Find the shortest path from a to z

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Find the shortest path from a to z 3 b 3 3 2 g

Find the shortest path from a to z 3 b 3 3 2 g d 2 1 h 6 a 3 z e 6 1 3 c 8 8 f 1 9 i 3

Label all vertices as ∞ and put vertex a in the vertex list. b

Label all vertices as ∞ and put vertex a in the vertex list. b 3 ∞ ∞ g d 3 2 2 ∞ a 6 8 9 f ∞ Vertex List: 1 ∞ 3 ∞ 1 3 8 1 h e 6 c ∞ 3 i 3 ∞ ∞ a: 0 b: ∞ c: ∞ d: ∞ e: ∞ f: ∞ g: ∞ h: ∞ i: ∞ z

Re-label all vertices that can be reached from a b 3 2(a) ∞ g

Re-label all vertices that can be reached from a b 3 2(a) ∞ g d 3 2 2 6(a) a 6 8 9 f 3(a) Vertex List: 1 ∞ 3 ∞ 1 3 8 1 h e 6 c ∞ 3 i 3 ∞ ∞ a: 0 b: 2 c: 3 d: ∞ e: 6 f: ∞ g: ∞ h: ∞ i: ∞ z

Choose the unvisited vertex with the smallest label, in this case b. b 3

Choose the unvisited vertex with the smallest label, in this case b. b 3 2(a) ∞ g d 3 2 2 6(a) a 6 8 9 f 3(a) Vertex List: 1 ∞ 3 ∞ 1 3 8 1 h e 6 c ∞ 3 i 3 ∞ ∞ a: 0 b: 2 c: 3 d: ∞ e: 6 f: ∞ g: ∞ h: ∞ i: ∞ z

Re-label all vertices that can be reached from b now. b 3 2(a) 5(a,

Re-label all vertices that can be reached from b now. b 3 2(a) 5(a, b) g d 3 2 2 5(a, b) a 6 8 9 f 3(a) Vertex List: 1 ∞ 3 ∞ 1 3 8 1 h e 6 c ∞ 3 i 3 ∞ ∞ a: 0 b: 2 c: 3 d: 5 e: 6 5 f: ∞ g: ∞ h: ∞ i: ∞ z

Choose the unvisited vertex with the smallest label, now c. b 3 2(a) 5(a,

Choose the unvisited vertex with the smallest label, now c. b 3 2(a) 5(a, b) g d 3 2 2 5(a, b) a 6 8 9 f 3(a) Vertex List: 1 ∞ 3 ∞ 1 3 8 1 h e 6 c ∞ 3 i 3 ∞ ∞ a: 0 b: 2 c: 3 d: 5 e: 5 f: ∞ g: ∞ h: ∞ i: ∞ z

Re-label, now including c b 3 2(a) 5(a, b) g d 3 2 2

Re-label, now including c b 3 2(a) 5(a, b) g d 3 2 2 5(a, b) a 6 8 9 f 3(a) Vertex List: 1 ∞ 3 ∞ 1 3 8 1 h e 6 c ∞ 3 i 3 4(a, c) ∞ a: 0 b: 2 c: 3 d: 5 e: 5 f: 4 g: ∞ h: ∞ i: ∞ z

Choose the smallest unvisited vertex, f b 3 2(a) 5(a, b) g d 3

Choose the smallest unvisited vertex, f b 3 2(a) 5(a, b) g d 3 2 2 5(a, b) a 6 8 9 f 3(a) Vertex List: 1 ∞ 3 ∞ 1 3 8 1 h e 6 c ∞ 3 i 3 4(a, c) ∞ a: 0 b: 2 c: 3 d: 5 e: 5 f: 4 g: ∞ h: ∞ i: ∞ z

Re-label, now using f b 3 2(a) 5(a, b) g d 3 2 2

Re-label, now using f b 3 2(a) 5(a, b) g d 3 2 2 5(a, b) a 6 8 9 f 3(a) Vertex List: 1 ∞ 3 12(a, c, f) 1 3 8 1 h e 6 c ∞ 3 i 3 4(a, c) 7(a, c, f) a: 0 b: 2 c: 3 d: 5 e: 5 f: 4 g: ∞ h: 12 i: 7 z: ∞ z

Smallest unvisited vertex is now d (alphabetical tie over e) b 3 2(a) 5(a,

Smallest unvisited vertex is now d (alphabetical tie over e) b 3 2(a) 5(a, b) g d 3 2 2 5(a, b) a 6 8 9 f 3(a) Vertex List: 1 ∞ 3 12(a, c, f) 1 3 8 1 h e 6 c ∞ 3 i 3 4(a, c) 7(a, c, f) a: 0 b: 2 c: 3 d: 5 e: 5 f: 4 g: ∞ h: 12 i: 7 z: ∞ z

Re-label using d b 3 2(a) 5(a, b) g 2 5(a, b) a 6

Re-label using d b 3 2(a) 5(a, b) g 2 5(a, b) a 6 8 9 f 3(a) Vertex List: 1 ∞ 3 12(a, c, f) 1 3 8 1 h e 6 c 8(a, b, d) d 3 2 3 i 3 4(a, c) 7(a, c, f) a: 0 b: 2 c: 3 d: 5 e: 5 f: 4 g: 8 h: 12 i: 7 z: ∞ z

