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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]...

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)

find_best_water_level 函数中,我们添加了 river_limits_minriver_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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