From 15810110b90f0f1a2c2c646c4fb312424436e956 Mon Sep 17 00:00:00 2001
From: Pedram_Mohajer <48964282+pedram-mohajer@users.noreply.github.com>
Date: Sat, 25 Nov 2023 20:03:46 -0500
Subject: [PATCH 01/16] Create smallestRange.py
---
greedy_methods/smallestRange.py | 59 +++++++++++++++++++++++++++++++++
1 file changed, 59 insertions(+)
create mode 100644 greedy_methods/smallestRange.py
diff --git a/greedy_methods/smallestRange.py b/greedy_methods/smallestRange.py
new file mode 100644
index 000000000000..db6586a95bc8
--- /dev/null
+++ b/greedy_methods/smallestRange.py
@@ -0,0 +1,59 @@
+import doctest
+import heapq
+
+def smallest_range(nums):
+ """
+ Finds the smallest range that includes at least one number from each of the k lists.
+
+ The function uses a min heap to efficiently find the smallest range.
+ Each time, it pops the smallest element from the heap and adds the next element
+ from the same list to maintain the invariant of having one element from each list in the heap.
+
+ Args:
+ nums (list of list of int): A list of k lists of sorted integers in non-decreasing order.
+
+ Returns:
+ list: A list containing two integers representing the smallest range.
+
+ Examples:
+ >>> smallest_range([[4,10,15,24,26], [0,9,12,20], [5,18,22,30]])
+ [20, 24]
+ >>> smallest_range([[1,2,3], [1,2,3], [1,2,3]])
+ [1, 1]
+ """
+
+ # Create a min heap to store the first element from each list
+ min_heap = []
+ current_max = float('-inf')
+
+ # Initialize the heap with the first element from each list
+ for i, list_ in enumerate(nums):
+ heapq.heappush(min_heap, (list_[0], i, 0))
+ current_max = max(current_max, list_[0])
+
+ # Initialize the smallest range as the largest possible
+ smallest_range = [float('-inf'), float('inf')]
+
+ while min_heap:
+ current_min, list_index, element_index = heapq.heappop(min_heap)
+
+ # Update the smallest range if the current range is smaller
+ if current_max - current_min < smallest_range[1] - smallest_range[0]:
+ smallest_range = [current_min, current_max]
+
+ # Break if rreaching the end of one of the lists
+ if element_index == len(nums[list_index]) - 1:
+ break
+
+ # Add the next element from the same list to the heap
+ next_element = nums[list_index][element_index + 1]
+ heapq.heappush(min_heap, (next_element, list_index, element_index + 1))
+ current_max = max(current_max, next_element)
+
+ return smallest_range
+
+if __name__ == "__main__":
+ doctest.testmod()
+ example1 = [[4,10,15,24,26], [0,9,12,20], [5,18,22,30]]
+ output1 = smallest_range(example1)
+ print("Smallest Range:", output1) # Smallest Range: [20, 24]
From d1fc4bfb4ed70ade8e2fe484a7a36c3c7c6853ec Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
<66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 26 Nov 2023 01:09:50 +0000
Subject: [PATCH 02/16] [pre-commit.ci] auto fixes from pre-commit.com hooks
for more information, see https://pre-commit.ci
---
greedy_methods/smallestRange.py | 8 +++++---
1 file changed, 5 insertions(+), 3 deletions(-)
diff --git a/greedy_methods/smallestRange.py b/greedy_methods/smallestRange.py
index db6586a95bc8..6be2aaa681d2 100644
--- a/greedy_methods/smallestRange.py
+++ b/greedy_methods/smallestRange.py
@@ -1,6 +1,7 @@
import doctest
import heapq
+
def smallest_range(nums):
"""
Finds the smallest range that includes at least one number from each of the k lists.
