河南省第一届ACM程序设计大赛解题报告

1.判断点是否落在凸多边形内

　　

 1 #include <iostream>

 2 #include <cstring>

 3 #include <cstdlib>

 4 #include <cstdio>

 5 #include <cmath>

 6 

 7 using namespace std;

 8 

 9 typedef struct Node 

10 {

11     int a,b;

12     

13 }Node;

14 Node node[25];

15 int N;

16 const double eps = 1e-7;

17 

18 double solve1() 

19 {

20     int i,j,k;

21     double sum = 0;

22     for(i=2; i<N; i++)

23     {

24         int x1 = node[1].a - node[i].a;

25         int x2 = node[1].a - node[i+1].a;

26         int y1 = node[1].b - node[i].b;

27         int y2 = node[1].b - node[i+1].b;

28         double temp = x1*y2 - x2*y1;

29         sum += temp;

30        

31     }

32     return 0.5*fabs(sum);

33 }

34 

35 

36 double solve2() 

37 {

38     int i,j,k;

39     double sum = 0;

40     for(i=1; i<N; i++)

41     {

42         int x1 = node[1].a - node[i].a;

43         int x2 = node[1].a - node[i+1].a;

44         int y1 = node[1].b - node[i].b;

45         int y2 = node[1].b - node[i+1].b;

46         double temp = x1*y2 - x2*y1;

47         /*

48         注意此处temp必须加上绝对值,求真实的面积,若是有向面积 ,则不论在内外都会成立 

49         */

50         sum += fabs(temp);

51        

52     }

53     return 0.5*fabs(sum);

54 }

55  

56 int main()

57 {

58     int i,j,k;

59     

60     int x,y;

61     while(cin>>N>>x>>y)

62     {

63         memset(node,0,sizeof(node));

64         for(i=1; i<=N; i++)

65         {

66             int a,b;

67             cin>>a>>b;

68             node[i].a = a;

69             node[i].b = b;

70         }

71         double ans1 = solve1();

72         double ans2 = solve2();

73         if(fabs(ans1 - ans2)<eps)

74             cout<<"YES"<<endl;

75         else

76             cout<<"NO"<<endl;

77         

78     }

79     //while(1);

80     return 0;

81      

82 }

2.最小生成树
　　

 1 #include <iostream>

 2 #include <cstring>

 3 #include <cstdlib>

 4 #include <cstdio>

 5 #include <cmath>

 6 using namespace std;

 7 

 8 const int maxn = 1010;

 9 int u[maxn], v[maxn], w[maxn];

10 int p[maxn], r[maxn];

11 int edge = 0;

12 int N;

13 

14 int find(int x)

15 {

16     if(p[x] == x)

17         return x;

18     else

19         return p[x] = find(p[x]);

20 }

21 

22 bool cmp(int i, int j)

23 {

24     return w[i] < w[j];

25 }

26 

27 int kruskal()

28 {

29     int i,j,k;

30     for(i=0; i<N; i++)      

31         p[i] = i;

32     for(i=0; i<edge; i++)   

33         r[i] = i;

34     sort(r,r+edge,cmp);//是edge 

35     int ans = 0;

36     for(i=0; i<edge; i++)

37     {

38         int e = r[i];

39         int x = find(u[e]);

40         int y = find(v[e]);

41         if(x!=y)

42         {

43             ans += w[e];

44             p[x] = y;

45             

46         }

47     }

48     return ans;

49 }

50 

51 int main()

52 {

53     int i,j,k;

54     

55     while(cin>>N)

56     {

57         memset(u,0,sizeof(u));

58         memset(v,0,sizeof(v));

59         memset(w,0,sizeof(w));

60         k = 0;

61         for(i=0; i<N; i++)

62             for(j=0; j<N; j++)

63             {

64                 int temp;

65                 if(j<=i)

66                 {

67                     cin>>temp;

68                     continue;

69                 }

70                 cin>>temp;

71                 if(temp>=0)

72                 {

73                     u[k] = i;

74                     v[k] = j;

75                     w[k++] = temp;  

76                     edge = k; 

77                 }                   

78             }

79         int ans = kruskal();

80         cout<<ans<<endl;    

81     }

82     return 0;

83 }

3.太水了
　　

 1 #include <iostream>

 2 #include <cstring>

 3 #include <cstdlib>

 4 #include <cstdio>

 5 #include <cmath>

 6 using namespace std;

 7 

 8 const int maxn = 1010;

 9 int N, L;

10 int a[maxn];

11 

12 int main()

13 {

14     int i,j,k;

15     while(cin>>N)

16     {

17         cin>>L;

18         for(i=0; i<N; i++)

19         {

20             cin>>a[i];

21         }

22         bool flag = false;

23         for(i=0; i<N&&!flag; i++)

24             for(j=i+1; j<N; j++)

25             {

26                 if(a[i] + a[j]==L)

27                 {

28                     cout<<i+1<<endl;

29                     cout<<j+1<<endl;

30                     flag = true;

31                     break;

32                     

33                 }

34                     

35             }

36     }    

37     return 0;

38 }

4.

 1 #include <iostream>

 2  #include <cstring>

 3  using namespace std;

 4  

 5  int c[5];

 6  int N,w;

 7  int m[5];

 8  int cnt = 0;

 9  

10  void dfs(int w, int k)

11  {

12      if(k==4)//k==4是出口，不是w==0 

13      {

14          if(w==0)

15          {

16              cnt++;

17              return ;

18              

19          }

20          return ;

21      } 

22      else

23          for(int i=m[k]; i>=0; i--)

24          {

25              if(w>=(c[k]*i))//若是i为0，则某一刻w始终不变，会死循环 

26                  dfs(w-c[k]*i, k+1);

27          }

28      

29  }

30  

31  int main()

32  {

33      int i,j,k;

34      for(i=0; i<4; i++)

35          cin>>c[i];

36      cin>>N;

37      for(i=0; i<N; i++)

38      {

39          cnt = 0;

40          for(j=0; j<4; j++)

41              cin>>m[j];

42          cin>>w;

43          dfs(w,0);

44          cout<<cnt<<endl;

45      }

46      //while(1);

47      return 0;

48  }

 

5.

 1 #include <iostream>

 2 #include <cstring>

 3 #include <cstdlib>

 4 #include <cstdio>

 5 #include <cmath>

 6 #include <algorithm>

 7 

 8 using namespace std;

 9 

10 const int maxn = 1000010;

11 long long a[maxn];

12 long long c[maxn];

13 int avg;

14 int N;

15 

16 void solve_c()

17 {

18     int i,j,k;

19     c[0] = 0;

20     c[1] = avg - a[1];

21     for(i=2; i<N; i++)

22     {

23         c[i] = c[i-1] + avg - a[i];

24         

25     }

26     

27 }

28 int main()

29 {

30     int i,j,k;

31     

32     while(cin>>N)

33     {

34         memset(a,0,sizeof(a));

35         memset(c,0,sizeof(c));

36         

37         long long sum = 0;

38         for(i=1; i<=N; i++)

39         {

40             cin>>a[i];

41             sum += a[i];

42         }

43         avg = sum/N;

44         solve_c();

45         sort(c,c+N);

46         long long temp = c[N/2];

47         long long ans = 0;

48         for(i=0; i<N; i++)

49         {

50             ans += abs(temp-c[i]);

51             

52         } 

53         cout<<ans<<endl;

54     }

55     return 0;

56     

57 }

6.

7.

8.