最小支配集:指從所有頂點中取盡量少的點組成一個集合,使得剩下的所有點都與取出來的點有邊相連。頂點個數最小的支配集被稱為最小支配集。這里用貪心法來求。
1.以1號點深度優先搜索整棵樹,求出每個點在DFS中的編號和每個點的父親節點編號。?
2.按DFS的反向序列檢查,如果當前點既不屬于支配集也不與支配集中的點相連,且它的父親也不屬于支配集,將其父親點加入支配集,支配集個數加1。?
3.標記當前結點、當前結點的父節點(屬于支配集)、當前結點的父節點的父節點(與支配集中的點相連)。
<code class="hljs cpp has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#include<iostream></span>
<span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#include<algorithm></span>
<span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#include<cstdio></span>
<span class="hljs-preprocessor" style="color: rgb(68, 68, 68); box-sizing: border-box;">#include<cstring></span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">using</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">namespace</span> <span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">std</span>;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">const</span> <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> MAXN = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">20020</span>;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">struct</span> EdgeNode
{<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> to;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> next;
}Edges[MAXN];
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> Head[MAXN],father[MAXN],NewPos[MAXN];
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">bool</span> vis[MAXN];
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//NewPos[]表示深度優先遍歷序列的第i個點是哪個點</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//now表示當前深度優先遍歷序列中已經有多少個點了</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//vis[]用來深度優先遍歷的判重</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//father[]表示點i的父親節點編號</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> N,M,now;
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">void</span> DFS(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> x) <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//得到深度優先隊列的反向序列</span>
{NewPos[now++] = x;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> k = Head[x]; k != -<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; k = Edges[k].next){<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(!vis[Edges[k].to]){vis[Edges[k].to] = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>;father[Edges[k].to] = x;DFS(Edges[k].to);}}
}<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//S[i]為true,表示第i個點被覆蓋了</span>
<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//Set[i]表示點i屬于要求的點集</span>
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">bool</span> S[MAXN],Set[MAXN];
<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> Greedy()<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//貪心求最小支配集</span>
{<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(S,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(S));<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(Set,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(Set));<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> ans = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i = N-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; i >= <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; i--)<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//反向序列檢查</span>{<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> t = NewPos[i];<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(!S[t])<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//當前點未被覆蓋,也就是當前點既不屬于支配集,也不與支配集中的點相連</span>{<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(!Set[father[t]])<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//當前點的父親結點不屬于支配集,</span>{Set[father[t]] = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>; <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//將父節點加入支配集</span>ans++; <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//頂點個數加1</span>}S[t] = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>;S[father[t]] = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>;S[father[father[t]]] = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>;<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//標記當前點、當前結點的父節點、當前結點的父節點的父節點</span>}}<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> ans;
}<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> main()
{<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> u,v;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">while</span>(~<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">scanf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"%d"</span>,&N)){ <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//初始化</span><span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(Edges,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(Edges));<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(Head,-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(Head));<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(father,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(father));<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(vis,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">false</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(vis));<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(NewPos,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(NewPos));<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> id = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>; i < N-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; ++i){<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">scanf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"%d%d"</span>,&u,&v);Edges[id].to = v;Edges[id].next = Head[u];Head[u] = id++;Edges[id].to = u;Edges[id].next = Head[v];Head[v] = id++;}now = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;vis[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>] = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>;father[<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>] = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>;DFS(<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>);<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">printf</span>(<span class="hljs-string" style="color: rgb(0, 136, 0); box-sizing: border-box;">"%d\n"</span>,Greedy());}<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;
}
</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li><li style="box-sizing: border-box; padding: 0px 5px;">20</li><li style="box-sizing: border-box; padding: 0px 5px;">21</li><li style="box-sizing: border-box; padding: 0px 5px;">22</li><li style="box-sizing: border-box; padding: 0px 5px;">23</li><li style="box-sizing: border-box; padding: 0px 5px;">24</li><li style="box-sizing: border-box; padding: 0px 5px;">25</li><li style="box-sizing: border-box; padding: 0px 5px;">26</li><li style="box-sizing: border-box; padding: 0px 5px;">27</li><li style="box-sizing: border-box; padding: 0px 5px;">28</li><li style="box-sizing: border-box; padding: 0px 5px;">29</li><li style="box-sizing: border-box; padding: 0px 5px;">30</li><li style="box-sizing: border-box; padding: 0px 5px;">31</li><li style="box-sizing: border-box; padding: 0px 5px;">32</li><li style="box-sizing: border-box; padding: 0px 5px;">33</li><li style="box-sizing: border-box; padding: 0px 5px;">34</li><li style="box-sizing: border-box; padding: 0px 5px;">35</li><li style="box-sizing: border-box; padding: 0px 5px;">36</li><li style="box-sizing: border-box; padding: 0px 5px;">37</li><li style="box-sizing: border-box; padding: 0px 5px;">38</li><li style="box-sizing: border-box; padding: 0px 5px;">39</li><li style="box-sizing: border-box; padding: 0px 5px;">40</li><li style="box-sizing: border-box; padding: 0px 5px;">41</li><li style="box-sizing: border-box; padding: 0px 5px;">42</li><li style="box-sizing: border-box; padding: 0px 5px;">43</li><li style="box-sizing: border-box; padding: 0px 5px;">44</li><li style="box-sizing: border-box; padding: 0px 5px;">45</li><li style="box-sizing: border-box; padding: 0px 5px;">46</li><li style="box-sizing: border-box; padding: 0px 5px;">47</li><li style="box-sizing: border-box; padding: 0px 5px;">48</li><li style="box-sizing: border-box; padding: 0px 5px;">49</li><li style="box-sizing: border-box; padding: 0px 5px;">50</li><li style="box-sizing: border-box; padding: 0px 5px;">51</li><li style="box-sizing: border-box; padding: 0px 5px;">52</li><li style="box-sizing: border-box; padding: 0px 5px;">53</li><li style="box-sizing: border-box; padding: 0px 5px;">54</li><li style="box-sizing: border-box; padding: 0px 5px;">55</li><li style="box-sizing: border-box; padding: 0px 5px;">56</li><li style="box-sizing: border-box; padding: 0px 5px;">57</li><li style="box-sizing: border-box; padding: 0px 5px;">58</li><li style="box-sizing: border-box; padding: 0px 5px;">59</li><li style="box-sizing: border-box; padding: 0px 5px;">60</li><li style="box-sizing: border-box; padding: 0px 5px;">61</li><li style="box-sizing: border-box; padding: 0px 5px;">62</li><li style="box-sizing: border-box; padding: 0px 5px;">63</li><li style="box-sizing: border-box; padding: 0px 5px;">64</li><li style="box-sizing: border-box; padding: 0px 5px;">65</li><li style="box-sizing: border-box; padding: 0px 5px;">66</li><li style="box-sizing: border-box; padding: 0px 5px;">67</li><li style="box-sizing: border-box; padding: 0px 5px;">68</li><li style="box-sizing: border-box; padding: 0px 5px;">69</li><li style="box-sizing: border-box; padding: 0px 5px;">70</li><li style="box-sizing: border-box; padding: 0px 5px;">71</li><li style="box-sizing: border-box; padding: 0px 5px;">72</li><li style="box-sizing: border-box; padding: 0px 5px;">73</li><li style="box-sizing: border-box; padding: 0px 5px;">74</li><li style="box-sizing: border-box; padding: 0px 5px;">75</li><li style="box-sizing: border-box; padding: 0px 5px;">76</li><li style="box-sizing: border-box; padding: 0px 5px;">77</li><li style="box-sizing: border-box; padding: 0px 5px;">78</li><li style="box-sizing: border-box; padding: 0px 5px;">79</li><li style="box-sizing: border-box; padding: 0px 5px;">80</li><li style="box-sizing: border-box; padding: 0px 5px;">81</li><li style="box-sizing: border-box; padding: 0px 5px;">82</li><li style="box-sizing: border-box; padding: 0px 5px;">83</li><li style="box-sizing: border-box; padding: 0px 5px;">84</li><li style="box-sizing: border-box; padding: 0px 5px;">85</li><li style="box-sizing: border-box; padding: 0px 5px;">86</li><li style="box-sizing: border-box; padding: 0px 5px;">87</li><li style="box-sizing: border-box; padding: 0px 5px;">88</li><li style="box-sizing: border-box; padding: 0px 5px;">89</li><li style="box-sizing: border-box; padding: 0px 5px;">90</li><li style="box-sizing: border-box; padding: 0px 5px;">91</li></ul>
最小點覆蓋:指從所有頂點中取盡量少的點組成一個集合,使得集合中所有的邊都與取出來的點有邊相連。頂點個數最小的覆蓋集被稱為最小點覆蓋。?
