PAT/source/html/a1003.html

Emergency
<div class="ques-view"><p>As an emergency rescue team leader of a city, you are given a special map of your country. The map shows several scattered cities connected by some roads. Amount of rescue teams in each city and the length of each road between any pair of cities are marked on the map. When there is an emergency call to you from some other city, your job is to lead your men to the place as quickly as possible, and at the mean time, call up as many hands on the way as possible.</p>
<h3 id="input-specification-">Input Specification:</h3>
<p>Each input file contains one test case. For each test case, the first line contains 4 positive integers: <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><mo>≤</mo><mn>5</mn><mn>0</mn><mn>0</mn></mrow>\le 500</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">5</span><span class="mord mathrm">0</span><span class="mord mathrm">0</span></span></span></span>) - the number of cities (and the cities are numbered from 0 to <span class="katex"><span class="katex-mathml"><math><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow>N-1</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;">N</span><span class="mbin">−</span><span class="mord mathrm">1</span></span></span></span>), <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> - the number of roads, <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>C</mi><mn>1</mn></msub></mrow>C_1</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.07153em;"><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> and <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>C</mi><mn>2</mn></msub></mrow>C_2</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.07153em;"><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">2</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> - the cities that you are currently in and that you must save, respectively. The next line contains <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> integers, where 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 integer is the number of rescue teams in 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 city. Then <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> lines follow, each describes a road with three integers <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>c</mi><mn>1</mn></msub></mrow>c_1</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">c</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>c</mi><mn>2</mn></msub></mrow>c_2</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.43056em;"></span><span class="strut bottom" style="height:0.58056em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit">c</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">2</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> and <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>, which are the pair of cities connected by a road and the length of that road, respectively. It is guaranteed that there exists at least one path from <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>C</mi><mn>1</mn></msub></mrow>C_1</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.07153em;"><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>C</mi><mn>2</mn></msub></mrow>C_2</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.07153em;"><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">2</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>
<h3 id="output-specification-">Output Specification:</h3>
<p>For each test case, print in one line two numbers: the number of different shortest paths between <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>C</mi><mn>1</mn></msub></mrow>C_1</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.07153em;"><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> and <span class="katex"><span class="katex-mathml"><math><mrow><msub><mi>C</mi><mn>2</mn></msub></mrow>C_2</math></span><span aria-hidden="true" class="katex-html"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.83333em;vertical-align:-0.15em;"></span><span class="base textstyle uncramped"><span class="mord"><span class="mord mathit" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.07153em;"><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">2</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>, and the maximum amount of rescue teams you can possibly gather.  All the numbers in a line must be separated by exactly one space, and there is no extra space allowed at the end of a line.</p>
<h3 id="sample-input-">Sample Input:</h3>
<pre><code class="lang-in">5 6 0 2
1 2 1 5 3
0 1 1
0 2 2
0 3 1
1 2 1
2 4 1
3 4 1
</code></pre>
<h3 id="sample-output-">Sample Output:</h3>
<pre><code class="lang-out">2 4
</code></pre>
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