@@ -24,7 +25,7 @@ def smallest_range(nums):
# Create a min heap to store the first element from each list
min_heap = []
- current_max = float('-inf')
+ current_max = float("-inf")
# Initialize the heap with the first element from each list
for i, list_ in enumerate(nums):
@@ -32,7 +33,7 @@ def smallest_range(nums):
current_max = max(current_max, list_[0])
# Initialize the smallest range as the largest possible
- smallest_range = [float('-inf'), float('inf')]
+ smallest_range = [float("-inf"), float("inf")]
while min_heap:
current_min, list_index, element_index = heapq.heappop(min_heap)
@@ -52,8 +53,9 @@ def smallest_range(nums):
return smallest_range
+
if __name__ == "__main__":
doctest.testmod()
- example1 = [[4,10,15,24,26], [0,9,12,20], [5,18,22,30]]
+ example1 = [[4, 10, 15, 24, 26], [0, 9, 12, 20], [5, 18, 22, 30]]
output1 = smallest_range(example1)
print("Smallest Range:", output1) # Smallest Range: [20, 24]
From 920de41d5137a631f9fdf7f05be250b879cc0d50 Mon Sep 17 00:00:00 2001
From: Pedram_Mohajer <48964282+pedram-mohajer@users.noreply.github.com>
Date: Sat, 25 Nov 2023 20:13:37 -0500
Subject: [PATCH 03/16] Update smallestRange.py
---
greedy_methods/smallestRange.py | 4 ++++
1 file changed, 4 insertions(+)
diff --git a/greedy_methods/smallestRange.py b/greedy_methods/smallestRange.py
index 6be2aaa681d2..463a596f2d18 100644
--- a/greedy_methods/smallestRange.py
+++ b/greedy_methods/smallestRange.py
@@ -1,3 +1,7 @@
+"""
+https://medium.com/@saiashish3760/leetcode-q632-smallest-range-covering-elements-from-k-lists-q507-496c21157914
+"""
+
import doctest
import heapq
From f7b3c7cea42a196260825a037e95f1e50e8914b4 Mon Sep 17 00:00:00 2001
From: Pedram_Mohajer <48964282+pedram-mohajer@users.noreply.github.com>
Date: Sat, 25 Nov 2023 20:15:25 -0500
Subject: [PATCH 04/16] Update smallestRange.py
---
greedy_methods/smallestRange.py | 11 +++++++----
1 file changed, 7 insertions(+), 4 deletions(-)
diff --git a/greedy_methods/smallestRange.py b/greedy_methods/smallestRange.py
index 463a596f2d18..b19624b5028c 100644
--- a/greedy_methods/smallestRange.py
+++ b/greedy_methods/smallestRange.py
@@ -8,14 +8,17 @@
def smallest_range(nums):
"""
- Finds the smallest range that includes at least one number from each of the k lists.
+ Finds the smallest range that includes at least one number
+ from each of the k lists.
The function uses a min heap to efficiently find the smallest range.
- Each time, it pops the smallest element from the heap and adds the next element
- from the same list to maintain the invariant of having one element from each list in the heap.
+ Each time, it pops the smallest element from the
+ heap and adds the next element from the same list to
+ maintain the invariant of having one element from each list in the heap.
Args:
- nums (list of list of int): A list of k lists of sorted integers in non-decreasing order.
+ nums (list of list of int): A list of k lists of sorted integers
+ in non-decreasing order.
Returns:
list: A list containing two integers representing the smallest range.
From 63a111f9dfcdf390dc1608ba97beb1d67e11e2ef Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
<66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 26 Nov 2023 01:16:01 +0000
Subject: [PATCH 05/16] [pre-commit.ci] auto fixes from pre-commit.com hooks
for more information, see https://pre-commit.ci
---
greedy_methods/smallestRange.py | 8 ++++----
1 file changed, 4 insertions(+), 4 deletions(-)
diff --git a/greedy_methods/smallestRange.py b/greedy_methods/smallestRange.py
index b19624b5028c..6624b88e0bb9 100644
--- a/greedy_methods/smallestRange.py
+++ b/greedy_methods/smallestRange.py
@@ -8,16 +8,16 @@
def smallest_range(nums):
"""
- Finds the smallest range that includes at least one number
+ Finds the smallest range that includes at least one number
from each of the k lists.
The function uses a min heap to efficiently find the smallest range.
- Each time, it pops the smallest element from the
- heap and adds the next element from the same list to
+ Each time, it pops the smallest element from the
+ heap and adds the next element from the same list to
maintain the invariant of having one element from each list in the heap.
