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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8" />
<meta content="width=device-width, initial-scale=1.0" name="viewport" />
<title>Kosaraju's Algorithm - AlgoVis.io</title>
<meta
content="AlgoVis is an online algorithm visualization tool."
name="description"
/>
<meta content="algorithm visualization tool online" name="keywords" />
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<li><a href="index.html">Home</a></li>
<li><a href="graphs.html">Graphs</a></li>
<li>Kosaraju's Algorithm</li>
</ol>
<h2>Kosaraju's algorithm visualization</h2>
</div>
</section>
<!-- End Breadcrumbs -->
<section class="inner-page pt-4">
<div class="container-fluid px-0 mt-0">
<div class="row w-100 mx-auto">
<div class="col-sm-9 col-md-10 mx-0 px-0">
<span style="font-weight: bold">Draw your graph:</span>
</div>
<div class="col-sm-3 col-md-2 mr-0 px-0 my-0 py-0 text-right">
<button onclick="clearCanvas()" class="button-top">Clear</button
><button class="button-top ml-1" onclick="randomGraph()">
Random
</button>
</div>
</div>
<div class="data-container border-dark-nb p-1 mb-0 mt-0 w-100">
<svg id="visu"></svg>
</div>
<div class="w-100 row mx-auto border-dark-nt my-0 py-0">
<p id="nodes" class="my-0 py-0"></p>
</div>
<div class="row mx-auto">
<div class="col-sm-12 col-md-12 col-lg-6 px-0 mr-0">
<div class="ide w-100">
<div class="row ml-auto mr-auto 1">
<span
><span class="op">for</span>(i = 0 to
graph.getVertCount())</span
>
</div>
<div class="row ml-auto mr-auto mt-1 2">
<span
>  <span class="op">if</span>(!visited[i])</span
>
</div>
<div class="row ml-auto mr-auto mt-1 3">
<span
>    stack =
<span class="op">dsf</span>(i)</span
>
</div>
<div class="row ml-auto mr-auto mt-1 4">
<span
><span class="op">setUnvisited(graph.vertices)</span></span
>
</div>
<div class="row ml-auto mr-auto mt-1 5">
<span><span class="op">transpose(graph)</span></span>
</div>
<div class="row ml-auto mr-auto mt-1 6">
<span><span class="op">while</span>(!stack.empty())</span>
</div>
<div class="row ml-auto mr-auto mt-1 7">
<span>  vert = stack.pop()</span>
</div>
<div class="row ml-auto mr-auto mt-1 8">
<span
>  <span class="op">if</span
>(!visited[vert])</span
>
</div>
<div class="row ml-auto mr-auto mt-1 9">
<span
>    scc =
<span class="op">dfs</span>(vert)</span
>
</div>
</div>
</div>
<div class="col-sm-12 col-md-12 col-lg-6 ml-0 px-0">
<div class="ide w-100 pl-0">
<div class="row ml-auto mr-auto">
<span class="comment w-100">SHORT EXPLANATION</span>
</div>
<div class="row ml-auto mr-auto mt-1">
<span class="comment w-100">---------------------</span>
</div>
<div class="row ml-auto mr-auto mt-1">
<span class="comment"
>1. Mark all vertices as unvisited.</span
>
</div>
<div class="row ml-auto mr-auto mt-1">
<span class="comment"
>2. Run a Depth-first search on every unvisited
vertex.</span
>
</div>
<div class="row ml-auto mr-auto mt-1">
<span class="comment"
>3. Whenever a DFS finishes add the vertex it was run on to
the stack.</span
>
</div>
<div class="row ml-auto mr-auto mt-1">
<span class="comment"
>4. Transpose the graph (-> reverse the direction of the
edges).</span
>
</div>
<div class="row ml-auto mr-auto mt-1">
<span class="comment"
>4. Pop from the stack and run a DFS on the vertex if it
hasn't been visited already.</span
>
</div>
<div class="row ml-auto mr-auto mt-1">
<span class="comment">
- every finished DFS yields a list of vertices, which is a
strongly connected component</span
>
</div>
<div class="row ml-auto mr-auto mt-1">
<span class="comment"
>5. Repeat step 4 until the stack is empty.</span
>
</div>
</div>
</div>
</div>
<hr data-content="Instructions" class="hr-text mb-3 mt-4" />
<div class="row mx-auto">
<div class="col-sm-12 col-md-12 col-lg-6">
<form>
<div class="row">
<div class="col-12">
To draw a new vertex, simply click anywhere on the canvas
above.<br />
To create an edge between two vertices, click on the first
vertex and then on the second one.<br />
You can create a random graph by clicking on the 'Random'
button above the canvas.<br />
To clear the canvas, use the 'Clear' button.
