Codeforces Round #337 (Div.2)

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原文链接：http://www.cnblogs.com/cyd308/p/5140498.html

本博客讨论了两个算法问题：如何将一根长度为n的木棍切割成四段，使得可以形成矩形但无法形成正方形；以及在有限纸张上绘制最多方块的策略。涉及数论和贪心算法的应用。

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Pasha has a wooden stick of some positive integer length n. He wants to perform exactly three cuts to get four parts of the stick. Each part must have some positive integer length and the sum of these lengths will obviously be n.

Pasha likes rectangles but hates squares, so he wonders, how many ways are there to split a stick into four parts so that it's possible to form a rectangle using these parts, but is impossible to form a square.

Your task is to help Pasha and count the number of such ways. Two ways to cut the stick are considered distinct if there exists some integer x, such that the number of parts of length x in the first way differ from the number of parts of length x in the second way.

Input

The first line of the input contains a positive integer n (1 ≤ n ≤ 2·109) — the length of Pasha's stick.

Output

The output should contain a single integer — the number of ways to split Pasha's stick into four parts of positive integer length so that it's possible to make a rectangle by connecting the ends of these parts, but is impossible to form a square.

Sample test(s)

input

output

input

output

Note

There is only one way to divide the stick in the first sample {1, 1, 2, 2}.

Four ways to divide the stick in the second sample are {1, 1, 9, 9}, {2, 2, 8, 8}, {3, 3, 7, 7} and {4, 4, 6, 6}. Note that {5, 5, 5, 5} doesn't work.

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 
 4 int main()
 5 {
 6     int n;
 7     int i,j,k;
 8     scanf("%d",&n);
 9     if(n%2==0)
10     {
11         int ans=n/4;
12         if(n%4==0)
13             ans--;
14         printf("%d\n",ans);
15     }
16     else
17         printf("0\n");
18 }

View Code

Vika has n jars with paints of distinct colors. All the jars are numbered from 1 to n and the i-th jar contains ai liters of paint of color i.

Vika also has an infinitely long rectangular piece of paper of width 1, consisting of squares of size 1 × 1. Squares are numbered 1, 2, 3and so on. Vika decided that she will start painting squares one by one from left to right, starting from the square number 1 and some arbitrary color. If the square was painted in color x, then the next square will be painted in color x + 1. In case of x = n, next square is painted in color 1. If there is no more paint of the color Vika wants to use now, then she stops.

Square is always painted in only one color, and it takes exactly 1 liter of paint. Your task is to calculate the maximum number of squares that might be painted, if Vika chooses right color to paint the first square.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 200 000) — the number of jars with colors Vika has.

The second line of the input contains a sequence of integers a1, a2, ..., an (1 ≤ ai ≤ 109), where ai is equal to the number of liters of paint in the i-th jar, i.e. the number of liters of color i that Vika has.

Output

The only line of the output should contain a single integer — the maximum number of squares that Vika can paint if she follows the rules described above.

Sample test(s)

input

5
2 4 2 3 3

output

input

3
5 5 5

output

input

6
10 10 10 1 10 10

output

Note

In the first sample the best strategy is to start painting using color 4. Then the squares will be painted in the following colors (from left to right): 4, 5, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5.

In the second sample Vika can start to paint using any color.

In the third sample Vika should start painting using color number 5.

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 const int inf=0x3f3f3f3f;
 4 int a[200005];
 5 int main()
 6 {
 7     int n;
 8     int i,j,k;
 9     scanf("%d",&n);
10     int mi=inf,ma=0;
11     for(i=1;i<=n;i++)
12     {
13         scanf("%d",&a[i]);
14         if(a[i]<mi)
15             mi=a[i];
16     }
17     int x=0;
18     for(i=1;i<=n;i++)
19     {
20         if(a[i]==mi)
21             x=0;
22         else
23             x++;
24         if(x>ma)
25             ma=x;
26     }
27     for(i=1;i<=n;i++)
28     {
29         if(a[i]==mi)
30             break;
31         x++;
32         if(x>ma)
33             ma=x;
34     }
35     printf("%I64d\n",1ll*mi*n+1ll*ma);
36 }

View Code

The semester is already ending, so Danil made an effort and decided to visit a lesson on harmony analysis to know how does the professor look like, at least. Danil was very bored on this lesson until the teacher gave the group a simple task: find 4 vectors in 4-dimensional space, such that every coordinate of every vector is 1 or - 1 and any two vectors are orthogonal. Just as a reminder, two vectors in n-dimensional space are considered to be orthogonal if and only if their scalar product is equal to zero, that is:

$\text{[math]}$ .

Danil quickly managed to come up with the solution for this problem and the teacher noticed that the problem can be solved in a more general case for 2k vectors in 2k-dimensinoal space. When Danil came home, he quickly came up with the solution for this problem. Can you cope with it?

Input

The only line of the input contains a single integer k (0 ≤ k ≤ 9).

