你好,以下是给代码添加河流最低限制流量的修改版:
from collections import defaultdict
class Graph:
def __init__(self, vertices):
self.graph = defaultdict(dict)
self.V = vertices
def add_edge(self, u, v, capacity):
self.graph[u][v] = capacity
self.graph[v][u] = 0 # Initialize reverse edge with 0 capacity
def bfs(self, parent, s, t):
visited = [False] * (self.V + 1)
queue = []
queue.append(s)
visited[s] = True
while queue:
u = queue.pop(0)
for v in range(1, self.V+1):
if not visited[v] and self.graph[u][v] > 0:
queue.append(v)
visited[v] = True
parent[v] = u
if v == t: # If we reach the sink node
return True
return False
def ford_fulkerson(self, source, sink):
parent = [-1] * (self.V + 1)
max_flow = 0
while self.bfs(parent, source, sink):
path_flow = float('inf')
s = sink
while s != source:
path_flow = min(path_flow, self.graph[parent[s]][s])
s = parent[s]
max_flow += path_flow
v = sink
while v != source:
u = parent[v]
self.graph[u][v] -= path_flow
self.graph[v][u] += path_flow
v = parent[v]
return max_flow
def find_best_water_level(lake_capacities, river_limits_min, river_limits_max, min_water_levels):
num_lakes = len(lake_capacities)
source = 0
sink = num_lakes + 1
graph = Graph(num_lakes + 2)
# Add edges from source to lakes with desired weights
for i in range(1, num_lakes+1):
graph.add_edge(source, i, float('inf'))
# Add edges from lakes to sink with capacities based on river limits
for i in range(1, num_lakes+1):
capacity = int(river_limits_max[i-1] * 10) # Multiply by 10 to get integer capacities for simplicity
graph.add_edge(i, sink, capacity)
# Add edges between lakes based on the flow direction and their respective capacities
for i in range(num_lakes - 1):
graph.add_edge(i+1, i+2, lake_capacities[i])
max_flow = graph.ford_fulkerson(source, sink)
best_water_levels = []
# Calculate best water levels for each lake using the obtained flows and river formula
for i in range(1, num_lakes+1):
upstream_capacity_sum_min = sum([graph.graph[j][i] / 10 for j in range(0,i)])
flow_ratio_min = (upstream_capacity_sum_min + river_limits_min[i-1]) / (river_limits_min[i-1] * 10)
best_water_level_min = flow_ratio_min * (lake_capacities[i-1] - min_water_levels[i-1]) + min_water_levels[i-1]
upstream_capacity_sum_max = sum([graph.graph[j][i] / 10 for j in range(0,i)])
flow_ratio_max = (upstream_capacity_sum_max + river_limits_max[i-1]) / (river_limits_max[i-1] * 10)
best_water_level_max = flow_ratio_max * (lake_capacities[i-1] - min_water_levels[i-1]) + min_water_levels[i-1]
best_water_levels.append((best_water_level_min, best_water_level_max))
return best_water_levels
# 测试样例
lake_capacities = [1000, 2000, 1500, 1200]
river_limits_min = [50, 80, 60, 70]
river_limits_max = [100, 150, 120, 130]
min_water_levels = [400, 1000, 600, 800]
best_levels = find_best_water_level(lake_capacities, river_limits_min, river_limits_max, min_water_levels)
print("Best Water Levels:", best_levels)
在 find_best_water_level
函数中,我们添加了 river_limits_min
和 river_limits_max
参数来表示每条河流的最低和最高限制流量。在添加边的过程中,我们使用 river_limits_max
参数作为边的容量,并相应地修改计算最佳水位的逻辑以考虑这两个参数。
注意:为了简化起见,我们将容量乘以10并将其转换为整数进行处理。请根据实际需求进行调整。
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