PAT/source/html/a1091.html

Acute Stroke
<div class="ques-view"><p>One important factor to identify acute stroke (急性脑卒中) is the volume of the stroke core. Given the results of image analysis in which the core regions are identified in each MRI slice, your job is to calculate the volume of the stroke core.</p>
<h3 id="input-specification-">Input Specification:</h3>
<p>Each input file contains one test case. For each case, the first line contains 4 positive integers: <span class="katex"><span class="katex-mathml"><math><mrow><mi>M</mi></mrow>M</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">M</span></span></span></span>, <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span>, <span class="katex"><span class="katex-mathml"><math><mrow><mi>L</mi></mrow>L</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">L</span></span></span></span> and <span class="katex"><span class="katex-mathml"><math><mrow><mi>T</mi></mrow>T</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.13889em;">T</span></span></span></span>, where <span class="katex"><span class="katex-mathml"><math><mrow><mi>M</mi></mrow>M</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">M</span></span></span></span> and <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi></mrow>N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span> are the sizes of each slice (i.e. pixels of a slice are in an <span class="katex"><span class="katex-mathml"><math><mrow><mi>M</mi><mo>×</mo><mi>N</mi></mrow>M \times N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.76666em;vertical-align:-0.08333em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">M</span><span class="mbin">×</span><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span> matrix, and the maximum resolution is 1286 by 128); <span class="katex"><span class="katex-mathml"><math><mrow><mi>L</mi></mrow>L</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">L</span></span></span></span> (<span class="katex"><span class="katex-mathml"><math><mrow><mo>≤</mo><mn>6</mn><mn>0</mn></mrow>\le 60</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.78041em;vertical-align:-0.13597em;"></span><span class="base textstyle uncramped"><span class="mrel">≤</span><span class="mord mathrm">6</span><span class="mord mathrm">0</span></span></span></span>) is the number of slices of a brain; and <span class="katex"><span class="katex-mathml"><math><mrow><mi>T</mi></mrow>T</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.13889em;">T</span></span></span></span> is the integer threshold (i.e. if the volume of a connected core is less than <span class="katex"><span class="katex-mathml"><math><mrow><mi>T</mi></mrow>T</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.13889em;">T</span></span></span></span>, then that core must not be counted).</p>
<p>Then <span class="katex"><span class="katex-mathml"><math><mrow><mi>L</mi></mrow>L</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">L</span></span></span></span> slices are given. Each slice is represented by an <span class="katex"><span class="katex-mathml"><math><mrow><mi>M</mi><mo>×</mo><mi>N</mi></mrow>M \times N</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.76666em;vertical-align:-0.08333em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.10903em;">M</span><span class="mbin">×</span><span class="mord mathit" style="margin-right:0.10903em;">N</span></span></span></span> matrix of 0's and 1's, where 1 represents a pixel of stroke, and 0 means normal. Since the thickness of a slice is a constant, we only have to count the number of 1's to obtain the volume. However, there might be several separated core regions in a brain, and only those with their volumes no less than <span class="katex"><span class="katex-mathml"><math><mrow><mi>T</mi></mrow>T</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.13889em;">T</span></span></span></span> are counted. Two pixels are <strong>connected</strong> and hence belong to the same region if they share a common side, as shown by Figure 1 where all the 6 red pixels are connected to the blue one.</p>
<p>【插图】</p>
<p>Figure 1</p>
<h3 id="output-specification-">Output Specification:</h3>
<p>For each case, output in a line the total volume of the stroke core.</p>
<h3 id="sample-input-">Sample Input:</h3>
<pre><code class="lang-in">3 4 5 2
1 1 1 1
1 1 1 1
1 1 1 1
0 0 1 1
0 0 1 1
0 0 1 1
1 0 1 1
0 1 0 0
0 0 0 0
1 0 1 1
0 0 0 0
0 0 0 0
0 0 0 1
0 0 0 1
1 0 0 0
</code></pre>
<h3 id="sample-output-">Sample Output:</h3>
<pre><code class="lang-out">26
</code></pre>
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