Output

Print 2k lines consisting of 2k characters each. The j-th character of the i-th line must be equal to ' * ' if the j-th coordinate of the i-th vector is equal to - 1, and must be equal to ' + ' if it's equal to + 1. It's guaranteed that the answer always exists.

If there are many correct answers, print any.

Sample test(s)

input

output

++**
+*+*
++++
+**+

Note

Consider all scalar products in example:

Vectors 1 and 2: ( + 1)·( + 1) + ( + 1)·( - 1) + ( - 1)·( + 1) + ( - 1)·( - 1) = 0
Vectors 1 and 3: ( + 1)·( + 1) + ( + 1)·( + 1) + ( - 1)·( + 1) + ( - 1)·( + 1) = 0
Vectors 1 and 4: ( + 1)·( + 1) + ( + 1)·( - 1) + ( - 1)·( - 1) + ( - 1)·( + 1) = 0
Vectors 2 and 3: ( + 1)·( + 1) + ( - 1)·( + 1) + ( + 1)·( + 1) + ( - 1)·( + 1) = 0
Vectors 2 and 4: ( + 1)·( + 1) + ( - 1)·( - 1) + ( + 1)·( - 1) + ( - 1)·( + 1) = 0
Vectors 3 and 4: ( + 1)·( + 1) + ( + 1)·( - 1) + ( + 1)·( - 1) + ( + 1)·( + 1) = 0

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 
 4 char a[600][600];
 5 int main()
 6 {
 7 
 8     int k,n=1;
 9     int i,j,l;
10     scanf("%d",&k);
11     a[1][1]='+';
12     for(i=1;i<=k;i++)
13     {
14         for(j=1;j<=n;j++)
15         {
16             for(l=1;l<=n;l++)
17             {
18                 a[j][l+n]=a[j][l];
19             }
20             for(l=1;l<=n;l++)
21             {
22                 if(a[j][l]=='+')
23                     a[j+n][l]='*';
24                 else
25                     a[j+n][l]='+';
26                 a[j+n][l+n]=a[j][l];
27             }
28         }
29         n=n*2;
30     }
31     for(i=1;i<=n;i++)
32     {
33         for(j=1;j<=n;j++)
34         {
35             printf("%c",a[i][j]);
36         }
37         printf("\n");
38     }
39     return 0;
40 }

View Code

Vika has an infinite sheet of squared paper. Initially all squares are white. She introduced a two-dimensional coordinate system on this sheet and drew n black horizontal and vertical segments parallel to the coordinate axes. All segments have width equal to 1 square, that means every segment occupy some set of neighbouring squares situated in one row or one column.

Your task is to calculate the number of painted cells. If a cell was painted more than once, it should be calculated exactly once.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 100 000) — the number of segments drawn by Vika.

Each of the next n lines contains four integers x1, y1, x2 and y2 ( - 109 ≤ x1, y1, x2, y2 ≤ 109) — the coordinates of the endpoints of the segments drawn by Vika. It is guaranteed that all the segments are parallel to coordinate axes. Segments may touch, overlap and even completely coincide.

Output

Print the number of cells painted by Vika. If a cell was painted more than once, it should be calculated exactly once in the answer.

Sample test(s)

input

output

input

output

Note

In the first sample Vika will paint squares (0, 1), (1, 1), (2, 1), (1, 2), (1, 3), (1, 4), (0, 3) and (2, 3).