Args:
- nums (list of list of int): A list of k lists of sorted integers
+ nums (list of list of int): A list of k lists of sorted integers
in non-decreasing order.
Returns:
From b0ab04082fae1e13c5129087c75744ba59b56cd7 Mon Sep 17 00:00:00 2001
From: Pedram_Mohajer <48964282+pedram-mohajer@users.noreply.github.com>
Date: Sat, 25 Nov 2023 20:28:02 -0500
Subject: [PATCH 06/16] Update smallestRange.py
---
greedy_methods/smallestRange.py | 38 +++++++++++----------------------
1 file changed, 13 insertions(+), 25 deletions(-)
diff --git a/greedy_methods/smallestRange.py b/greedy_methods/smallestRange.py
index 6624b88e0bb9..fa97e2bb82c3 100644
--- a/greedy_methods/smallestRange.py
+++ b/greedy_methods/smallestRange.py
@@ -1,27 +1,21 @@
"""
https://medium.com/@saiashish3760/leetcode-q632-smallest-range-covering-elements-from-k-lists-q507-496c21157914
"""
-
import doctest
import heapq
+import sys
-
-def smallest_range(nums):
+def smallest_range(nums: list[list[int]]) -> list[int]:
"""
- Finds the smallest range that includes at least one number
- from each of the k lists.
-
- The function uses a min heap to efficiently find the smallest range.
- Each time, it pops the smallest element from the
- heap and adds the next element from the same list to
- maintain the invariant of having one element from each list in the heap.
+ Find the smallest range from each list in nums.
+
+ Uses min heap for efficiency. The range includes at least one number from each list.
Args:
- nums (list of list of int): A list of k lists of sorted integers
- in non-decreasing order.
+ nums (list of list of int): List of k sorted integer lists.
Returns:
- list: A list containing two integers representing the smallest range.
+ list: Smallest range as a two-element list.
Examples:
>>> smallest_range([[4,10,15,24,26], [0,9,12,20], [5,18,22,30]])
@@ -30,39 +24,33 @@ def smallest_range(nums):
[1, 1]
"""
- # Create a min heap to store the first element from each list
- min_heap = []
- current_max = float("-inf")
+ min_heap: list[tuple[int, int, int]] = []
+ current_max = -sys.maxsize - 1
- # Initialize the heap with the first element from each list
for i, list_ in enumerate(nums):
heapq.heappush(min_heap, (list_[0], i, 0))
current_max = max(current_max, list_[0])
- # Initialize the smallest range as the largest possible
- smallest_range = [float("-inf"), float("inf")]
+ # Initialize smallest_range with large integer values
+ smallest_range = [-sys.maxsize - 1, sys.maxsize]
while min_heap:
current_min, list_index, element_index = heapq.heappop(min_heap)
- # Update the smallest range if the current range is smaller
if current_max - current_min < smallest_range[1] - smallest_range[0]:
smallest_range = [current_min, current_max]
- # Break if rreaching the end of one of the lists
if element_index == len(nums[list_index]) - 1:
break
- # Add the next element from the same list to the heap
next_element = nums[list_index][element_index + 1]
heapq.heappush(min_heap, (next_element, list_index, element_index + 1))
current_max = max(current_max, next_element)
return smallest_range
-
if __name__ == "__main__":
doctest.testmod()
- example1 = [[4, 10, 15, 24, 26], [0, 9, 12, 20], [5, 18, 22, 30]]
+ example1 = [[4,10,15,24,26], [0,9,12,20], [5,18,22,30]]
output1 = smallest_range(example1)
- print("Smallest Range:", output1) # Smallest Range: [20, 24]
+ print("Smallest Range:", output1) # Output: [20, 24]
From 5a9fcdd11ddc4348d82454584dcb1e18ef0188a8 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
<66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Sun, 26 Nov 2023 01:28:37 +0000
Subject: [PATCH 07/16] [pre-commit.ci] auto fixes from pre-commit.com hooks
for more information, see https://pre-commit.ci
---
greedy_methods/smallestRange.py | 6 ++++--
1 file changed, 4 insertions(+), 2 deletions(-)
diff --git a/greedy_methods/smallestRange.py b/greedy_methods/smallestRange.py
index fa97e2bb82c3..96480efba816 100644
--- a/greedy_methods/smallestRange.py
+++ b/greedy_methods/smallestRange.py
@@ -5,10 +5,11 @@
import heapq
import sys
+
def smallest_range(nums: list[list[int]]) -> list[int]:
"""
Find the smallest range from each list in nums.
