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Updated exercise 4.4.37
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@reneargento
reneargento committed Mar 4, 2024
1 parent 7aa3ff7 commit 0e7ead4
Showing 1 changed file with 53 additions and 40 deletions.
93 changes: 53 additions & 40 deletions src/chapter4/section4/Exercise37_CriticalEdges.java
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Original file line number Diff line number Diff line change
Expand Up @@ -8,7 +8,9 @@
/**
* Created by Rene Argento on 18/12/17.
*/
//Based on http://bababadalgharaghtakamminarronnkonnbro.blogspot.com.br/2012/06/interviewstreet-going-office.html
// Based on http://bababadalgharaghtakamminarronnkonnbro.blogspot.com.br/2012/06/interviewstreet-going-office.html
// Thanks to qiuhaha (https://github.com/qiuhaha) for reporting a bug on the getIslands() method.
// https://github.com/reneargento/algorithms-sedgewick-wayne/issues/303
public class Exercise37_CriticalEdges {

// O(E lg V)
Expand All @@ -25,7 +27,6 @@ public DirectedEdge getCriticalEdge(EdgeWeightedDigraph edgeWeightedDigraph, int

// 2- Get shortest paths from source
DijkstraSP dijkstraSP = new DijkstraSP(edgeWeightedDigraph, source);

if (!dijkstraSP.hasPathTo(target)) {
return null;
}
Expand All @@ -36,7 +37,7 @@ public DirectedEdge getCriticalEdge(EdgeWeightedDigraph edgeWeightedDigraph, int
// 4- Get the islands in the graph.
// The i-th island is the set of all vertices v, such that there exists a shortest path
// from source to v using no more than i shortest-path vertices.
int[] islands = getIslands(edgeWeightedDigraph, dijkstraSP, source, target);
int[] islands = getIslands(reverseDigraph, dijkstraSP, target);

// 5- Compute bypass path lengths
SegmentTree bypassPathLengths = computeBypassPathLengths(edgeWeightedDigraph, islands, dijkstraSP,
Expand All @@ -46,48 +47,47 @@ public DirectedEdge getCriticalEdge(EdgeWeightedDigraph edgeWeightedDigraph, int
return getCriticalEdge(bypassPathLengths, dijkstraSP, target);
}

private int[] getIslands(EdgeWeightedDigraph edgeWeightedDigraph, DijkstraSP dijkstraSP, int source, int target) {
int[] islands = new int[edgeWeightedDigraph.vertices()];

for (int vertex = 0; vertex < edgeWeightedDigraph.vertices(); vertex++) {
private int[] getIslands(EdgeWeightedDigraph reverseDigraph, DijkstraSP dijkstraSP, int target) {
int[] islands = new int[reverseDigraph.vertices()];
for (int vertex = 0; vertex < reverseDigraph.vertices(); vertex++) {
islands[vertex] = -1;
}

boolean[] isInShortestPath = new boolean[reverseDigraph.vertices()];
int islandId = 0;

for (DirectedEdge edge : dijkstraSP.pathTo(target)) {
if (islands[edge.from()] == -1) {
islands[edge.from()] = islandId++;
}

islands[edge.to()] = islandId++;
isInShortestPath[edge.from()] = true;
isInShortestPath[edge.to()] = true;
}

// Do a breadth-first walk to find the island number of vertices that are not on the shortest path
// from source to target.
// These vertices are on a path from source to target that is not a shortest path.
boolean[] visited = new boolean[edgeWeightedDigraph.vertices()];
boolean[] visited = new boolean[reverseDigraph.vertices()];
Queue<Integer> queue = new Queue<>();
queue.enqueue(source);
visited[source] = true;
queue.enqueue(target);
visited[target] = true;

while (!queue.isEmpty()) {
int currentVertex = queue.dequeue();

for (DirectedEdge edge : edgeWeightedDigraph.adjacent(currentVertex)) {
for (DirectedEdge edge : reverseDigraph.adjacent(currentVertex)) {
int neighbor = edge.to();

if (!visited[neighbor]) {
visited[neighbor] = true;

if (islands[currentVertex] > islands[neighbor]) {
if (!isInShortestPath[neighbor] && islands[currentVertex] > islands[neighbor]) {
islands[neighbor] = islands[currentVertex];
}
queue.enqueue(edge.to());
}
}
}

return islands;
}

Expand Down Expand Up @@ -126,13 +126,12 @@ private SegmentTree computeBypassPathLengths(EdgeWeightedDigraph edgeWeightedDig
}
}
}

return segmentTree;
}

private DirectedEdge getCriticalEdge(SegmentTree bypassPathLengths, DijkstraSP dijkstraSP, int target) {
// key = edge in shortest path from source to target
// value = id of edge in the path
// key = index of edge in the shortest path from source to target
// value = edge in the shortest path from source to target
SeparateChainingHashTable<Integer, DirectedEdge> edgesInShortestPath = new SeparateChainingHashTable<>();
int edgeIndex = 0;

