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kruskals.html
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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>Kruskal'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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<div class="container-fluid d-flex align-items-center">
<a class="btn back-button mr-4" href="graphs.html"
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<li><a href="index.html">Home</a></li>
<li><a href="graphs.html">Graphs</a></li>
<li>Kruskal's Algorithm</li>
</ol>
<h2>Kruskal'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>
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<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>q = graph.getEdges().sortAscending()</span>
</div>
<div class="row ml-auto mr-auto mt-1 2">
<span>mst = []</span>
</div>
<div class="row ml-auto mr-auto mt-1 3">
<span
><span class="op">while</span>(mst <
graph.numVertices()-1)</span
>
</div>
<div class="row ml-auto mr-auto mt-1 4">
<span>  next = q.popFirst()</span>
</div>
<div class="row ml-auto mr-auto mt-1 5">
<span
>  <span class="op">if</span>(!formsCycle(mst,
next))</span
>
</div>
<div class="row ml-auto mr-auto mt-1 6">
<span>    mst.push(next)</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. Sort all edges by weight (non-decreasing).</span
>
</div>
<div class="row ml-auto mr-auto mt-1">
<span class="comment"
>2. Pick the edge with the smallest weight.</span
>
</div>
<div class="row ml-auto mr-auto mt-1">
<span class="comment"
>3. Check if adding that edge to the MST forms a cycle. If
it doesn't, add it.</span
>
</div>
<div class="row ml-auto mr-auto mt-1">
<span class="comment"
>4. Repeat steps 2 and 3 until MST has a lenght of (number
of Vertices - 1).</span
>
</div>
</div>
</div>
</div>
<hr data-content="Instructions" class="hr-text mb-3 mt-4" />
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<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.
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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="kruskals()"
class="btn btn-danger red w-100"
>
Start
</button>
</div>
</div>
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})
.curve(d3.curveLinear);
if (xy0.x != xy1.x || xy0.y != xy1.y) {
if (
!g.edgeExists(data_nodes[firstVert], data_nodes[secVert])
) {
g.addEdge(
{
x: data_nodes[firstVert].x,
y: data_nodes[firstVert].y,
id: firstVert,
},
{
x: data_nodes[secVert].x,
y: data_nodes[secVert].y,
id: 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("id", function (d, i) {
data_edges.push({
v1: firstVert,
v2: secVert,
id: data_edges.length,
});
return "path" + (data_edges.length - 1);
});
var text = svg
.append("g")
.attr("id", "text-path-" + firstVert + "" + secVert)
.append("text")
.append("textPath") //append a textPath to the text element
.attr("xlink:href", "#path" + (data_edges.length - 1)) //place the ID of the path here
.style("text-anchor", "middle") //place the text halfway on the arc
.attr("startOffset", "50%")
.attr("font-size", "18px")
.attr("font-weight", "bold")
.text(g.getEdgeLength(firstVert, secVert));
}
}
drawing = false;
svg.select("#circle" + firstVert).attr("stroke", "black");
svg.select("#circle" + secVert).attr("stroke", "black");
setTimeout(() => {
svg
.select("#text-path-" + firstVert + "" + secVert)
.attr("transform", function (d) {
if (
!(
isVector(data_nodes[firstVert]) &&
isVector(data_nodes[secVert])
)
) {
return "";
}
// Get the geometric center of this element
var box = this.getBBox();
var center = {
x: box.x + box.width / 2,
y: box.y + box.height / 2,
};
