PAT/source/html/t1014.html

Circles of Friends
<div class="ques-view"><p>A circle of friends is a network of friend relationships. If A is a friend of B, then B is considered a friend of A no matter B admits or not, and they are said to belong to the same circle. Here we assume that friendship is transitive, that is, if A is a friend of B, and B is a friend of C, then A is a friend of C and the three of them all belong to the same circle.</p>
<p>On the other hand, A is not so close to C as B is. We define the distance D(X, Y) between two friends X and Y as the minimum number of friends between them. For example, D(A, B) = 0, and D(C, A) = 1. The diameter of a friends circle is the maximum distance between any pair of friends in the circle.</p>
<p>Now given some people's relationships, you are supposed to find the number of friends circles and the circle with the largest diameter.</p>
<h3 id="input-specification-">Input Specification:</h3>
<p>Each input file contains one test case. For each case, the first line gives an integer <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><mn>2</mn><mo>≤</mo><mi>N</mi><mo>≤</mo><mn>1</mn><mn>0</mn><mn>0</mn><mn>0</mn></mrow>2 \le N \le 1000</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.8193em;vertical-align:-0.13597em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">2</span><span class="mrel">≤</span><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="mrel">≤</span><span class="mord mathrm">1</span><span class="mord mathrm">0</span><span class="mord mathrm">0</span><span class="mord mathrm">0</span></span></span></span>), which is the total number of people involved, and hence they are numbered from 1 to <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>. Then <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> lines follow, each in the format:</p>
<p><span class="katex"><span class="katex-mathml"><math><mrow><mi>k</mi></mrow>k</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span></span></span></span> <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>p</mi><mn>1</mn></msub></mrow>p_1</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">p</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span> ... <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>p</mi><mi>k</mi></msub></mrow>p_k</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">p</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span></p>
<p>where <span class="katex"><span class="katex-mathml"><math><mrow><mi>k</mi></mrow>k</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span></span></span></span> (<span class="katex"><span class="katex-mathml"><math><mrow><mn>0</mn><mo>≤</mo><mi>k</mi><mo>&lt;</mo><mi>m</mi><mi>i</mi><mi>n</mi><mo>(</mo><mn>1</mn><mn>0</mn><mo separator="true">,</mo><mi>N</mi><mo>)</mo></mrow>0 \le k &lt; min(10, N)</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">0</span><span class="mrel">≤</span><span class="mord mathit" style="margin-right:0.03148em;">k</span><span class="mrel">&lt;</span><span class="mord mathit">m</span><span class="mord mathit">i</span><span class="mord mathit">n</span><span class="mopen">(</span><span class="mord mathrm">1</span><span class="mord mathrm">0</span><span class="mpunct">,</span><span class="mord mathit" style="margin-right:0.10903em;">N</span><span class="mclose">)</span></span></span></span>) is the number of friends and <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>p</mi><mn>1</mn></msub></mrow>p_1</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">p</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathrm mtight">1</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span> to <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>p</mi><mi>k</mi></msub></mrow>p_k</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">p</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.03148em;">k</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">​</span></span>​</span></span></span></span></span></span></span> (if <span class="katex"><span class="katex-mathml"><math><mrow><mi>k</mi><mo>&gt;</mo><mn>0</mn></mrow>k&gt;0</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.73354em;vertical-align:-0.0391em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.03148em;">k</span><span class="mrel">&gt;</span><span class="mord mathrm">0</span></span></span></span>) are the friends' indices. The <span class="katex"><span class="katex-mathml"><math><mrow><mi>i</mi></mrow>i</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.65952em;"></span><span class="strut bottom" style="height:0.65952em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">i</span></span></span></span>-th line corresponds to the <span class="katex"><span class="katex-mathml"><math><mrow><mi>i</mi></mrow>i</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.65952em;"></span><span class="strut bottom" style="height:0.65952em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">i</span></span></span></span>-th person. All the numbers in a line are separated by spaces. It is guaranteed that no one is given as a friend of oneself.</p>
<h3 id="output-specification-">Output Specification:</h3>
<p>For each case, print in a line the number of friends circles, and the largest diameter, separated by exactly one space.</p>
<h3 id="sample-input-">Sample Input:</h3>
<pre><code class="lang-in">17
2 15 12
1 17
2 16 9
1 8
4 10 13 15 14
0
2 11 14
1 4
2 2 3
2 13 11
2 15 7
2 1 14
2 5 15
0
0
1 3
1 2
</code></pre>
<h3 id="sample-output-">Sample Output:</h3>
<pre><code class="lang-out">4 3
</code></pre>
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