![\begin{picture}(328,154)(26,660)
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...box(0,0)[lb]{\raisebox{0pt}[0pt][0pt]{\twlrm Transitive Closure}}}
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What nodes can I get to from here?
Train Schedule: can I get from City i to City j somehow?
Warshall's Algorithm: A[i][j] = A[i][k] && A[k][j]
If you can travel to any City from any other City,
what kind of graph is the Transitive Closure?
TC: tc [193]
% gcc -o tc tc.c > tcc tc.c
Data File with Test Case: tc.dat
4 0 1 0 1 0 0 1 0 0 0 0 1 0 0 0 0 % tc tc.dat n: 4 steps: 64 % tc tc.dat graph 1 1 1 1 0 1 1 1 0 0 1 1 0 0 0 1
TC: tc [194]
% tc tc.dat step u v step u v step u v step u v step ------------------------------------------------------------------ 1 1 1 + 1 1 17 + 1 1 33 + 1 1 49 + 1 2 2 + 1 2 18 + 1 2 34 + 1 2 50 + 1 3 3 - 1 3 19 + 1 3 35 + 1 3 51 + 1 4 4 + 1 4 20 + 1 4 36 + 1 4 52 + 2 1 5 - 2 1 21 - 2 1 37 - 2 1 53 - 2 2 6 + 2 2 22 + 2 2 38 + 2 2 54 + 2 3 7 + 2 3 23 + 2 3 39 + 2 3 55 + 2 4 8 - 2 4 24 - 2 4 40 + 2 4 56 + 3 1 9 - 3 1 25 - 3 1 41 - 3 1 57 - 3 2 10 - 3 2 26 - 3 2 42 - 3 2 58 - 3 3 11 + 3 3 27 + 3 3 43 + 3 3 59 + 3 4 12 + 3 4 28 + 3 4 44 + 3 4 60 + 4 1 13 - 4 1 29 - 4 1 45 - 4 1 61 - 4 2 14 - 4 2 30 - 4 2 46 - 4 2 62 - 4 3 15 - 4 3 31 - 4 3 47 - 4 3 63 - 4 4 16 + 4 4 32 + 4 4 48 + 4 4 64 +
TC: tc.c [195]
int A[MAX][MAX], B[MAX][MAX]; /* transitive closure */
int n;
void TC() {
int i, j, k;
/* compute B^0 */
for (i=1; i<=n; i++)
for (j=1; j<=n; j++){
B[i][j] = A[i][j];
}
/* compute B^k for k=1,2,...n */
for (k=1; k<=n; k++)
for (i=1; i<=n; i++)
for (j=1; j<=n; j++)
if (!B[i][j])
B[i][j] = B[i][k] && B[k][j];
}
ANALYSIS: O( )