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4. Please use the Floyd-Warshall Algorithm to find the shortest paths for every two vertices. You need to show the shortest distance matrix and shortest path matrix in each iteration.

          4. Please use the Floyd-Warshall Algorithm to find the shortest paths for every two vertices. You need to show the shortest distance matrix and shortest path matrix in each iteration.
        
4. Please use the Floyd-Warshall Algorithm to find the shortest paths for every two vertices. You need to show the shortest distance matrix and shortest path matrix in each iteration.

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Computer Science and Information Technology
Computer Science and Information Technology
Trishna Knowledge Systems 2018 Edition
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Please use the Floyd-Warshall Algorithm to find the shortest paths for every two vertices. You need to show the shortest distance matrix and shortest path matrix in each iteration. 3 10
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Transcript

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00:01 Hello, as in this question we have to find shortest distance between a and h vertices.
00:06 So if we start from a, b, c, d, e, f, g and h.
00:15 These are our given vertices.
00:16 If we start from a, as we are here at a, so other vertices distance are equals to infinite.
00:24 So here we plot infinite as the smallest point is here 0.
00:30 So if we start from a here and this one we select.
00:34 Now come to the next vertices as we are here.
00:38 If we go to vertices b, then here cover up distance is 1.
00:43 So as here is 0.
00:44 If we start from a, then distance from a to b is 1 and a to c is 2.
00:51 And all other distance are from a are equals to infinite because we only go to b and c.
00:59 So as from 1 and 2 our minimum value is 1.
01:03 So we select here b.
01:05 So as now here we are at point b, 0 and 1.
01:09 These are already selected.
01:11 So here is 0 and here is 1.
01:13 These are already selected.
01:14 If we go to point c, then cover distance from a to c is 2.
01:20 And if we go from b, we can go to from b to d.
01:25 So cover up distance is 1 and 3.
01:27 So total is 4.
01:29 So this one is from d to 4 and from e, this one is 1 and 4, 5.
01:34 So here we can go to d.
01:35 So cover distance is 4 and 1 plus 4 equals to 5.
01:40 And rest distance are equals to infinite here.
01:43 As we can see our smallest value is here 2.
01:46 So here we select 2.
01:47 Now as here 0, 1, 0, 1, 2 are already selected.
01:55 So now come to point c.
01:57 A, b, c.
01:58 Here we can go a, b, c.
02:00 So start from a.
02:01 Here we can go to c as here c is already selected, b is already selected.
02:07 So here if we go to d, so total cover distance is 4 which is minimum.
02:12 So here is 4.
02:13 And if we go to here e, so cover distance is 2 plus 6 is 8 and 1 plus 4 equals to 5.
02:20 So smallest distance is 5 here and if we go to here, other points are infinite.
02:27 So if we select here, smallest value is here our 4.
02:31 So here we select 4 and rest values are, we can write here 0, 1, 2 and 4 are already selected.
02:40 And as here we add point b here.
02:42 So now come to other points.
02:46 So from d we can go to here e which is 1 plus 3 plus 9 which is 4, 9, 13 here...
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