Expand All @@ -144,12 +143,12 @@ private DirectedEdge getCriticalEdge(SegmentTree bypassPathLengths, DijkstraSP d
double highestBypassPathLength = Double.NEGATIVE_INFINITY;

for (int edgeId = 0; edgeId < edgeIndex; edgeId++) {
if (bypassPathLengths.rangeSumQuery(edgeId, edgeId) > highestBypassPathLength) {
highestBypassPathLength = bypassPathLengths.rangeSumQuery(edgeId, edgeId);
double lengthBypassingEdge = bypassPathLengths.rangeSumQuery(edgeId, edgeId);
if (lengthBypassingEdge > highestBypassPathLength) {
highestBypassPathLength = lengthBypassingEdge;
criticalEdgeId = edgeId;
}
}

return edgesInShortestPath.get(criticalEdgeId);
}

Expand Down Expand Up @@ -179,23 +178,15 @@ public static void main(String[] args) {

StdOut.print("Critical edge 1: ");
DirectedEdge criticalEdge1 = criticalEdges.getCriticalEdge(edgeWeightedDigraph1, source1, target1);
if (criticalEdge1 == null) {
StdOut.println("There is no path from " + source1 + " to " + target1);
} else {
StdOut.println(criticalEdge1);
}
printResult(criticalEdge1, source1, target1);
StdOut.println("Expected: 1->2 2.00");

int source2 = 7;
int target2 = 3;

StdOut.print("\nCritical edge 2: ");
DirectedEdge criticalEdge2 = criticalEdges.getCriticalEdge(edgeWeightedDigraph1, source2, target2);
if (criticalEdge2 == null) {
StdOut.println("There is no path from " + source2 + " to " + target2);
} else {
StdOut.println(criticalEdge2);
}
printResult(criticalEdge2, source2, target2);
StdOut.println("Expected: There is no path from 7 to 3");

EdgeWeightedDigraph edgeWeightedDigraph2 = new EdgeWeightedDigraph(9);
Expand Down Expand Up @@ -223,11 +214,7 @@ public static void main(String[] args) {

StdOut.print("\nCritical edge 3: ");
DirectedEdge criticalEdge3 = criticalEdges.getCriticalEdge(edgeWeightedDigraph2, source3, target3);
if (criticalEdge3 == null) {
StdOut.println("There is no path from " + source3 + " to " + target3);
} else {
StdOut.println(criticalEdge3);
}
printResult(criticalEdge3, source3, target3);
StdOut.println("Expected: 0->1 1.00");

// Digraph with a bridge: 2->3 is a bridge which disconnects source and target vertices when removed
Expand All @@ -249,11 +236,37 @@ public static void main(String[] args) {

StdOut.print("\nCritical edge 4: ");
DirectedEdge criticalEdge4 = criticalEdges.getCriticalEdge(edgeWeightedDigraph3, source4, target4);
if (criticalEdge4 == null) {
StdOut.println("There is no path from " + source4 + " to " + target4);
printResult(criticalEdge4, source4, target4);
StdOut.println("Expected: 2->3 3.00");

EdgeWeightedDigraph edgeWeightedDigraph4 = new EdgeWeightedDigraph(9);
edgeWeightedDigraph4.addEdge(new DirectedEdge(0, 1, 10));
edgeWeightedDigraph4.addEdge(new DirectedEdge(1, 2, 10));
edgeWeightedDigraph4.addEdge(new DirectedEdge(2, 3, 10));
edgeWeightedDigraph4.addEdge(new DirectedEdge(3, 4, 10));
edgeWeightedDigraph4.addEdge(new DirectedEdge(4, 5, 10));
// Other path
edgeWeightedDigraph4.addEdge(new DirectedEdge(3, 7, 1));
edgeWeightedDigraph4.addEdge(new DirectedEdge(7, 2, 1));
edgeWeightedDigraph4.addEdge(new DirectedEdge(2, 6, 10));
edgeWeightedDigraph4.addEdge(new DirectedEdge(6, 8, 1));
edgeWeightedDigraph4.addEdge(new DirectedEdge(8, 7, 1));
edgeWeightedDigraph4.addEdge(new DirectedEdge(0, 2, 30));
edgeWeightedDigraph4.addEdge(new DirectedEdge(3, 5, 30));
int source5 = 0;
int target5 = 5;

StdOut.print("\nCritical edge 5: ");
DirectedEdge criticalEdge5 = criticalEdges.getCriticalEdge(edgeWeightedDigraph4, source5, target5);
printResult(criticalEdge5, source5, target5);
StdOut.println("Expected: 2->3 10.00");
}

private static void printResult(DirectedEdge criticalEdge, int source, int target) {
if (criticalEdge == null) {
StdOut.println("There is no path from " + source + " to " + target);
} else {
StdOut.println(criticalEdge4);
StdOut.println(criticalEdge);
}
StdOut.println("Expected: 2->3 3.00");
}
}

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