# 7-17题解整理

# A - A Card Game

简单公式推导 >   ( n - 1 ) ! * a [ 1 ] / n !

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <algorithm>
 4 #include <cstring>
 5 using namespace std;
 6
 7 int a[105], n;
 8
 9 int main() {
10     int t; scanf("%d", &t);
11     int cnt = 0;
12     while (t--) {
13         scanf("%d", &n);
14         int sum = 0;
15         for(int i = 1;i <= n; ++i) {
16             scanf("%d", &a[i]);
17             sum += a[i];
18         }
19         double ans = (double) a[1] / sum;
20         printf("Case %d: %.6lf\n", ++cnt, ans);
21     }
22     return 0;
23 }

# [F - Random Sequence]

暴力找规律＋打表

 // 打表 1 #include <cstdio>
 2 #include <algorithm>
 3 #include <cmath>
 4 using namespace std;
 5
 6 int a[20];
 7
 8 int main() {
 9     for (int n = 1; n <= 15; ++n) {
10         double ans = 0;
11         for (int i = 0; i < (1 << n); ++i) {
12             for (int j = 0; j < n; ++j) {
13                 if (i & (1 << j)) a[j] = 1;
14                 else a[j] = -1;
15             }
16             int maxn = 0;
17             for (int len = 1; len <= n; ++len)
18                 for (int j = 0; j + len - 1 < n; ++j) {
19                     int sum = 0;
20                     for (int k = j; k <= j + len - 1; ++k) {
21                         sum += a[k];
22                         maxn = max(maxn, abs(sum));
23                     }
24                 }
25             ans += maxn;
26         }
27         printf("%.6f\n", ans / pow(2, n));
28     }
29     return 0;
30 }

找规律：

 1 #include <cstdio>
 2
 3 double a[1505];
 4
 5 void init() {
 6     double d = 1.0 / 2;
 7     a[1] = 1;
 8     for (int i = 2; i <= 1500; ++i) {
 9         if (i % 2 == 0 && i != 2)
10             d *= 1.0 * (i - 1) / i;
11         a[i] = a[i - 1] + d;
12     }
13 }
14
15 int main() {
16     init();
17     int t; scanf("%d", &t);
18     int cas = 0, n;
19     while (t--) {
20         scanf("%d", &n);
21         printf("Case %d: %.6f\n", ++cas, a[n]);
22     }
23     return 0;
24 }

# [H - SanguoSHA]

６!*6!全排列暴力，注意全排列是从当前字典序开始的，用之前需要重新排序．

 1 #include <iostream>
 2 #include <cstdio>
 3 #include <algorithm>
 4 #include <cstring>
 5 #include <map>
 6 #include <vector>
 7 using namespace std;
 8
 9 vector <string> vec[7], ans;
10 string name[7];
11
12 int main() {
13     int t; scanf("%d", &t);
14     int cnt = 0;
15     while (t--) {
16         int n; scanf("%d", &n);
17         ans.clear();
18         for (int i = 0; i < 7; ++i) vec[i].clear();
19         for (int i = 1; i <= n; ++i) cin >> name[i];
20         for (int i = 1; i <= n; ++i) {
21             int y; scanf("%d", &y);
22             while (y--) {
23                 string x; cin >> x;
24                 vec[i].push_back(x);
25             }
26         }
27         int tmp[7];
28         sort(name + 1, name + n + 1);
29         do {
30             for (int i = 1; i <= n; ++i) tmp[i] = i;
31             bool flag2 = 0;
32             do {
33                 int p1 = 1, p2 = 1;
34                 while (1) {
35                     int flag = 1;
36                     for (int i = 0; i < (int) vec[tmp[p1]].size(); ++i)
37                         if (vec[tmp[p1]][i] == name[p2]) {
38                             p2++;
39                             flag = 0;
40                             break;
41                         }
42                     if (flag) p1++;
43                     if (p1 == n + 1 && p2 <= n)
44                         break;
45                     if (p2 == n + 1 && p1 <= n){
46                         flag2 = 1;
47                         break;
48                     }
49                 }
50                 if (flag2) break;
51             } while (next_permutation(tmp + 1, tmp + n + 1));
52             if (flag2 == 0) {
53                 string t; t.append(name[1]);
54                 for (int i = 2; i <= n; ++i)
55                     t.append(" " + name[i]);
56                 ans.push_back(t);
57             }
58         } while (next_permutation(name + 1, name + n + 1));
59         int f = ans.size();
60         printf("Case %d: %s\n", ++cnt, f ? "Yes" : "No");
61         if (f) cout << ans[0] << endl;
62     }
63     return 0;
64 }

# J - Phage War

是一道简单的贪心，让等待时间最长的最先来就行．

 1 #include <cstdio>
 2 #include <algorithm>
 3 #include <cstring>
 4 using namespace std;
 5 const int N = 1e5 + 5;
 6
 7 struct node {
 8     int s, t;
 9 } a[N];
10
11 bool cmp(node a, node b) {
12     if (a.t == b.t) return a.s > b.s;
13     return a.t > b.t;
14 }
15
16 int main() {
17     int cnt = 0, n;
18     int t; scanf("%d", &t);
19     while (t--) {
20         scanf("%d", &n);
21         for (int i = 1; i <= n; ++i)  scanf("%d%d", &a[i].s, &a[i].t);
22         sort(a + 1, a + n + 1, cmp);
23         int t = 0, maxn = 0;
24         for (int i = 1; i <= n; ++i) {
25             t += a[i].s;
26             maxn = max(t + a[i].t, maxn);
27         }
28         printf("Case %d: %d\n", ++cnt, maxn);
29     }
30     return 0;
31 }