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difference-between-maximum-and-minimum-price-sum.py
177 lines (164 loc) · 5.34 KB
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difference-between-maximum-and-minimum-price-sum.py
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# Time: O(n)
# Space: O(n)
# iterative dfs, tree dp
class Solution(object):
def maxOutput(self, n, edges, price):
"""
:type n: int
:type edges: List[List[int]]
:type price: List[int]
:rtype: int
"""
def iter_dfs():
result = 0
stk = [(1, (0, -1, [price[0], 0]))]
while stk:
step, args = stk.pop()
if step == 1:
u, p, ret = args
stk.append((2, (u, p, ret, 0)))
elif step == 2:
u, p, ret, i = args
if i == len(adj[u]):
continue
stk.append((2, (u, p, ret, i+1)))
v = adj[u][i]
if v == p:
continue
new_ret = [price[v], 0] # [max_path_sum, max_path_sum_without_last_node]
stk.append((3, (u, new_ret, ret)))
stk.append((1, (v, u, new_ret)))
elif step == 3:
u, new_ret, ret = args
result = max(result, ret[0]+new_ret[1], ret[1]+new_ret[0])
ret[0] = max(ret[0], new_ret[0]+price[u])
ret[1] = max(ret[1], new_ret[1]+price[u])
return result
adj = [[] for _ in xrange(n)]
for u, v in edges:
adj[u].append(v)
adj[v].append(u)
return iter_dfs()
# Time: O(n)
# Space: O(n)
# dfs, tree dp
class Solution2(object):
def maxOutput(self, n, edges, price):
"""
:type n: int
:type edges: List[List[int]]
:type price: List[int]
:rtype: int
"""
def dfs(u, p):
dp = [price[u], 0] # [max_path_sum, max_path_sum_without_last_node]
for v in adj[u]:
if v == p:
continue
new_dp = dfs(v, u)
result[0] = max(result[0], dp[0]+new_dp[1], dp[1]+new_dp[0])
dp[0] = max(dp[0], new_dp[0]+price[u])
dp[1] = max(dp[1], new_dp[1]+price[u])
return dp
result = [0]
adj = [[] for _ in xrange(n)]
for u, v in edges:
adj[u].append(v)
adj[v].append(u)
dfs(0, -1)
return result[0]
# Time: O(n)
# Space: O(n)
# iterative dfs, tree dp
class Solution3(object):
def maxOutput(self, n, edges, price):
"""
:type n: int
:type edges: List[List[int]]
:type price: List[int]
:rtype: int
"""
def iter_dfs():
dp = [0]*n # max_sum
stk = [(1, 0, -1)]
while stk:
step, u, p = stk.pop()
if step == 1:
stk.append((2, u, p))
for v in adj[u]:
if v == p:
continue
stk.append((1, v, u))
elif step == 2:
dp[u] = price[u]
for v in adj[u]:
if v == p:
continue
dp[u] = max(dp[u], dp[v]+price[u])
return dp
def iter_dfs2():
result = 0
stk = [(0, -1, 0)]
while stk:
u, p, curr = stk.pop()
result = max(result, curr, dp[u]-price[u])
top2 = [[curr, p], [0, -1]]
for v in adj[u]:
if v == p:
continue
curr = [dp[v], v]
for i in xrange(len(top2)):
if curr > top2[i]:
top2[i], curr = curr, top2[i]
for v in adj[u]:
if v == p:
continue
stk.append((v, u, (top2[0][0] if top2[0][1] != v else top2[1][0])+price[u]))
return result
adj = [[] for _ in xrange(n)]
for u, v in edges:
adj[u].append(v)
adj[v].append(u)
dp = iter_dfs()
return iter_dfs2()
# Time: O(n)
# Space: O(n)
# dfs, tree dp
class Solution4(object):
def maxOutput(self, n, edges, price):
"""
:type n: int
:type edges: List[List[int]]
:type price: List[int]
:rtype: int
"""
def dfs(u, p):
dp[u] = price[u]
for v in adj[u]:
if v == p:
continue
dp[u] = max(dp[u], dfs(v, u)+price[u])
return dp[u]
def dfs2(u, p, curr):
result[0] = max(result[0], curr, dp[u]-price[u])
top2 = [[curr, p], [0, -1]]
for v in adj[u]:
if v == p:
continue
curr = [dp[v], v]
for i in xrange(len(top2)):
if curr > top2[i]:
top2[i], curr = curr, top2[i]
for v in adj[u]:
if v == p:
continue
dfs2(v, u, (top2[0][0] if top2[0][1] != v else top2[1][0])+price[u])
result = [0]
dp = [0]*n # max_sum
adj = [[] for _ in xrange(n)]
for u, v in edges:
adj[u].append(v)
adj[v].append(u)
dfs(0, -1)
dfs2(0, -1, 0)
return result[0]