A visualisation of the maximum rectangular area in a histogram. Check this useful video for good explanation of the O(N) algorithm.
Single code base visualisations on svg and canvas thanks to d3-canvas-transition module.
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January 17, 2017 19:52
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Maximum rectangular area
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| license: bsd-3-clause |
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| <!DOCTYPE html> | |
| <html lang="en"> | |
| <head> | |
| <meta charset="utf-8"> | |
| <title>Maximum rectangular area on histogram</title> | |
| <script src="https://d3js.org/d3.v4.js"></script> | |
| <script src="https://giottojs.org/d3-canvas-transition/0.3.4/d3-canvas-transition.js"></script> | |
| <style> | |
| #panel { | |
| background-color: rgba(245,245,245,0.9); | |
| padding: 5px; | |
| position: absolute; | |
| display: block; | |
| } | |
| </style> | |
| </head> | |
| <body> | |
| <div id="panel"> | |
| <div id="paper"> | |
| <label> | |
| <input id='svg' name="type" type="radio" checked> | |
| <span>svg</span> | |
| </label> | |
| <label> | |
| <input id='canvas' name="type" type="radio"> | |
| <span>canvas</span> | |
| </label> | |
| </div> | |
| </div> | |
| <div id="example" style="max-width: 960px"></div> | |
| <script> | |
| (function () { | |
| d3.select('#svg').on('click', function () { | |
| draw('svg'); | |
| }); | |
| d3.select('#canvas').on('click', function () { | |
| draw('canvas'); | |
| }); | |
| if (d3.resolution() > 1) { | |
| d3.select('#paper').append('label').html( | |
| "<input id='canvas-low' name='type' type='radio'><span>canvas low resolution</span>" | |
| ); | |
| d3.select('#canvas-low').on('click', function () { | |
| draw('canvas', 1); | |
| }); | |
| } | |
| var N = 20, | |
| H = 15, | |
| generator = d3.randomUniform(1, H-2), | |
| color = d3.scaleSequential(d3.interpolateViridis).domain([0, H+5]), | |
| areaColor = color(H+5), | |
| data = d3.range(0, N).map(function () {return generator();}); | |
| draw('svg'); | |
| function draw(type, r) { | |
| var example = d3.select("#example"), | |
| width = d3.getSize(example.style('width')), | |
| height = Math.min(500, width), | |
| barWidth = width / data.length, | |
| y = d3.scaleLinear().domain([0, H]).range([height, 0]), | |
| animation = {}; | |
| example.select('.paper').remove(); | |
| var paper = example | |
| .append(type) | |
| .classed('paper', true) | |
| .attr('width', width).attr('height', height).canvasResolution(r).canvas(true); | |
| paper.append('rect') | |
| .attr('width', width) | |
| .attr('height', height) | |
| .style('fill', '#fff'); | |
| paper.append('g') | |
| .selectAll('rect') | |
| .data(data) | |
| .enter() | |
| .append("rect") | |
| .attr("transform", function (d, i) {return "translate(" + i*barWidth + ")";}) | |
| .attr("y", function (d) {return y(d);}) | |
| .attr("height", function(d) {return height - y(d); }) | |
| .attr("width", barWidth - 1) | |
| .attr("fill", function (d) {return color(d);}) | |
| .attr("stroke", '#fff') | |
| .attr("stroke-width", 1) | |
| .attr("stroke-linejoin", "round"); | |
| var area = paper | |
| .append('rect') | |
| .style("fill", areaColor) | |
| .style("fill-opacity", 0.6); | |
| paper.select('g').selectAll('rect') | |
| .call(update, data) | |
| .call(animate, 2000); | |
| function update (histogram, di) { | |
| var ad = largest_rectangle(di); | |
| histogram | |
| .data(di) | |
| .attr("y", function (d) {return y(d);}) | |
| .attr("height", function(d) {return height - y(d); }) | |
| .attr("fill", function (d) {return color(d);}); | |
| area | |
| .attr("transform", "translate(" + ad[0]*barWidth + "," + y(ad[2]) + ")") | |
| .attr('width', barWidth*(ad[1] - ad[0]) - 1) | |
| .attr('height', height - y(ad[2])); | |
| } | |
| function animate (histogram, duration) { | |
| var data1 = d3.range(0, N).map(function () {return generator();}), | |
| Ht = d3.interpolateArray(data, data1); | |
| d3.select(animation) | |
| .transition() | |
| .duration(duration) | |
| .tween("attr:y", function () { | |
| return function (t) { | |
| update(histogram, Ht(t)); | |
| } | |
| }); | |
| d3.timeout(function () { | |
| data = data1; | |
| animate(histogram, duration); | |
| }, (Math.random() + 1) * duration); | |
| } | |
| } | |
| function largest_rectangle (Height) { | |
| var stack = [], | |
| max_area = 0, | |
| area, x1, x2, y; | |
| Height.map(function (h, i) { | |
| while (stack.length && h < Height[stack[stack.length-1]]) | |
| calc_area(i); | |
| stack.push(i); | |
| }); | |
| while (stack.length) calc_area(H.length); | |
| return [x1, x2, y]; | |
| function calc_area (i) { | |
| var j = stack.splice(stack.length-1); | |
| var t = stack.length ? stack[stack.length-1] + 1 : 0; | |
| area = Height[j] * (i - t); | |
| if (area > max_area) { | |
| max_area = area; | |
| y = Height[j]; | |
| x1 = t; | |
| x2 = i; | |
| } | |
| } | |
| } | |
| }()); | |
| </script> | |
| </body> |
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