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NOIP1999 拦截导弹

2024-07-14 12:53:53   227人阅读

<meta http-equiv="Content-Type" content="text/html; charset=gb2312" />NOIP1999 拦截导弹 <style>@font-face{font-family:"Times New Roman";}@font-face{font-family:"宋体";}@font-face{font-family:"Symbol";}@font-face{font-family:"Wingdings";}@font-face{font-family:"黑体";}@list l0:level1{mso-level-number-format:bullet;mso-level-suffix:tab;mso-level-text:\F0B7;mso-level-tab-stop:36.0000pt;mso-level-number-position:left;margin-left:18.0000pt; margin-bottom:0pt; margin-top:0pt; text-indent:0.0000pt;font-size:12.0000pt; font-family:‘Symbol‘; }@list l0:level2{mso-level-number-format:decimal;mso-level-suffix:tab;}@list l0:level3{mso-level-number-format:decimal;mso-level-suffix:tab;}@list l0:level4{mso-level-number-format:decimal;mso-level-suffix:tab;}@list l0:level5{mso-level-number-format:decimal;mso-level-suffix:tab;}@list l0:level6{mso-level-number-format:decimal;mso-level-suffix:tab;}@list l0:level7{mso-level-number-format:decimal;mso-level-suffix:tab;}@list l0:level8{mso-level-number-format:decimal;mso-level-suffix:tab;}@list l0:level9{mso-level-number-format:decimal;mso-level-suffix:tab;}@list l1:level1{mso-level-number-format:decimal;mso-level-suffix:tab;mso-level-text:"%1.";mso-level-tab-stop:39.0000pt;mso-level-number-position:left;margin-left:39.0000pt; text-indent:-18.0000pt; margin-bottom:0pt; margin-top:0pt; font-family:‘Times New Roman‘; }@list l2:level1{mso-level-number-format:bullet;mso-level-suffix:tab;mso-level-text:\F06C;mso-level-tab-stop:81.0000pt;mso-level-number-position:left;margin-left:81.0000pt; text-indent:-18.0000pt; margin-bottom:0pt; margin-top:0pt; font-family:‘Wingdings‘; }@list l3:level1{mso-level-number-format:decimal;mso-level-suffix:tab;mso-level-text:"%1.";mso-level-tab-stop:18.0000pt;mso-level-number-position:left;margin-left:18.0000pt; text-indent:-18.0000pt; margin-bottom:0pt; margin-top:0pt; font-family:‘Times New Roman‘; }@list l4:level1{mso-level-number-format:bullet;mso-level-suffix:tab;mso-level-text:\F06C;mso-level-tab-stop:18.0000pt;mso-level-number-position:left;margin-left:18.0000pt; text-indent:-18.0000pt; margin-bottom:0pt; margin-top:0pt; font-family:‘Wingdings‘; }@list l5:level1{mso-level-number-format:bullet;mso-level-suffix:tab;mso-level-text:\F06C;mso-level-tab-stop:60.0000pt;mso-level-number-position:left;margin-left:60.0000pt; text-indent:-18.0000pt; margin-bottom:0pt; margin-top:0pt; font-family:‘Wingdings‘; }@list l6:level1{mso-level-number-format:decimal;mso-level-suffix:tab;mso-level-text:"%1.";mso-level-tab-stop:60.0000pt;mso-level-number-position:left;margin-left:60.0000pt; text-indent:-18.0000pt; margin-bottom:0pt; margin-top:0pt; font-family:‘Times New Roman‘; }@list l7:level1{mso-level-number-format:bullet;mso-level-suffix:tab;mso-level-text:\F06C;mso-level-tab-stop:39.0000pt;mso-level-number-position:left;margin-left:39.0000pt; text-indent:-18.0000pt; margin-bottom:0pt; margin-top:0pt; font-family:‘Wingdings‘; }@list l8:level1{mso-level-number-format:bullet;mso-level-suffix:tab;mso-level-text:\F06C;mso-level-tab-stop:102.0000pt;mso-level-number-position:left;margin-left:102.0000pt; text-indent:-18.0000pt; margin-bottom:0pt; margin-top:0pt; font-family:‘Wingdings‘; }@list l9:level1{mso-level-number-format:decimal;mso-level-suffix:tab;mso-level-text:"%1.";mso-level-tab-stop:81.0000pt;mso-level-number-position:left;margin-left:81.0000pt; text-indent:-18.0000pt; margin-bottom:0pt; margin-top:0pt; font-family:‘Times New Roman‘; }@list l10:level1{mso-level-number-format:decimal;mso-level-suffix:tab;mso-level-text:"%1.";mso-level-tab-stop:102.0000pt;mso-level-number-position:left;margin-left:102.0000pt; text-indent:-18.0000pt; margin-bottom:0pt; margin-top:0pt; font-family:‘Times New Roman‘; }p.p0{margin:0pt;margin-bottom:0.0001pt;margin-bottom:0pt;margin-top:0pt;text-align:justify;font-size:10.5000pt; font-family:‘Times New Roman‘; }span.10{font-family:‘Times New Roman‘; }p.p15{margin-bottom:0pt;margin-top:0pt;border-top:none; ;mso-border-top-alt:none; ;border-right:none; ;mso-border-right-alt:none; ;border-bottom:none; ;mso-border-bottom-alt:none; ;border-left:none; ;mso-border-left-alt:none; ;padding:1pt 4pt 1pt 4pt ;text-align:justify;font-size:9.0000pt; font-family:‘Times New Roman‘; }p.p16{margin-bottom:0pt;margin-top:0pt;text-align:left;font-size:9.0000pt; font-family:‘Times New Roman‘; }@page{mso-page-border-surround-header:no;mso-page-border-surround-footer:no;}@page Section0{margin-top:72.0000pt;margin-bottom:72.0000pt;margin-left:90.0000pt;margin-right:90.0000pt;size:595.3000pt 841.9000pt;layout-grid:15.6000pt;}div.Section0{page:Section0;}</style>