</div>
</div>
</form>
</div>
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<form>
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<div class="col-sm-5">Speed:</div>
<div class="col-sm-7">
<span>Slow </span>
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type="text"
data-slider-min="350"
data-slider-max="1000"
data-slider-step="10"
data-slider-value="500"
/>
<span> Fast</span>
</div>
</div>
<div class="form-group row">
<div class="col-sm-12">
<button
id="start-button"
type="button"
onclick="kosarajus()"
class="btn btn-danger red w-100"
>
Start
</button>
</div>
</div>
</form>
</div>
</div>
</div>
</section>
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return i;
})
.attr("x", function (d) {
return xScale(d.x) - 5;
}) // Get attributes from circleAttrs var
.attr("y", function (d) {
return yScale(d.y) + 5;
})
.attr("font-family", "sans-serif")
.attr("font-size", "18px")
.attr("font-weight", "bold");
}, 300);
groups.on("click", function (d, i) {
var e = d3.event;
e.cancelBubble = true;
if (e.stopPropagation) e.stopPropagation();
if (!running) {
if (!drawing) {
drawing = true;
var choords = d3.mouse(this);
xy0 = {
x: Math.round(xScale.invert(coords[0])), // Takes the pixel number to convert to number
y: Math.round(yScale.invert(coords[1])),
};
firstVert = i;
svg.select("#circle" + i).attr("stroke", "#CC1616");
} else {
//drawing = false;
var choords = d3.mouse(this);
secVert = i;
xy1 = {
x: Math.round(xScale.invert(coords[0])), // Takes the pixel number to convert to number
y: Math.round(yScale.invert(coords[1])),
};
var line = d3
.line()
.x(function (d) {
return d.x;
})
.y(function (d) {
return d.y;
})
.curve(d3.curveLinear);
if (xy0.x != xy1.x || xy0.y != xy1.y) {
if (!g.edgeExists(firstVert, secVert)) {
g.addEdge(firstVert, secVert);
svg
.select("#g-paths")
.append("path")
.transition()
.duration(300)
.attr("d", line([xy0, xy1]))
.attr("stroke", "#171717")
.attr("stroke-width", 4)
.attr("fill", "none")
.attr("marker-end", "url(#triangle)")
.attr("id", function (d, i) {
data_edges.push({
v1: firstVert,
v2: secVert,
xy0: xy0,
xy1: xy1,
id: data_edges.length,
});
return "path" + (data_edges.length - 1);
});
}
}
drawing = false;
svg.select("#circle" + firstVert).attr("stroke", "#171717");
svg.select("#circle" + secVert).attr("stroke", "#171717");
}
}
});
setTimeout(() => {
groups.on("mouseover", function (d, i) {
if (!running) {
svg
.select("#circle" + i)
.transition()
.duration(250)
.attr("stroke", "#CC1616")
.attr("stroke-width", "10px");
}
});
groups.on("mouseout", function (d, i) {
if (!running) {
if (!drawing) {
svg
.select("#circle" + i)
.transition()
.duration(250)
.attr("stroke", "#171717")
.attr("stroke-width", "5px");
} else {
svg
.select("#circle" + i)
.transition()
.duration(250)
.attr("stroke-width", "5px");
}
}
});
}, 510);
setTimeout(() => {
resolve();
}, 350);
});
}
async function newEdge(v1, v2) {
return new Promise((resolve) => {
var xy0 = data_nodes[v1];
var xy1 = data_nodes[v2];
var line = d3
.line()
.x(function (d) {
return d.x;
})
.y(function (d) {
return d.y;
})
.curve(d3.curveLinear);
if (!g.edgeExists(v1, v2)) {
g.addEdge(v1, v2);
svg
.select("#g-paths")
.append("path")
.transition()
.duration(300)
.attr("d", line([xy0, xy1]))
.attr("stroke", "#171717")
.attr("stroke-width", 4)
.attr("marker-end", "url(#triangle)")
.attr("fill", "none")
.attr("id", function (d, i) {
data_edges.push({
v1: v1,
v2: v2,
xy0: xy0,
xy1: xy1,
id: data_edges.length,
});
return "path" + (data_edges.length - 1);
});
}
setTimeout(() => {
resolve();
}, 300);
});
}