Smallest unvisited vertex is now e b 3 2(a) 5(a, b) g 2 5(a,

Smallest unvisited vertex is now e b 3 2(a) 5(a, b) g 2 5(a, b) a 6 8 9 f 3(a) Vertex List: 1 ∞ 3 12(a, c, f) 1 3 8 1 h e 6 c 8(a, b, d) d 3 2 3 i 3 4(a, c) 7(a, c, f) a: 0 b: 2 c: 3 d: 5 e: 5 f: 4 g: 8 h: 12 i: 7 z: ∞ z

Re-label using e, but no vertex gets updated b 3 2(a) 5(a, b) g

Re-label using e, but no vertex gets updated b 3 2(a) 5(a, b) g 2 5(a, b) a 6 8 9 f 3(a) Vertex List: 1 ∞ 3 12(a, c, f) 1 3 8 1 h e 6 c 8(a, b, d) d 3 2 3 i 3 4(a, c) 7(a, c, f) a: 0 b: 2 c: 3 d: 5 e: 5 f: 4 g: 8 h: 12 i: 7 z: ∞ z

Smallest unvisited vertex is i b 3 2(a) 5(a, b) g 2 5(a, b)

Smallest unvisited vertex is i b 3 2(a) 5(a, b) g 2 5(a, b) a 6 8 9 f 3(a) Vertex List: 1 ∞ 3 12(a, c, f) 1 3 8 1 h e 6 c 8(a, b, d) d 3 2 3 i 3 4(a, c) 7(a, c, f) a: 0 b: 2 c: 3 d: 5 e: 5 f: 4 g: 8 h: 12 i: 7 z: ∞ z

Re-label using i b 3 2(a) 5(a, b) g 2 5(a, b) a 6

Re-label using i b 3 2(a) 5(a, b) g 2 5(a, b) a 6 8 Vertex List: 1 16(a, c, f, i) z 9 f 3(a) 3 12(a, c, f) 1 3 8 1 h e 6 c 8(a, b, d) d 3 2 3 i 3 4(a, c) 7(a, c, f) a: 0 b: 2 c: 3 d: 5 e: 5 f: 4 g: 8 h: 12 i: 7 z: 16

Now, choose g b 3 2(a) 5(a, b) g 2 5(a, b) a 6

Now, choose g b 3 2(a) 5(a, b) g 2 5(a, b) a 6 8 Vertex List: 1 16(a, c, f, i) z 9 f 3(a) 3 12(a, c, f) 1 3 8 1 h e 6 c 8(a, b, d) d 3 2 3 i 3 4(a, c) 7(a, c, f) a: 0 b: 2 c: 3 d: 5 e: 5 f: 4 g: 8 h: 12 i: 7 z: 16

Re-label, using g b 3 2(a) 5(a, b) g 2 5(a, b) a 6

Re-label, using g b 3 2(a) 5(a, b) g 2 5(a, b) a 6 8 Vertex List: 1 16(a, c, f, i) z 9 f 3(a) 3 9(a, b, d, g) 1 3 8 1 h e 6 c 8(a, b, d) d 3 2 3 i 3 4(a, c) 7(a, c, f) a: 0 b: 2 c: 3 d: 5 f: 4 g: 8 h: 12 9 i: 7 e: 5 z: 16

Now choose h b 3 2(a) 5(a, b) g 2 5(a, b) a 6

Now choose h b 3 2(a) 5(a, b) g 2 5(a, b) a 6 8 Vertex List: 1 16(a, c, f, i) z 9 f 3(a) 3 9(a, b, d, g) 1 3 8 1 h e 6 c 8(a, b, d) d 3 2 3 i 3 4(a, c) 7(a, c, f) a: 0 b: 2 c: 3 d: 5 e: 5 f: 4 g: 8 h: 9 i: 7 z: 16

Re-label using h b 3 2(a) 5(a, b) g 2 5(a, b) a 6

Re-label using h b 3 2(a) 5(a, b) g 2 5(a, b) a 6 8 Vertex List: 1 12(a, b, d, g, h) z 9 f 3(a) 3 9(a, b, d, g) 1 3 8 1 h e 6 c 8(a, b, d) d 3 2 3 i 3 4(a, c) 7(a, c, f) a: 0 b: 2 c: 3 d: 5 e: 5 f: 4 g: 8 h: 9 i: 7 z: 16 12

No vertices left to consider, so we have the shortest path b 3 2(a)

No vertices left to consider, so we have the shortest path b 3 2(a) 5(a, b) g 2 5(a, b) a 6 8 Vertex List: 1 12(a, b, d, g, h) z 9 f 3(a) 3 9(a, b, d, g) 1 3 8 1 h e 6 c 8(a, b, d) d 3 2 3 i 3 4(a, c) 7(a, c, f) a: 0 b: 2 c: 3 d: 5 e: 5 f: 4 g: 8 h: 9 i: 7 z: 16 12

Dijkstras Shortest Path Algorithm Find shortest path fromDijkstras Shortest Path Algorithm Find shortest path from
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Dijkstras Shortest Path Algorithm Find shortest path fromDijkstras Shortest Path Algorithm Find shortest path from
Dijkstras Shortest Path Algorithm Find shortest path fromDijkstras Shortest Path Algorithm Find shortest path from
Dijkstras Shortest Path Algorithm Find shortest path fromDijkstras Shortest Path Algorithm Find shortest path from
Dijkstras Shortest Path Algorithm Find shortest path fromDijkstras Shortest Path Algorithm Find shortest path from
Dijkstras Shortest Path Algorithm Find shortest path fromDijkstras Shortest Path Algorithm Find shortest path from
Dijkstras Shortest Path Algorithm Find shortest path fromDijkstras Shortest Path Algorithm Find shortest path from
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