// Get the vector of the link
var delta = {
x: data_nodes[secVert].x - data_nodes[firstVert].x,
y: data_nodes[secVert].y - data_nodes[firstVert].y,
};
// Get a unitary vector orthogonal to delta
var norm = Math.sqrt(
delta.x * delta.x + delta.y * delta.y
);
var orth = {
x: delta.y / norm,
y: -delta.x / norm,
};
// Replace this with your ACTUAL font size
// Needed to calculate the offset later, so the
// text doesn't clip the path
var fontSize = 18;
// Flip the text and translate it beyond the link line
// if the link goes towards the left
return delta.x < 0
? "rotate(180 " +
center.x +
" " +
center.y +
") translate(" +
orth.x * fontSize +
" " +
orth.y * fontSize +
")"
: "translate(" + orth.x * 2 + " " + orth.y * 2 + ")";
});
}, 100);
}
}
});
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", "black")
.attr("stroke-width", "5px");
} else {
svg
.select("#circle" + i)
.transition()
.duration(250)
.attr("stroke-width", "5px");
}
}
});
}, 510);
setTimeout(() => {
resolve();
}, 350);
});
}
function isFiniteNumber(x) {
return typeof x === "number" && Math.abs(x) < Infinity;
}
function isVector(v) {
return isFiniteNumber(v.x) && isFiniteNumber(v.y);
}
async function newEdge(v1, v2) {
return new Promise((resolve) => {
var xy_0 = data_nodes[v1];
var xy_1 = 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(data_nodes[v1], data_nodes[v2])) {
g.addEdge(
{ x: data_nodes[v1].x, y: data_nodes[v1].y, id: v1 },
{ x: data_nodes[v2].x, y: data_nodes[v2].y, id: v2 }
);
svg
.select("#g-paths")
.append("path")
.transition()
.duration(300)
.attr("d", line([xy_0, xy_1]))
.attr("stroke", "#171717")
.attr("stroke-width", 4)
.attr("fill", "none")
.attr("id", function (d, i) {
data_edges.push({ v1: v1, v2: v2, id: data_edges.length });
return "path" + (data_edges.length - 1);
});
var text = svg
.append("g")
.attr("id", "text-path-" + v1 + "" + v2)
.append("text")
.append("textPath") //append a textPath to the text element
.attr("xlink:href", "#path" + (data_edges.length - 1)) //place the ID of the path here
.style("text-anchor", "middle") //place the text halfway on the arc
.attr("startOffset", "50%")
.attr("font-size", "18px")
.attr("font-weight", "bold")
.text(g.getEdgeLength(v1, v2));
}
setTimeout(() => {
resolve();
}, 300);
});
}
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");
setTimeout(() => {
resolve(i);
}, DELAY * 2);
break;
}
}
}, 1000);
}
function highlightCode(elementClass) {
$(".code-highlight").removeClass("code-highlight");
$(`.${elementClass}`).addClass("code-highlight");
}
async function timeout(delay) {
await new Promise((resolve) =>
setTimeout(() => {
resolve();
}, delay)
);
}
function find(parent, i) {
if (parent[i] == i) return i;
return this.find(parent, parent[i]);
}
function union(parent, rank, x, y) {
var xroot = find(parent, x);
var yroot = find(parent, y);
if (rank[xroot] < rank[yroot]) {
parent[xroot] = yroot;
} else if (rank[xroot] > rank[yroot]) {
parent[yroot] = xroot;
} else {
parent[yroot] = xroot;
rank[xroot] += 1;
}
}
function seen(seenEdges, check) {
for (const i in seenEdges) {
if (seenEdges[i][0] == check[0] && seenEdges[i][1] == check[1]) {
return true;
}
}
return false;
}
async function kruskals() {
$("#start-button").prop("disabled", true);
$(".button-top").prop("disabled", true);
running = true;
var q = [];
var result = [];
var graph = g;
var len = 0;
d3.selectAll("circle,path").attr("stroke", "#999");
var parent = [];
var rank = [];
var seenEdges = [];
for (let i = 0; i < graph.adjList.size; i++) {
parent.push(i);
rank.push(0);
var nbs = graph.adjList.get(i);
for (let j = 0; j < nbs.length; j++) {
if (!seen(seenEdges, [i, nbs[j].id])) {