-
+
Uses min heap for efficiency. The range includes at least one number from each list.
Args:
@@ -49,8 +50,9 @@ def smallest_range(nums: list[list[int]]) -> list[int]:
return smallest_range
+
if __name__ == "__main__":
doctest.testmod()
- example1 = [[4,10,15,24,26], [0,9,12,20], [5,18,22,30]]
+ example1 = [[4, 10, 15, 24, 26], [0, 9, 12, 20], [5, 18, 22, 30]]
output1 = smallest_range(example1)
print("Smallest Range:", output1) # Output: [20, 24]
From dec45ffd0b57c31a84149a3d0445801550c4e94b Mon Sep 17 00:00:00 2001
From: Pedram_Mohajer <48964282+pedram-mohajer@users.noreply.github.com>
Date: Sat, 25 Nov 2023 20:31:14 -0500
Subject: [PATCH 08/16] Update and rename smallestRange.py to smallestrange.py
---
greedy_methods/{smallestRange.py => smallestrange.py} | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
rename greedy_methods/{smallestRange.py => smallestrange.py} (96%)
diff --git a/greedy_methods/smallestRange.py b/greedy_methods/smallestrange.py
similarity index 96%
rename from greedy_methods/smallestRange.py
rename to greedy_methods/smallestrange.py
index 96480efba816..4919094aae17 100644
--- a/greedy_methods/smallestRange.py
+++ b/greedy_methods/smallestrange.py
@@ -55,4 +55,4 @@ def smallest_range(nums: list[list[int]]) -> list[int]:
doctest.testmod()
example1 = [[4, 10, 15, 24, 26], [0, 9, 12, 20], [5, 18, 22, 30]]
output1 = smallest_range(example1)
- print("Smallest Range:", output1) # Output: [20, 24]
+ print("smallest range:", output1) # Output: [20, 24]
From c2fdc3f6f75715159c204f1f091b01bdf62c45a9 Mon Sep 17 00:00:00 2001
From: Pedram_Mohajer <48964282+pedram-mohajer@users.noreply.github.com>
Date: Wed, 29 Nov 2023 18:02:14 -0500
Subject: [PATCH 09/16] Update smallestrange.py
---
greedy_methods/smallestrange.py | 3 ---
1 file changed, 3 deletions(-)
diff --git a/greedy_methods/smallestrange.py b/greedy_methods/smallestrange.py
index 4919094aae17..678b9fe4f30d 100644
--- a/greedy_methods/smallestrange.py
+++ b/greedy_methods/smallestrange.py
@@ -1,6 +1,3 @@
-"""
-https://medium.com/@saiashish3760/leetcode-q632-smallest-range-covering-elements-from-k-lists-q507-496c21157914
-"""
import doctest
import heapq
import sys
From 961c2f1ed96d6a48e159bf7e41cdd661adf27de0 Mon Sep 17 00:00:00 2001
From: Pedram_Mohajer <48964282+pedram-mohajer@users.noreply.github.com>
Date: Thu, 30 Nov 2023 08:37:51 -0500
Subject: [PATCH 10/16] Update smallestrange.py
---
greedy_methods/smallestrange.py | 7 +++++++
1 file changed, 7 insertions(+)
diff --git a/greedy_methods/smallestrange.py b/greedy_methods/smallestrange.py
index 678b9fe4f30d..01b75cdab757 100644
--- a/greedy_methods/smallestrange.py
+++ b/greedy_methods/smallestrange.py
@@ -1,3 +1,10 @@
+"""
+ smallest_range function takes a list of sorted integer lists and
+ finds the smallest range that includes at least one number from each list,
+ using a min heap for efficiency.
