def leastInterval(self, tasks, n):
"""
Solution: Calculating Idle Slot
Time Complexity: O(n)
Space Complexity: O(n)
Inspired By: MySELF!! (684ms, beat 20.24%)
:type tasks: List[str]
:type n: int
:rtype: int
"""
freq2task_map = collections.Counter(tasks)
max_freq = max(freq2task_map.values())
base_sec = []
for k, v in freq2task_map.iteritems():
if v == max_freq:
base_sec.append(k)
for key in base_sec:
freq2task_map.pop(key)
res = len(base_sec)
_heap = []
for i in range(max_freq-1):
pq.heappush(_heap, (len(base_sec), base_sec[:]))
freq2task_map = [(k, v) for k, v in freq2task_map.iteritems()]
while freq2task_map:
k, v = freq2task_map.pop()
for i in range(v):
sec_len, sec = pq.heappop(_heap)
sec.append(k)
pq.heappush(_heap, (1 + sec_len, sec))
while _heap:
sec_len, sec = _heap.pop()
res += max(n+1, sec_len)
return res
def mincostToHireWorkers(self, quality, wage, K):
"""
Solution: Heap
Time Complexity: O(nlog(n))
Space Complexity: O(n)
Perf: Runtime: 424 ms, faster than 31.63% / Memory Usage: 14.1 MB, less than 12.00%
Inspired By:
- https://leetcode.com/problems/minimum-cost-to-hire-k-workers/discuss/237268/Python-heap-solution-with-clean-code-and-explanation
- https://leetcode.com/problems/minimum-cost-to-hire-k-workers/solution/
TP:
- Using wage[i]/quality[i] as sorting points
:type quality: List[int]
:type wage: List[int]
:type K: int
:rtype: float
"""
m = len(quality)
wkr_ratio = []
for i in range(m):
wkr_ratio.append((float(wage[i]) / quality[i], quality[i]))
wkr_ratio.sort()
h = []
min_cost = float('inf')
total_qua = 0
for ratio, qua in wkr_ratio:
total_qua += qua
pq.heappush(h, -qua)
if len(h) == K:
min_cost = min(min_cost, total_qua * ratio)
elif len(h) > K:
total_qua += pq.heappop(h)
min_cost = min(min_cost, total_qua * ratio)
return min_cost
def findCheapestPrice(self, n, flights, src, dst, K):
"""
Solution: BFS + Dijsktra
Time Complexity:
Space Complexity: O(n) (n: heap length)
Inspired By:
- https://leetcode.com/problems/cheapest-flights-within-k-stops/solution/
- https://leetcode.com/problems/cheapest-flights-within-k-stops/discuss/115541/JavaPython-Priority-Queue-Solution
TP:
- Using Dijkstra Algorithm but at same time keep the stops under K
:type n: int
:type flights: List[List[int]]
:type src: int
:type dst: int
:type K: int
:rtype: int
"""
graph = collections.defaultdict(dict)
for u, v, w in flights:
graph[u][v] = w
best = dict()
pq = [(0, 0, src)]
while pq:
curr_cost, curr_stop, curr_city = pq.heappop(pq)
if curr_stop > K+1 or curr_cost > best.get((curr_stop, curr_city), float('inf')):
continue
if curr_city == dst:
return curr_cost
for next_stop, cost in graph[curr_city].iteritems():
new_cost = cost + curr_cost
if new_cost < best.get((curr_stop+1, dst), float('inf')):
best[(curr_stop+1, next_stop)] = new_cost
pq.heappush(pq, (new_cost, curr_stop + 1, next_stop))
return -1
def minPathSum(self, grid):
"""
Solution: Dijkestra
Time Complexity:
Space Complexity: O(m*n)
Inspired By: MySELF!!
TP:
- In this question we are not allowed to go up or left
:type grid: List[List[int]]
:rtype: int
"""
pq = []
pq.heappush(pq, (grid[0][0], (0, 0)))
visited = set()
m = len(grid)
n = len(grid[0])
#directions = [(-1, 0),(0, -1), (1, 0), (0, 1)]
directions = [(1, 0), (0, 1)]
while pq:
cost, cord = pq.heappop(pq)
i, j = cord
if not (i, j) in visited:
visited.add(cord)
if (i, j) == (m - 1, n - 1):
return cost
else:
for x_dir, y_dir in directions:
x = x_dir + cord[0]
y = y_dir + cord[1]
if 0 <= x < m and 0 <= y < n:
pq.heappush(pq, (cost + grid[x][y], (x, y)))
def trapRainWater(self, heightMap):
"""
Solution: Heap (Priority Q)
Time Complexity: O(m*n)
Space Complexity: O(m*n)
Inspired By:
- https://leetcode.com/problems/trapping-rain-water-ii/discuss/89466/python-solution-with-heap
- https://www.youtube.com/watch?time_continue=7&v=cJayBq38VYw
TP:
- first we have to define "how to trap a water"
- since all border can't "trap" any water, we can put all border elements into the heapQ
- The we go through the following procedure:
- pop from heapQ (the pop will give us lowest height cell)
- visit all its 'unvisited neighbor'
- if neighbor's height is smaller than 'pop' height, means we can trap water, so add the height diff to res
- then we push this neighbor into heap
- !!! Tricky: we need to update this neighbor's height with max(height_of_neighbor, height_pop)