nbs[j].v1 = i;
seenEdges.push([nbs[j].id, i]);
} else {
nbs[j].rem = true;
}
}
q = q.concat(nbs);
}
for (let i = 0; i < q.length; i++) {
if (q[i].rem == true) {
q.splice(i, 1);
i -= 1;
}
}
q = q.sort((a, b) => (a.len > b.len ? 1 : -1));
while (result.length < graph.getNoOfVertices() - 1) {
var nextEdge = q.shift();
d3.select("#circle" + nextEdge.v1)
.transition()
.duration(DELAY)
.attr("stroke", "#CC1616")
.attr("stroke-width", "10px");
d3.select("#circle" + nextEdge.id)
.transition()
.duration(DELAY)
.attr("stroke", "#CC1616")
.attr("stroke-width", "10px");
await findEdgeForAnim(nextEdge.v1, nextEdge.id);
var x = find(parent, nextEdge.v1);
var y = find(parent, nextEdge.id);
if (x != y) {
d3.select("#circle" + nextEdge.v1).attr("class", "MST");
d3.select("#circle" + nextEdge.id).attr("class", "MST");
for (var i in data_edges) {
if (
(data_edges[i].v1 == nextEdge.v1 &&
data_edges[i].v2 == nextEdge.id) ||
(data_edges[i].v1 == nextEdge.id &&
data_edges[i].v2 == nextEdge.v1)
) {
d3.select("#path" + data_edges[i].id).attr("class", "MST");
}
}
len += nextEdge.len;
result.push(nextEdge);
union(parent, rank, x, y);
} else {
d3.select("#circle" + nextEdge.v1)
.filter(function () {
return !this.classList.contains("MST");
})
.transition()
.duration(DELAY)
.attr("stroke", "#DDD")
.attr("stroke-width", "5px");
d3.select("#circle" + nextEdge.id)
.filter(function () {
return !this.classList.contains("MST");
})
.transition()
.duration(DELAY)
.attr("stroke", "#DDD")
.attr("stroke-width", "5px");
}
for (var i in data_edges) {
if (
(data_edges[i].v1 == nextEdge.v1 &&
data_edges[i].v2 == nextEdge.id) ||
(data_edges[i].v1 == nextEdge.id &&
data_edges[i].v2 == nextEdge.v1)
) {
d3.select("#path" + data_edges[i].id)
.filter(function () {
return !this.classList.contains("MST");
})
.transition()
.duration(DELAY)
.attr("stroke", "#DDD");
}
}
}
for (var i in data_edges) {
d3.select("#path" + data_edges[i].id)
.filter(function () {
return !this.classList.contains("MST");
})
.transition()
.duration(DELAY / 10)
.attr("stroke", "#DDD");
}
$("#nodes").html("Length of the MST: " + len);
running = false;
$("#start-button").prop("disabled", false);
$(".button-top").prop("disabled", false);
}
function clearCanvas() {
data_edges = [];
data_nodes = [];
vertexCount = 0;
g = new WeightedUndirectedGraph();
drawing = false;
svg.selectAll("*").remove();
svg.append("g").attr("id", "g-paths");
}
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);
if (!drawGraph) {
drawGraph = true;
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));
} else {
break;
}
breaker++;
}
if (breaker < 100) await newEdge(v1, v2);
svg
.select("#text-path-" + v1 + "" + v2)
.attr("transform", function (d) {
if (!(isVector(data_nodes[v1]) && isVector(data_nodes[v2]))) {
return "";
}
// Get the geometric center of this element
var box = this.getBBox();
var center = {
x: box.x + box.width / 2,
y: box.y + box.height / 2,
};
// Get the vector of the link
var delta = {
x: data_nodes[v2].x - data_nodes[v1].x,
y: data_nodes[v2].y - data_nodes[v1].y,
};
// Get a unitary vector orthogonal to delta
var norm = Math.sqrt(delta.x * delta.x + delta.y * delta.y);
var orth = {
x: delta.y / norm,
y: -delta.x / norm,
};
// Replace this with your ACTUAL font size
var fontSize = 18;
// Flip the text and translate it beyond the link line
// if the link goes towards the left
return delta.x < 0
? "rotate(180 " +
center.x +
" " +
center.y +
") translate(" +
orth.x * fontSize +
" " +
orth.y * fontSize +
")"
: "translate(" + orth.x * 2 + " " + orth.y * 2 + ")";
});
}
drawGraph = false;
}
$("#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>