+"""
+
+
import doctest
import heapq
import sys
From 104037c7ed34ee59cde6551d53eb3ad24f133b0d Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
<66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Thu, 30 Nov 2023 13:39:50 +0000
Subject: [PATCH 11/16] [pre-commit.ci] auto fixes from pre-commit.com hooks
for more information, see https://pre-commit.ci
---
greedy_methods/smallestrange.py | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)
diff --git a/greedy_methods/smallestrange.py b/greedy_methods/smallestrange.py
index 01b75cdab757..4109e3c13af0 100644
--- a/greedy_methods/smallestrange.py
+++ b/greedy_methods/smallestrange.py
@@ -1,6 +1,6 @@
"""
smallest_range function takes a list of sorted integer lists and
- finds the smallest range that includes at least one number from each list,
+ finds the smallest range that includes at least one number from each list,
using a min heap for efficiency.
"""
From 7901221b928f0816af5c8b99f60ae192a92e6487 Mon Sep 17 00:00:00 2001
From: Pedram_Mohajer <48964282+pedram-mohajer@users.noreply.github.com>
Date: Thu, 30 Nov 2023 08:43:16 -0500
Subject: [PATCH 12/16] Update smallestrange.py
---
greedy_methods/smallestrange.py | 7 +++----
1 file changed, 3 insertions(+), 4 deletions(-)
diff --git a/greedy_methods/smallestrange.py b/greedy_methods/smallestrange.py
index 4109e3c13af0..c579b55501d5 100644
--- a/greedy_methods/smallestrange.py
+++ b/greedy_methods/smallestrange.py
@@ -1,10 +1,9 @@
"""
- smallest_range function takes a list of sorted integer lists and
- finds the smallest range that includes at least one number from each list,
- using a min heap for efficiency.
+smallest_range function takes a list of sorted integer lists and
+finds the smallest range that includes at least one number from each list,
+using a min heap for efficiency.
"""
-
import doctest
import heapq
import sys
From 06f64b7a6b5eabedd74056fdf88861d0200458c2 Mon Sep 17 00:00:00 2001
From: Pedram_Mohajer <48964282+pedram-mohajer@users.noreply.github.com>
Date: Thu, 30 Nov 2023 08:55:12 -0500
Subject: [PATCH 13/16] Rename smallestrange.py to smallest_range.py
---
greedy_methods/{smallestrange.py => smallest_range.py} | 0
1 file changed, 0 insertions(+), 0 deletions(-)
rename greedy_methods/{smallestrange.py => smallest_range.py} (100%)
diff --git a/greedy_methods/smallestrange.py b/greedy_methods/smallest_range.py
similarity index 100%
rename from greedy_methods/smallestrange.py
rename to greedy_methods/smallest_range.py
From 8ac97c9831916b59bf8c4c8ff169d4c0c083042f Mon Sep 17 00:00:00 2001
From: Pedram_Mohajer <48964282+pedram-mohajer@users.noreply.github.com>
Date: Fri, 1 Dec 2023 10:47:59 -0500
Subject: [PATCH 14/16] Update smallest_range.py
From 5f29c6b2598c52e5d2ebeb43eefde0877a68da4b Mon Sep 17 00:00:00 2001
From: Christian Clauss <cclauss@me.com>
Date: Fri, 1 Dec 2023 17:21:23 +0100
Subject: [PATCH 15/16] Update smallest_range.py
---
greedy_methods/smallest_range.py | 40 +++++++++++++++-----------------
1 file changed, 19 insertions(+), 21 deletions(-)
diff --git a/greedy_methods/smallest_range.py b/greedy_methods/smallest_range.py
index c579b55501d5..eeb47b0cb322 100644
--- a/greedy_methods/smallest_range.py
+++ b/greedy_methods/smallest_range.py
@@ -1,12 +1,10 @@
"""
-smallest_range function takes a list of sorted integer lists and
-finds the smallest range that includes at least one number from each list,
-using a min heap for efficiency.
+smallest_range function takes a list of sorted integer lists and finds the smallest
+range that includes at least one number from each list, using a min heap for efficiency.
"""
-import doctest
-import heapq
-import sys
+from heapq import heappop, heappush
+from sys import maxsize
def smallest_range(nums: list[list[int]]) -> list[int]:
@@ -16,30 +14,30 @@ def smallest_range(nums: list[list[int]]) -> list[int]:
Uses min heap for efficiency. The range includes at least one number from each list.
