Please help explain the loop invariant for the code above. Why does this code work? Provide proof of correctness using a loop invariant technique.(Note you need to provide the loop invariant, then prove that it is correct during initiation, maintenance, and termination).
Types of Linked List
A sequence of data elements connected through links is called a linked list (LL). The elements of a linked list are nodes containing data and a reference to the next node in the list. In a linked list, the elements are stored in a non-contiguous manner and the linear order in maintained by means of a pointer associated with each node in the list which is used to point to the subsequent node in the list.
Linked List
When a set of items is organized sequentially, it is termed as list. Linked list is a list whose order is given by links from one item to the next. It contains a link to the structure containing the next item so we can say that it is a completely different way to represent a list. In linked list, each structure of the list is known as node and it consists of two fields (one for containing the item and other one is for containing the next item address).
class Solution:
def minCostConnectPoints(self, points: List[List[int]]) -> int:
# start a visited set and min heap
vis = set()
min_heap = [(0,points[0])]
res = 0
while min_heap:
for _ in range(len(min_heap)):
# check if point at top of heap is not already visited
while tuple(min_heap[0][1]) in vis:
heapq.heappop(min_heap)
dist, point = heapq.heappop(min_heap)
# add distance to the result and add that point to the visited set
res += dist
vis.add(tuple(point))
# we'll stop when the len of visited set becomes equal to length of all points
if len(vis) == len(points):
return res
for i in range(len(points)):
if points[i] == point or tuple(points[i]) in vis:
continue
# add distance of points in the heap along with the point
heapq.heappush(min_heap, (abs(points[i][0] - point[0]) + abs(points[i][1] - point[1]), points[i]))
Please help explain the loop invariant for the code above.
Why does this code work? Provide proof of correctness using a loop invariant technique.(Note you need to provide the loop invariant, then prove that it is correct during initiation, maintenance, and termination).
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