async function highlightSCC(scc) {
seen = [];
for (const i in scc) {
for (let j = 0; j < scc.length; j++) {
if (j != i) {
for (var x in data_edges) {
var stop = false;
if (
((data_edges[x].v1 == scc[i] && data_edges[x].v2 == scc[j]) ||
(data_edges[x].v1 == scc[j] &&
data_edges[x].v2 == scc[i])) &&
seen.indexOf(data_edges[x].id) == -1
) {
d3.select("#path" + data_edges[x].id).attr("class", "scc");
seen.push(data_edges[x].id);
break;
} //if
} //for
} //if
} //for
d3.select("#circle" + scc[i]).attr("class", "scc");
} //for
} //function
async function transposeGraph() {
return new Promise((resolve) => {
var line = d3
.line()
.x(function (d) {
return d.x;
})
.y(function (d) {
return d.y;
})
.curve(d3.curveLinear);
var test = d3.selectAll("path").filter(function () {
return !this.id.includes("triangle");
});
test
.data(data_edges)
.transition()
.duration(DELAY)
.attr("d", function (d, i) {
var id = this.id.replace(/^\D+/g, "");
var l = line([data_edges[id].xy1, data_edges[id].xy0]);
temp = data_edges[id].xy1;
data_edges[id].xy1 = data_edges[id].xy0;
data_edges[id].xy0 = temp;
return l;
})
.attr("marker-end", "url(#triangle)");
setTimeout(() => {
resolve();
}, DELAY * 2);
}, 1000);
}
async function findEdgeForAnim(qe, nb) {
return new Promise((resolve) => {
for (var i in data_edges) {
var stop = false;
if (
(data_edges[i].v1 == qe && data_edges[i].v2 == nb) ||
(data_edges[i].v1 == nb && data_edges[i].v2 == qe)
) {
d3.select("#path" + data_edges[i].id)
.transition()
.duration(DELAY)
.attr("stroke", "#CC1616")
.attr("stroke-width", 10);
setTimeout(() => {
d3.select("#path" + data_edges[i].id)
.transition()
.duration(DELAY)
.attr("stroke", "#171717")
.attr("stroke-width", 4);
}, DELAY);
setTimeout(() => {
resolve();
}, DELAY * 2);
break;
}
}
}, 1000);
}
function highlightCode(elementClass) {
$(".code-highlight").removeClass("code-highlight");
$(`.${elementClass}`).addClass("code-highlight");
}
async function runDfs(graph, v, run) {
await dfs(graph, v, run);
}
async function timeout(delay) {
await new Promise((resolve) =>
setTimeout(() => {
resolve();
}, delay)
);
}
async function dfs(graph, v, run) {
visited[v] = true;
d3.select("#circle" + v)
.transition()
.duration(DELAY)
.attr("stroke", "#CC1616")
.attr("stroke-width", "10px");
var neighbours = graph.adjList.get(v);
for (var i in neighbours) {
await findEdgeForAnim(v, neighbours[i]);
if (!visited[neighbours[i]]) {
d3.select("#circle" + v)
.transition()
.duration(DELAY)
.attr("stroke", "#171717")
.attr("stroke-width", "5px");
await dfs(graph, neighbours[i], run);
d3.select("#circle" + v)
.transition()
.duration(DELAY)
.attr("stroke", "#CC1616")
.attr("stroke-width", "10px");
}
d3.select("#circle" + neighbours[i])
.transition()
.duration(DELAY)
.attr("stroke", "#171717")
.attr("stroke-width", "5px");
}
d3.select("#circle" + v)
.transition()
.duration(DELAY)
.attr("stroke", "#171717")
.attr("stroke-width", "5px");
if (run == 1) {
stack.push(v);
} else {
sccStack.push(v);
}
}
async function kosarajus() {
$("#start-button").prop("disabled", true);
$(".button-top").prop("disabled", true);
running = true;
$("#nodes").html("");
vertices = [];
d3.selectAll("path, circle").attr("stroke", "#171717");
for (var x = 0; x < data_nodes.length; x++) {
visited[x] = false;
}
for (let i = 0; i < g.getNoOfVertices(); i++) {
vertices.push(i);
}
highlightCode("1");
await timeout(DELAY / 2);
for (const j in vertices) {
highlightCode("2");
await timeout(DELAY / 2);
if (!visited[vertices[j]]) {
highlightCode("3");
await runDfs(g, vertices[j], 1);
}
}
highlightCode("4");
await timeout(DELAY / 2);
