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Floyd 演算法介紹

Floyd 演算法介紹. M0224005 劉奕顯. Floyd 演算法 (1/8). 完全最短路徑問題 (All-pairs shortest-paths problem) ：找到每個節點到其他所有節點的最短距離 距離矩陣：記錄最短路徑的長度. Floyd 演算法 (2/8). 生成距離矩陣 代表從第 i 個節點到第 j 個節點的最短路徑的長度， 且路徑中經過的中間節點數量不大於 k 當 時. Floyd 演算法 (3/8). Floyd 演算法 (4/8). Floyd 演算法 (5/8).

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Floyd 演算法介紹

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  1. Floyd演算法介紹 M0224005 劉奕顯

  2. Floyd演算法(1/8) • 完全最短路徑問題(All-pairs shortest-paths problem)：找到每個節點到其他所有節點的最短距離 • 距離矩陣：記錄最短路徑的長度

  3. Floyd演算法(2/8) • 生成距離矩陣 • 代表從第i個節點到第j個節點的最短路徑的長度， 且路徑中經過的中間節點數量不大於k • 當 時

  4. Floyd演算法(3/8)

  5. Floyd演算法(4/8)

  6. Floyd演算法(5/8)

  7. Floyd演算法(6/8)

  8. Floyd演算法(7/8)

  9. Floyd演算法(8/8) Floyd（W [1..n, 1..n]） //輸入：圖形的加權矩陣W //輸出：最短路徑長度的距離矩陣D D← W for k ← 1 to n do for i ← 1 to n do for j ← 1 to n do D[i,j] ← min{ D[i,j] , D[i,k]＋D[k,j] } return D

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