Args:
- nums (list of list of int): List of k sorted integer lists.
+ nums: List of k sorted integer lists.
Returns:
- list: Smallest range as a two-element list.
+ Smallest range as a two-element list.
Examples:
- >>> smallest_range([[4,10,15,24,26], [0,9,12,20], [5,18,22,30]])
+ >>> smallest_range([[4, 10, 15, 24, 26], [0, 9, 12, 20], [5, 18, 22, 30]])
[20, 24]
- >>> smallest_range([[1,2,3], [1,2,3], [1,2,3]])
+ >>> smallest_range([[1, 2, 3], [1, 2, 3], [1, 2, 3]])
[1, 1]
"""
min_heap: list[tuple[int, int, int]] = []
- current_max = -sys.maxsize - 1
+ current_max = -maxsize - 1
- for i, list_ in enumerate(nums):
- heapq.heappush(min_heap, (list_[0], i, 0))
- current_max = max(current_max, list_[0])
+ for i, items in enumerate(nums):
+ heappush(min_heap, (items[0], i, 0))
+ current_max = max(current_max, items[0])
# Initialize smallest_range with large integer values
- smallest_range = [-sys.maxsize - 1, sys.maxsize]
+ smallest_range = [-maxsize - 1, maxsize]
while min_heap:
- current_min, list_index, element_index = heapq.heappop(min_heap)
+ current_min, list_index, element_index = heappop(min_heap)
if current_max - current_min < smallest_range[1] - smallest_range[0]:
smallest_range = [current_min, current_max]
@@ -48,14 +46,14 @@ def smallest_range(nums: list[list[int]]) -> list[int]:
break
next_element = nums[list_index][element_index + 1]
- heapq.heappush(min_heap, (next_element, list_index, element_index + 1))
+ heappush(min_heap, (next_element, list_index, element_index + 1))
current_max = max(current_max, next_element)
return smallest_range
if __name__ == "__main__":
- doctest.testmod()
- example1 = [[4, 10, 15, 24, 26], [0, 9, 12, 20], [5, 18, 22, 30]]
- output1 = smallest_range(example1)
- print("smallest range:", output1) # Output: [20, 24]
+ from doctest import testmod
+
+ testmod()
+ print(f"{smallest_range([[1, 2, 3], [1, 2, 3], [1, 2, 3]])}") # Output: [1, 1]
From 4cf8821aca59dfbc53bf727dcca62083244b4d67 Mon Sep 17 00:00:00 2001
From: Christian Clauss <cclauss@me.com>
Date: Fri, 1 Dec 2023 17:51:06 +0100
Subject: [PATCH 16/16] Update smallest_range.py
---
greedy_methods/smallest_range.py | 14 +++++++++++++-
1 file changed, 13 insertions(+), 1 deletion(-)
diff --git a/greedy_methods/smallest_range.py b/greedy_methods/smallest_range.py
index eeb47b0cb322..e2b7f8d7e96a 100644
--- a/greedy_methods/smallest_range.py
+++ b/greedy_methods/smallest_range.py
@@ -17,13 +17,25 @@ def smallest_range(nums: list[list[int]]) -> list[int]:
nums: List of k sorted integer lists.
Returns:
- Smallest range as a two-element list.
+ list: Smallest range as a two-element list.
Examples:
>>> smallest_range([[4, 10, 15, 24, 26], [0, 9, 12, 20], [5, 18, 22, 30]])
[20, 24]
>>> smallest_range([[1, 2, 3], [1, 2, 3], [1, 2, 3]])
[1, 1]
+ >>> smallest_range(((1, 2, 3), (1, 2, 3), (1, 2, 3)))
+ [1, 1]
+ >>> smallest_range(((-3, -2, -1), (0, 0, 0), (1, 2, 3)))
+ [-1, 1]
+ >>> smallest_range([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
+ [3, 7]
+ >>> smallest_range([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
+ [0, 0]
+ >>> smallest_range([[], [], []])
+ Traceback (most recent call last):
+ ...
+ IndexError: list index out of range
"""
min_heap: list[tuple[int, int, int]] = []