- WHY ?? --> if neighbor's height is smaller, then we already add the 'trap' water during this iteration
thus next time when its 'neighbor' turn from heapQ we can have correct amount of water
- consider this:
5 7 3 <-- current pop is 7
4 6 1 <-- visit neighbor 6, collect water 7-6 = 1, push 6 with height of 7 into heap
6 5 7 <-- next time when pop 6 and visit neighbor 5, neighbor should able to trap water 7 - 5 = 2
7 7 8
- Since we start from lowest point from all borders, we can guarantee for following procedure the water will be trapped correctly
:type heightMap: List[List[int]]
:rtype: int
"""
if not heightMap or not heightMap[0]: return 0
import pq
m = len(heightMap)
n = len(heightMap[0])
visited = [[False for _ in range(n)] for _ in range(m)]
res = 0
heap = []
for i in range(m):
for j in range(n):
if i == 0 or i == m-1 or j == 0 or j == n-1:
pq.heappush(heap, (heightMap[i][j], i, j))
visited[i][j] = True
while heap:
height, i, j = pq.heappop(heap)
for x, y in [(i-1, j), (i+1, j), (i, j-1), (i, j+1)]:
if 0 <= x < m and 0 <= y < n and not visited[x][y]:
res += max(0, height - heightMap[x][y])
pq.heappush(heap, (max(heightMap[x][y], height), x, y))
visited[x][y] = True
return res
def findMinCost(self, numTotalAvailableCities, numTotalAvailableRoads, roadsAvailable, numNewRoadsConstruct, costNewRoadsConstruct):
UF = UnionFind(numTotalAvailableCities, roadsAvailable)
candidate_road = []
for city1, city2, cost in costNewRoadsConstruct:
pq.heappush(candidate_road, (cost, city1, city2))
res = 0
while numTotalAvailableRoads < numTotalAvailableCities-1:
cost, city1, city2 = pq.heappop(candidate_road)
r1 = UF.find(city1)
r2 = UF.find(city2)
if r1 != r2:
UF.union(city1, city2)
numTotalAvailableRoads += 1
res += cost
return res
def mergeKSortedLists(self, lists):
"""
Time: O(nlog(k))
Space: O(n)
:param lists:
:return:
"""
pq = []
res = []
for idx, list in enumerate(lists):
pq.heappush(pq, (list.pop(0), idx))
while pq:
val, idx = pq.heappop(pq)
res.append(val)
if lists[idx]:
pq.heappush(pq, (lists[idx].pop(0), idx))
return res
def minMeetingRooms(self, intervals):
"""
Solution: Heapq + Sorting
Time Complexity: O(nlog(n))
Space Complexity: O(n)
Perf: Runtime: 80 ms, faster than 22.20% / Memory Usage: 17.9 MB, less than 5.35%
Inspired By: https://leetcode.com/problems/meeting-rooms-ii/solution/
:type intervals: List[Interval]
:rtype: int
"""
intervals.sort(key=lambda x: x.start)
schedule = []
for interval in intervals:
if not schedule:
schedule.append(interval.end)
else:
if interval.start >= schedule[0]:
pq.heappushpop(schedule, interval.end)
else:
pq.heappush(schedule, interval.end)
return len(schedule)
def mergeKLists(self, lists):
"""
Time: O(nlog(k)) n: number of nodes, k: len of lists
Perf: Runtime: 108 ms, faster than 57.15% / Memory Usage: 17.6 MB, less than 38.93%
:type lists: List[ListNode]
:rtype: ListNode
"""
if not lists:
return None
stack = []
head = ListNode(None)
start = head
for node in lists:
if node:
pq.heappush(stack, (node.val, node))
while stack:
val, curNode = pq.heappop(stack)
head.next = curNode
if curNode.next:
pq.heappush(stack, (curNode.next.val, curNode.next))
head = head.next
return start.next
def nthUglyNumber(self, n):
"""
Facebook
T:O(nlogn) S:O(n)
Solution: heapq (priority queue)
Time Complexity: O(3*n)
Space Complexity: O(3*n)
Perf: Runtime: 896 ms, faster than 8.14% / Memory Usage: 10.9 MB, less than 35.21%
Inspired By: MySELF!!
:type n: int
:rtype: int
"""
cand = [1]
for i in range(n - 1):
k = pq.heappop(cand)
if k * 2 not in cand:
pq.heappush(cand, k * 2)
if k * 3 not in cand:
pq.heappush(cand, k * 3)
if k * 5 not in cand:
pq.heappush(cand, k * 5)
return pq.heappop(cand)
def sortNArray(self, nums1, nums2, nums3):
"""
Time Complexity: O(nlog(k))
Space Complexity: O(k)
:param nums1:
:param nums2:
:param nums3:
:return:
"""
pq = []
res = []
if nums1:
pq.heappush(pq, (nums1.pop(0), 1))
if nums2:
pq.heappush(pq, (nums2.pop(0), 2))
if nums3:
pq.heappush(pq, (nums3.pop(0), 3))
while pq:
num, arrayIdx = pq.heappop(pq)
if num not in res:
res.append(num)
if arrayIdx == 1:
if nums1:
pq.heappush(pq, (nums1.pop(0), 1))
elif arrayIdx == 2:
if nums2:
pq.heappush(pq, (nums2.pop(0), 2))
else:
if nums3:
pq.heappush(pq, (nums3.pop(0), 3))
return res
