All Pair Shortest Paths Instructor Prof JyhShing Roger

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All Pair Shortest Paths Instructor : Prof. Jyh-Shing Roger Jang Designer：Shao-Huan Wang The ideas

All Pair Shortest Paths Instructor : Prof. Jyh-Shing Roger Jang Designer：Shao-Huan Wang The ideas are reference to the textbook “Fundamentals of Data Structures in C “.

All Pair Shortest Path Set a cost adjacency matrix, which blanks are infinite Give

All Pair Shortest Path Set a cost adjacency matrix, which blanks are infinite Give a variable “k” from 0 to n, change all the distance[i][j] if distance[i][j] > distance[i][k] + distance[k][j] K=1 0 LA 4 1 3 2 SF DEN CHI NY 0 250 MIA NO 900 1400 0 1000 0 300 0 1000 800 0 1200 5 0 1500 0 1000 7 BOST 6 1700 0 0

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give a variable “k” from 0 to n, change all the distance[i][j] if distance[i][j] < distance[i][k] + distance[k][j] K=2 LA 4 1 3 2 5 SF DEN 1000+ +1200= =2000 2200< <+∞ +∞ 800 CHI NY 0 250 MIA NO 900 1400 0 1000 0 300 0 1000 800 0 2200 2000 1200 0 1500 0 1000 7 BOST 6 1700 0 0

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give a variable “k” from 0 to n, change all the distance[i][j] if distance[i][j] < distance[i][k] + distance[k][j] K=3 LA 4 1 3 2 5 SF DEN 2200 + 1500 = 3500 2000 3700 < +∞ CHI NY 0 250 MIA NO 900 1400 0 1000 0 300 0 1000 800 0 2200 2000 1200 3700 3500 0 0 1500 1000 7 BOST 6 1700 0 0

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give a variable “k” from 0 to n, change all the distance[i][j] if distance[i][j] < distance[i][k] + distance[k][j] K=3 LA 4 1 3 2 5 0 DEN CHI BOST NY 0 250 MIA NO 900 1400 0 1000 0 300 0 1000 800 0 2200 2000 1200 0 3700 3500 2700 1500 3200 7 SF 1200 2200 + 1500 1000 = 2700 3200 < +∞ 6 1700 1000 0 0

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give a variable “k” from 0 to n, change all the distance[i][j] if distance[i][j] < distance[i][k] + distance[k][j] K=3 LA 4 1 3 2 5 0 7 SF DEN 2000 + 1000 = 2200 1200 3000 < +∞ CHI BOST NY 0 250 MIA NO 900 1400 0 1000 0 300 0 1000 800 0 2200 2000 1200 0 3700 3500 2700 1500 3200 3000 2200 1000 6 1700 0 0

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give a variable “k” from 0 to n, change all the distance[i][j] if distance[i][j] < distance[i][k] + distance[k][j] K=5 4 LA 4 1 3 2 5 0 7 SF DEN 250 + 3000 3200 2200 = 3250 3450 2450 < 3500 3700 2700 CHI BOST NY MIA NO 0 250 1150 0 900 1400 0 1000 0 300 0 1000 800 0 2200 2000 1200 0 3450 3700 3250 3500 2700 2450 1250 3200 3000 2200 1000 6 1700 0

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give a variable “k” from 0 to n, change all the distance[i][j] if distance[i][j] < distance[i][k] + distance[k][j] K=5 LA 4 1 3 2 5 0 7 SF DEN 250 + 900 1000==1150 1250<<+∞ 1500 CHI BOST NY MIA NO 0 250 1150 0 900 1400 0 1000 0 300 0 1000 800 0 2200 2000 1200 0 3450 3250 2450 1250 1500 3200 3000 2200 1000 6 1700 0

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give a variable “k” from 0 to n, change all the distance[i][j] if distance[i][j] < distance[i][k] + distance[k][j] K=5 6 LA 4 1 3 2 5 0 7 SF DEN 250 + 1400 = 1650 < +∞ CHI BOST NY MIA NO 0 250 1150 1650 0 900 1400 0 1000 0 300 0 1000 800 0 2200 2000 1200 0 3450 3250 2450 1250 3200 3000 2200 1000 6 1700 0

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give a variable “k” from 0 to n, change all the distance[i][j] if distance[i][j] < distance[i][k] + distance[k][j] K=7 LA 4 1 3 2 5 0 7 SF DEN 1400 1650 + 1700 = 3100 3350 < 3200 3450 CHI BOST NY MIA NO 0 250 1150 1650 0 900 1400 0 1000 0 300 0 1000 800 0 2200 2000 1200 0 3350 3450 3250 2450 1250 3200 3100 3000 2200 1000 6 1700 0

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give

All Pair Shortest Path Set a cost matrix, which blank spaces are infinite Give a variable “k” from 0 to n, change all the distance[i][j] if distance[i][j] < distance[i][k] + distance[k][j] K=7 LA 4 1 3 2 5 0 7 6 SF DEN 1000 + 1700 = 2700 < +∞ CHI BOST NY MIA NO 0 250 1150 1650 0 900 1400 0 1000 0 300 0 1000 800 0 2200 2000 1200 0 3350 3250 2450 1250 3100 3000 2200 1000 2700 1700 0

AllPairs Shortest Paths Allpairs Shortest Paths GV EVnAllPairs Shortest Paths Allpairs Shortest Paths GV EVn
AllPairs Shortest Paths Allpairs Shortest Paths GV EVnAllPairs Shortest Paths Allpairs Shortest Paths GV EVn
Shortest Paths Shortest Paths Problem Instance A digraphShortest Paths Shortest Paths Problem Instance A digraph
Shortest paths Algorithms and Networks Shortest paths ContentsShortest paths Algorithms and Networks Shortest paths Contents
SingleSource Shortest Paths Problem Definition Shortest paths andSingleSource Shortest Paths Problem Definition Shortest paths and
Shortest Paths A 8 B 2 Shortest PathsShortest Paths A 8 B 2 Shortest Paths
Chapter 24 SingleSource Shortest Paths Shortest Paths HowChapter 24 SingleSource Shortest Paths Shortest Paths How
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