (3)...
✅ TRUE: The task at the front of the queue has finished its cooldown!
👉 Action: Popping from Queue and pushing 2 copies back into the Max Heap.

📊 End of Tick 3 Status -> Heap: [2] | Queue: [[2, 4]]
------------------------------------------------------------

⏰ [Time = 4] Loop condition evaluated: 'while maxHeap or q' is TRUE because:
-> Elements in Heap? True (Frequencies: [2])
-> Elements in Queue? True (Queue: [[2, 4]])

❓ Checking condition: 'if maxHeap:'
✅ TRUE: There is at least one task type available to run.
👉 Action: Popped task from heap (had 2 remaining). It is now executing.
❓ Checking sub-condition: 'if cnt:' (Are there more copies of this task left? New count = 1)
✅ TRUE: 1 copies remain. Sending task to cooldown queue.
👉 Calculation: Current Time (4) + Cooldown (2) = Available again at Time 6

❓ Checking condition: 'if q and q[0][1] == time:'
... Queue has items. Checking if the front task's ready time (4) matches Current Time (4)...
✅ TRUE: The task at the front of the queue has finished its cooldown!
👉 Action: Popping from Queue and pushing 2 copies back into the Max Heap.

📊 End of Tick 4 Status -> Heap: [2] | Queue: [[1, 6]]
------------------------------------------------------------

⏰ [Time = 5] Loop condition evaluated: 'while maxHeap or q' is TRUE because:
-> Elements in Heap? True (Frequencies: [2])
-> Elements in Queue? True (Queue: [[1, 6]])

❓ Checking condition: 'if maxHeap:'
✅ TRUE: There is at least one task type available to run.
👉 Action: Popped task from heap (had 2 remaining). It is now executing.
❓ Checking sub-condition: 'if cnt:' (Are there more copies of this task left? New count = 1)
✅ TRUE: 1 copies remain. Sending task to cooldown queue.
👉 Calculation: Current Time (5) + Cooldown (2) = Available again at Time 7

❓ Checking condition: 'if q and q[0][1] == time:'
... Queue has items. Checking if the front task's ready time (6) matches Current Time (5)...
❌ FALSE: The front task isn't ready yet. It needs to wait until Time = 6.

📊 End of Tick 5 Status -> Heap: [] | Queue: [[1, 6], [1, 7]]
------------------------------------------------------------

⏰ [Time = 6] Loop condition evaluated: 'while maxHeap or q' is TRUE because:
-> Elements in Heap? False (Frequencies: [])
-> Elements in Queue? True (Queue: [[1, 6], [1, 7]])

❓ Checking condition: 'if maxHeap:'
❌ FALSE: The heap is completely empty. The CPU has no choice but to sit IDLE this turn.

❓ Checking condition: 'if q and q[0][1] == time:'
... Queue has items. Checking if the front task's ready time (6) matches Current Time (6)...
✅ TRUE: The task at the front of the queue has finished its cooldown!
👉 Action: Popping from Queue and pushing 1 copies back into the Max Heap.

📊 End of Tick 6 Status -> Heap: [1] | Queue: [[1, 7]]
------------------------------------------------------------

⏰ [Time = 7] Loop condition evaluated: 'while maxHeap or q' is TRUE because:
-> Elements in Heap? True (Frequencies: [1])
-> Elements in Queue? True (Queue: [[1, 7]])

❓ Checking condition: 'if maxHeap:'
✅ TRUE: There is at least one task type available to run.
👉 Action: Popped task from heap (had 1 remaining). It is now executing.
❓ Checking sub-condition: 'if cnt:' (Are there more copies of this task left? New count = 0)
❌ FALSE: That was the absolute last copy of this task type. It is completely finished!

❓ Checking condition: 'if q and q[0][1] == time:'
... Queue has items. Checking if the front task's ready time (7) matches Current Time (7)...
✅ TRUE: The task at the front of the queue has finished its cooldown!
👉 Action: Popping from Queue and pushing 1 copies back into the Max Heap.

📊 End of Tick 7 Status -> Heap: [1] | Queue: []
------------------------------------------------------------

⏰ [Time = 8] Loop condition evaluated: 'while maxHeap or q' is TRUE because:
-> Elements in Heap? True (Frequencies: [1])
-> Elements in Queue? False (Queue: [])

❓ Checking condition: 'if maxHeap:'
✅ TRUE: There is at least one task type available to run.
👉 Action: Popped task from heap (had 1 remaining). It is now executing.
❓ Checking sub-condition: 'if cnt:' (Are there more copies of this task left? New count = 0)
❌ FALSE: That was the absolute last copy of this task type. It is completely finished!

❓ Checking condition: 'if q and q[0][1] == time:'
❌ FALSE: The cooldown queue is completely empty. Nothing to bring back.

📊 End of Tick 8 Status -> Heap: [] | Queue: []
------------------------------------------------------------

--- SIMULATION END ---
Total Time Required: 8