47 lines
1.7 KiB
Markdown
47 lines
1.7 KiB
Markdown
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---
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title: Floyd Warshall Algorithm
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localeTitle: Floyd Warshall Algorithm
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---
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## Floyd Warshall Algorithm
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خوارزمية Floyd Warshall هي خوارزمية رائعة للعثور على أقصر مسافة بين جميع الرؤوس في الرسم البياني. يحتوي على خوارزمية موجزة جداً و O (V ^ 3) تعقيد وقت (حيث V عدد الرؤوس). يمكن استخدامه مع الأوزان السلبية ، على الرغم من أن دورات الوزن السلبية يجب ألا تكون موجودة في الرسم البياني.
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### تقييم
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تعقيد الفضاء: O (V ^ 2)
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تعقيد وقت حالة أسوأ: O (V ^ 3)
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### تنفيذ بايثون
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`# A large value as infinity
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inf = 1e10
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def floyd_warshall(weights):
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V = len(weights)
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distance_matrix = weights
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for k in range(V):
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next_distance_matrix = [list(row) for row in distance_matrix] # make a copy of distance matrix
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for i in range(V):
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for j in range(V):
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# Choose if the k vertex can work as a path with shorter distance
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next_distance_matrix[i][j] = min(distance_matrix[i][j], distance_matrix[i][k] + distance_matrix[k][j])
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distance_matrix = next_distance_matrix # update
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return distance_matrix
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# A graph represented as Adjacency matrix
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graph = [
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[0, inf, inf, -3],
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[inf, 0, inf, 8],
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[inf, 4, 0, -2],
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[5, inf, 3, 0]
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]
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print(floyd_warshall(graph))
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`
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#### معلومات اكثر:
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[الرسوم البيانية](https://github.com/freecodecamp/guides/computer-science/data-structures/graphs/index.md)
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[فلويد وارهال - ويكيبيديا](https://en.wikipedia.org/wiki/Floyd%E2%80%93Warshall_algorithm)
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