貪心策略:如果當前點和當前點的父節點都不屬于頂點覆蓋集合,則將父節點加入到頂點覆蓋集合中,并標記當前節點和其父節點都被覆蓋。
<code class="hljs cpp has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> Greedy()<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//貪心求最小點覆蓋</span>
{<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(S,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(S));<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(Set,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(Set));<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> ans = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i = N-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; i >= <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; i--)<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//反向序列檢查</span>{<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> t = NewPos[i];<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(!S[t] && !S[father[t]])<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//當前點和當前點的父節點都不屬于頂點覆蓋集合</span>{Set[father[t]] = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>; <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//當前點的父節點加入到頂點覆蓋集合中</span>ans++; <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//頂點個數+1</span>S[t] = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>;S[father[t]] = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>;<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//標記當前點、當前結點的父節點</span>}}<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> ans;
}</code><ul class="pre-numbering" style="box-sizing: border-box; position: absolute; width: 50px; top: 0px; left: 0px; margin: 0px; padding: 6px 0px 40px; border-right-width: 1px; border-right-style: solid; border-right-color: rgb(221, 221, 221); list-style: none; text-align: right; background-color: rgb(238, 238, 238);"><li style="box-sizing: border-box; padding: 0px 5px;">1</li><li style="box-sizing: border-box; padding: 0px 5px;">2</li><li style="box-sizing: border-box; padding: 0px 5px;">3</li><li style="box-sizing: border-box; padding: 0px 5px;">4</li><li style="box-sizing: border-box; padding: 0px 5px;">5</li><li style="box-sizing: border-box; padding: 0px 5px;">6</li><li style="box-sizing: border-box; padding: 0px 5px;">7</li><li style="box-sizing: border-box; padding: 0px 5px;">8</li><li style="box-sizing: border-box; padding: 0px 5px;">9</li><li style="box-sizing: border-box; padding: 0px 5px;">10</li><li style="box-sizing: border-box; padding: 0px 5px;">11</li><li style="box-sizing: border-box; padding: 0px 5px;">12</li><li style="box-sizing: border-box; padding: 0px 5px;">13</li><li style="box-sizing: border-box; padding: 0px 5px;">14</li><li style="box-sizing: border-box; padding: 0px 5px;">15</li><li style="box-sizing: border-box; padding: 0px 5px;">16</li><li style="box-sizing: border-box; padding: 0px 5px;">17</li><li style="box-sizing: border-box; padding: 0px 5px;">18</li><li style="box-sizing: border-box; padding: 0px 5px;">19</li></ul>
最大獨立集:指從所有頂點中取盡量多的點組成一個集合,使得這些點之間沒有邊相連。頂點個數最多的獨立集被稱為最大獨立集。?
貪心策略:如果當前節點沒有被覆蓋,則將當前節點加入獨立集,并標記當前節點和其父節點都被覆蓋。
<code class="hljs cpp has-numbering" style="display: block; padding: 0px; color: inherit; box-sizing: border-box; font-family: 'Source Code Pro', monospace;font-size:undefined; white-space: pre; border-radius: 0px; word-wrap: normal; background: transparent;"><span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> Greedy()<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//貪心求最大獨立集</span>
{<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(S,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(S));<span class="hljs-built_in" style="color: rgb(102, 0, 102); box-sizing: border-box;">memset</span>(Set,<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>,<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">sizeof</span>(Set));<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> ans = <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">0</span>;<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">for</span>(<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> i = N-<span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; i >= <span class="hljs-number" style="color: rgb(0, 102, 102); box-sizing: border-box;">1</span>; i--)<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//反向序列檢查</span>{<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">int</span> t = NewPos[i];<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">if</span>(!S[t])<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//當前點未被覆蓋</span>{Set[t] = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>; <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//將當前點加入獨立集</span>ans++; <span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//獨立集點個數加1</span>S[t] = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>;S[father[t]] = <span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">true</span>;<span class="hljs-comment" style="color: rgb(136, 0, 0); box-sizing: border-box;">//標記當前點、當前結點的父節點都被覆蓋</span>}}<span class="hljs-keyword" style="color: rgb(0, 0, 136); box-sizing: border-box;">return</span> ans;
}</code>
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