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Program to find island count by adding blocks into grid one by one in Python
Suppose we have one infinite grid of water. We can add blocks of land to that grid one by one. We have a list of coordinates called land_requests where each coordinate is in the form [r, c] where r is for row and c is for column. We have to find a list where each element represents the number of islands that exist after adding each block of land from land_requests.
So, if the input is like land_requests = [[1, 1],[2, 4],[1, 2],[1, 4],[1, 3]], then the output will be [1, 2, 2, 2, 1] as
To solve this, we will follow these steps −
d := a list of directions like [(−1, 0) ,(0, 1) ,(1, 0) ,(0, −1) ]
idx := 0
mp := a new map
p := a new list
size := a new list
comp := 0
ans := a new list
Define a function search() . This will take u
if u is same as p[u], then
return u
p[u] := search(p[u])
return p[u]
Define a function connect() . This will take u, v
pu := search(u), pv := search(v)
if pu is same as pv, then
return
comp := comp − 1
if size[pu] >= size[pv], then
p[pv] := pu
size[pu] := size[pu] + size[pv]
otherwise,
p[pu] := pv
size[pv] := size[pv] + size[pu]
From the main method do the following −
for each request in land_requests, do
(i, j) := request
mp[i, j] := idx
insert idx at the end of p
insert 1 at the end of size
idx := idx + 1
comp := comp + 1
for each k in d, do
ni := i + k[1]
nj := j + k[0]
if (ni, nj) is in mp, then
connect(mp[(i, j)], mp[(ni, nj)])
insert comp at the end of ans
return ans
Let us see the following implementation to get better understanding −
Example
d = [(−1, 0), (0, 1), (1, 0), (0, −1)] class Solution: def search(self, u): if u == self.p[u]: return u self.p[u] = self.search(self.p[u]) return self.p[u] def connect(self, u, v): pu = self.search(u) pv = self.search(v) if pu == pv: return self.comp −= 1 if self.size[pu] >= self.size[pv]: self.p[pv] = pu self.size[pu] += self.size[pv] else: self.p[pu] = pv self.size[pv] += self.size[pu] def solve(self, land_requests): self.idx = 0 self.mp = dict() self.p = [] self.size = [] self.comp = 0 ans = [] for request in land_requests: i, j = request self.mp[(i, j)] = self.idx self.p.append(self.idx) self.size.append(1) self.idx += 1 self.comp += 1 for k in d: ni = i + k[1] nj = j + k[0] if (ni, nj) in self.mp: self.connect(self.mp[(i, j)], self.mp[(ni, nj)]) ans.append(self.comp) return ans ob = Solution() land_requests = [[1, 1],[2, 4],[1, 2],[1, 4],[1, 3]] print(ob.solve(land_requests))
Input
[[1, 1],[2, 4],[1, 2],[1, 4],[1, 3]]
Output
[1, 2, 2, 2, 1]
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