  1 #include <bits/stdc++.h>
  2 using namespace std;
  3 const int inf=0x3f3f3f3f;
  4 struct Node
  5 {
  6     int u;
  7     int v;
  8     int h;
  9     int c;
 10 };
 11 
 12 Node a[200005],e[100005],f[100005];
 13 int tree[200005],n,l,m1,m2,num,b[200005];
 14 long long sum;
 15 map <int,int> d;
 16 
 17 void add(int k,int val)
 18 {
 19     while(k<=num)
 20     {
 21         tree[k]+=val;
 22         k+=k&-k;
 23     }
 24 }
 25 
 26 int read(int k)
 27 {
 28     int Sum=0;
 29     while(k)
 30     {
 31         Sum+=tree[k];
 32         k-=k&-k;
 33     }
 34     return Sum;
 35 }
 36 
 37 bool cmp(Node o,Node p)
 38 {
 39     if(o.h!=p.h)
 40     {
 41         return o.h<p.h;
 42     }
 43     else
 44         return o.u<p.u;
 45 }
 46 
 47 bool cmp2(Node o,Node p)
 48 {
 49     if(o.h!=p.h)
 50     {
 51         return o.h<p.h;
 52     }
 53     else
 54     {
 55         return o.c>p.c;
 56     }
 57 }
 58 
 59 void Unite()
 60 {
 61     int i,j,now,newu,newv;
 62     sort(e+1,e+m1+1,cmp);
 63     sort(f+1,f+m2+1,cmp);
 64 
 65     now=inf;
 66     for(i=1;i<=m1;i++)
 67     {
 68         if(e[i].h!=now)
 69         {
 70             //printf("h\n");
 71             if(now!=inf)
 72             {
 73                 l++;
 74                 a[l].u=now,a[l].h=newu,a[l].c=1;
 75                 l++;
 76                 a[l].u=now,a[l].h=newv,a[l].c=-1;
 77                 sum=sum+newv-newu+1;
 78                 if(d[now]!=1)
 79                 {
 80                     b[++num]=now;d[now]=1;
 81                 }
 82             }
 83             now=e[i].h;
 84             newu=e[i].u,newv=e[i].v;
 85         }
 86         else
 87         {
 88             if(e[i].u<=newv)
 89             {
 90                 newv=max(newv,e[i].v);
 91             }
 92             else
 93             {
 94                 l++;
 95                 a[l].u=now,a[l].h=newu,a[l].c=1;
 96                 l++;
 97                 a[l].u=now,a[l].h=newv,a[l].c=-1;
 98                 sum=sum+newv-newu+1;
 99                 if(d[now]!=1)
100                 {
101                     b[++num]=now;d[now]=1;
102                 }
103                 newu=e[i].u,newv=e[i].v;
104             }
105         }
106     }
107     if(now!=inf)
108     {
109         l++;
110         a[l].u=now,a[l].h=newu,a[l].c=1;
111         l++;
112         a[l].u=now,a[l].h=newv,a[l].c=-1;
113         sum=sum+newv-newu+1;
114         if(d[now]!=1)
115         {
116             b[++num]=now;d[now]=1;
117         }
118     }
119     //printf("^%I64d\n",sum);
120     now=inf;
121     for(i=1;i<=m2;i++)
122     {
123         if(f[i].h!=now)
124         {
125             if(now!=inf)
126             {
127                 l++;
128                 a[l].u=newu,a[l].v=newv,a[l].h=now,a[l].c=0;
129                 sum=sum+newv-newu+1;
130                 if(d[newu]!=1)
131                 {
132                     b[++num]=newu;d[newu]=1;
133                 }
134                 if(d[newv]!=1)
135                 {
136                     b[++num]=newv;d[newv]=1;
137                 }
138             }
139             now=f[i].h;
140             newu=f[i].u,newv=f[i].v;
141         }
142         else
143         {
144             if(f[i].u<=newv)
145             {
146                 newv=max(newv,f[i].v);
147             }
148             else
149             {
150                 l++;
151                 a[l].u=newu,a[l].v=newv,a[l].h=now,a[l].c=0;
152                 sum=sum+newv-newu+1;
153                 if(d[newu]!=1)
154                 {
155                     b[++num]=newu;d[newu]=1;
156                 }
157                 if(d[newv]!=1)
158                 {
159                     b[++num]=newv;d[newv]=1;
160                 }
161                 newu=f[i].u,newv=f[i].v;
162             }
163         }
164     }
165     if(now!=inf)
166     {
167         l++;
168         a[l].u=newu,a[l].v=newv,a[l].h=now,a[l].c=0;
169         sum=sum+newv-newu+1;
170         if(d[newu]!=1)
171         {
172             b[++num]=newu;d[newu]=1;
173         }
174         if(d[newv]!=1)
175         {
176             b[++num]=newv;d[newv]=1;
177         }
178     }
179 }
180 
181 int main()
182 {
183     int i,j;
184     int x1,x2,y1,y2;
185     memset(tree,0,sizeof(tree));d.clear();
186     m1=0,m2=0,l=0,num=0;  sum=0;
187 
188     scanf("%d",&n);
189     for(i=1;i<=n;i++)
190     {
191         scanf("%d %d %d %d",&x1,&y1,&x2,&y2);
192 
193         if(x1==x2 && y1!=y2)            //垂直
194         {
195             if(y1>y2)
196                 swap(y1,y2);
197             m1++;
198             e[m1].u=y1,e[m1].v=y2,e[m1].h=x1,e[m1].c=1;
199         }
200         else                            //水平
201         {
202             if(x1>x2)
203                 swap(x1,x2);
204             m2++;
205             f[m2].u=x1,f[m2].v=x2,f[m2].h=y1,f[m2].c=2;
206         }
207     }
208 
209     Unite();
210     sort(b+1,b+num+1);
211     sort(a+1,a+l+1,cmp2);
212     //printf("%d %d %d %d\n",m1,m2,num,l);
213     //printf("%I64d\n",sum);
214     for(i=1;i<=l;i++)
215     {
216         if(a[i].c==0)
217         {
218             int s;
219             x1=lower_bound(b+1,b+num+1,a[i].u)-b;
220             x2=lower_bound(b+1,b+num+1,a[i].v)-b;
221             s=read(x2)-read(x1-1);
222             //printf("^^%d:%d %d:%d %d\n",x1,read(x1-1),x2,read(x2),s);
223             sum=sum-s;
224         }
225         else
226         {
227             x1=lower_bound(b+1,b+num+1,a[i].u)-b;
228             //printf("^^^%d %d\n",x1,a[i].c);
229             add(x1,a[i].c);
230         }
231     }
232 
233     printf("%I64d\n",sum);
234 
235 }