for (let x = 0; x < g.adjList.size; x++) {
g.adjList.set(x, []);
}
for (const i in data_edges) {
g.addEdge(data_edges[i].v2, data_edges[i].v1);
}
highlightCode("5");
await transposeGraph();
for (var x = 0; x < data_nodes.length; x++) {
visited[x] = false;
}
numComp = 0;
highlightCode("6");
await timeout(DELAY / 2);
while (stack.length != 0) {
highlightCode("7");
await timeout(DELAY / 2);
source = stack.pop();
highlightCode("8");
await timeout(DELAY / 2);
if (!visited[source]) {
highlightCode("9");
await runDfs(g, source, 2);
await highlightSCC(sccStack);
sccStack = [];
numComp++;
}
}
for (let x = 0; x < g.adjList.size; x++) {
g.adjList.set(x, []);
}
for (const i in data_edges) {
g.addEdge(data_edges[i].v1, data_edges[i].v2);
}
await transposeGraph();
test = d3.selectAll("path").filter(function () {
return !this.classList.contains("scc");
});
test.attr("stroke", "#DDD");
test2 = d3.selectAll(".scc");
test2.attr("stroke", "#CC1616").attr("class", "");
$("#nodes").html("Number of strongly connected components: " + numComp);
$("#start-button").prop("disabled", false);
$(".button-top").prop("disabled", false);
}
function clearCanvas() {
running = false;
var ids = [
"g-paths",
"defs",
"triangle",
"triangle-path",
"triangle-red",
"triangle-path-red",
];
data_edges = [];
data_nodes = [];
vertexCount = 0;
g = new UnweightedDirectedGraph();
drawing = false;
svg
.selectAll("*")
.filter(function (d, i) {
return !ids.includes(this.id);
})
.remove();
}
function getRowCol(numVerts, taken) {
row = Math.round(Math.random() * (numVerts - 1));
col = Math.round(Math.random() * (numVerts - 1));
while (taken[row][col]) {
row = Math.round(Math.random() * (numVerts - 1));
col = Math.round(Math.random() * (numVerts - 1));
}
taken[row][col] = true;
return { row: row, col: col, taken: taken };
}
async function randomGraph() {
$("#start-button").prop("disabled", true);
$(".button-top").prop("disabled", true);
running = false;
var numberVerts = Math.round(Math.random() * 4 + 4);
var maxEdges = (numberVerts * (numberVerts - 1)) / 2;
var numberEdges = Math.round(
Math.random() * (maxEdges - numberVerts) + numberVerts
);
var cellHeight = Math.round(h / 6);
var cellWidth = Math.round(w / 6);
var row = 0;
var col = 0;
var x = 0;
var y = 0;
var v1;
var v2;
var taken = [];
for (let x = 0; x < 6; x++) {
var row = [];
for (let y = 0; y < 6; y++) {
row.push(false);
}
taken.push(row);
}
clearCanvas();
for (let i = 0; i < numberVerts; i++) {
var rowcol = getRowCol(6, taken);
row = rowcol.row;
col = rowcol.col;
taken = rowcol.taken;
x = Math.round(cellWidth * col + Math.random() * 25);
y = Math.round(cellHeight * row + Math.random() * 25);
await newVertex([x, y]);
}
for (let j = 0; j < numberEdges; j++) {
v1 = Math.round(Math.random() * (numberVerts - 1));
v2 = Math.round(Math.random() * (numberVerts - 1));
let breaker = 0;
while (v1 == v2 || g.edgeExists(v1, v2)) {
if (breaker < 100) {
v2 = Math.round(Math.random() * (numberVerts - 1));
}
await new Promise((resolve) =>
setTimeout(() => {
resolve();
}, DELAY / 10)
);
breaker++;
}
if (breaker < 100) await newEdge(v1, v2);
}
$("#start-button").prop("disabled", false);
$(".button-top").prop("disabled", false);
}
</script>
<script>
$(document).ready(function () {
d3.select("#visu")
.attr("width", "100%")
.attr("height", "370")
.attr("viewBox", "0 0 " + globalThis.screen.availWidth + " 370");
var speedSlider = new Slider("#speedslider", {
reversed: true,
tooltip: "none",
handle: "square",
});
speedSlider.on("slide", function (slideEvt) {
setDelay(slideEvt);
});
});
</script>
</body>
</html>