NOIP1999 拦截导弹 

题目描述 Description

    某国为了防御敌国的导弹袭击，发展出一种导弹拦截系统。但是这种导弹拦截系统有一个缺陷：虽然它的第一发炮弹能够到达任意的高度，但是以后每一发炮弹都不 能高于前一发的高度。某天，雷达捕捉到敌国的导弹来袭。由于该系统还在试用阶段，所以只有一套系统，因此有可能不能拦截所有的导弹。

  

输入描述 Input Description

输入导弹依次飞来的高度（雷达给出的高度数据是不大于30000的正整数）

  

输出描述 Output Description

输出这套系统最多能拦截多少导弹，如果要拦截所有导弹最少要配备多少套这种导弹拦截系统。

样例输入 Sample Input

389 207 155 300 299 170 158 65 

样例输出 Sample Output

6

2

数据范围及提示 Data Size & Hint

导弹的高度<=30000，导弹个数<=20

 

 

 

 

思路

这道题的突破口在于问题的转化= =

先是第一问： “最多能拦截的导弹数”。根据题目中导弹的毛病，可以把问题转化成经典的最长不上升子序列，动态规划O(cnt2)完美解决；

再看第二问： “最少需要的系统数”。顺延上一问的思路，“不可能由之前已经确定的系统拦截下来的导弹”应当添加到当前位置前的最长上升子序列中。同样是经典问题，动态规划O(cnt2)。

最后稍微得瑟一下→_→在没有优化的情况下，这段代码在发帖前包揽了wikioi上“最快”“最短”以及“内存最少”三项指标~（好吧是因为这题太水了）

 

 1 #include <cstdio>
 2 using namespace std;
 3 int H[22], Suc[22]={1}, Cnt[22]={1}, mS=0, mC=0;
 4 int main()
 5 {
 6     freopen("testin","r",stdin);
 7     freopen("testout","w",stdout);
 8     int i,j,t,cnt=0;
 9     while(scanf("%d", &t)==1)
10         H[cnt++]=t;
11     for(i=1;i<cnt;++i) {
12         Suc[i]=Cnt[i]=1;
13         for(j=i-1;j>=0;--j) {
14             if(H[j]>=H[i]&&Suc[j]>=Suc[i])
15                 Suc[i]=Suc[j]+1;
16             if(H[j]<H[i]&&Cnt[j]>=Cnt[i])
17                 Cnt[i]=Cnt[j]+1;
18         }
19         if(Suc[i]>mS)mS=Suc[i];
20         if(Cnt[i]>mC)mC=Cnt[i];
21     }
22     printf("%d\n%d", mS, mC);
23     return 0;
24 }

 


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