CodeForces 377C/378E Captains Mode 状态压缩动态规划

CF的题目描述都好长。。

令dp[i][state]表示此时队1与队2的力量差。

考察dp[i-1][state]能更新的答案。

有dp[i][state|(1<<j)],若state的第j位为0。

对于ban的情况，并不改变答案。

对于pick，如果是队1，那么上状态答案加上该英雄的力量值，队2减去。

可开滚动数组。

复杂度O(m^2*2^m)，Tutorial说有O(m*2^m)，然而能水过就行233。

#include <cstdio>
#include <algorithm>
#include <set>
using namespace std;
const int N = 100, M = 20, STATE = 1 << 20, inf = 2147483647;
int s
, team[M], wa[STATE], wb[STATE];
char action[M][2];

int countBit(int n) {
int ans = 0;
for (; n; ans++) n &= n - 1;
return ans;
}

int main() {
int n, i, m, *best = wa, *nbest = wb;
scanf("%d", &n);
for (i = 0; i < n; i++)
scanf("%d", s + i);
sort (s, s + n, greater<int>());
scanf("%d", &m);
for (i = 0; i < m; i++)
scanf("%s%d", action[i], team + i);
for (i = m - 1; i >= 0; i--) {
fill(nbest, nbest + STATE, team[i] == 1 ? -inf : inf);
for (int sta = 0; sta < STATE; sta++) {
if (countBit(sta) != i) continue;
for (int j = 0; j < m; j++)
if ((sta & (1 << j)) == 0) {
int nsta = sta | (1 << j);
if (action[i][0] == 'b')
if (team[i] == 1)
nbest[sta] = max(nbest[sta], best[nsta]);
else
nbest[sta] = min(nbest[sta], best[nsta]);
else
if (team[i] == 1)
nbest[sta] = max(nbest[sta], best[nsta] + s[j]);
else
nbest[sta] = min(nbest[sta], best[nsta] - s[j]);
}
}
swap(best, nbest);
}
printf("%d", best[0]);
return 0;
}
http://codeforces.com/problemset/problem/377/C
C. Captains Mode

time limit per test
2 seconds

memory limit per test
256 megabytes

input
standard input

output
standard output

Kostya is a progamer specializing in the discipline of Dota 2. Valve Corporation, the developer of this game, has recently released a new patch which turned the balance of the game upside down. Kostya, as the captain of the team, realizes that the greatest
responsibility lies on him, so he wants to resort to the analysis of innovations patch from the mathematical point of view to choose the best heroes for his team in every game.

A Dota 2 match involves two teams, each of them must choose some heroes that the players of the team are going to play for, and it is forbidden to choose the same hero several times, even in different teams. In large electronic sports competitions where Kostya's
team is going to participate, the matches are held in the Captains Mode. In this mode the captains select the heroes by making one of two possible actions in a certain, predetermined order: pick or ban.

To pick a hero for the team. After the captain picks, the picked hero goes to his team (later one of a team members will play it) and can no longer be selected by any of the teams.

To ban a hero. After the ban the hero is not sent to any of the teams, but it still can no longer be selected by any of the teams.

The team captain may miss a pick or a ban. If he misses a pick, a random hero is added to his team from those that were available at that moment, and if he misses a ban, no hero is banned, as if there was no ban.

Kostya has already identified the strength of all the heroes based on the new patch fixes. Of course, Kostya knows the order of picks and bans. The strength of a team is the sum of the strengths of the team's heroes and both teams that participate in the match
seek to maximize the difference in strengths in their favor. Help Kostya determine what team, the first one or the second one, has advantage in the match, and how large the advantage is.

Input

The first line contains a single integer n (2 ≤ n ≤ 100) —
the number of heroes in Dota 2.

The second line contains n integers s1, s2,
..., sn (1 ≤ si ≤ 106) —
the strengths of all the heroes.

The third line contains a single integer m (2 ≤ m ≤ min(n, 20)) —
the number of actions the captains of the team must perform.

Next m lines look like "action team",
where action is the needed action: a pick (represented as a "p")
or a ban (represented as a "b"), and team is
the number of the team that needs to perform the action (number 1 or 2).

It is guaranteed that each team makes at least one pick. Besides, each team has the same number of picks and the same number of bans.

Output

Print a single integer — the difference between the strength of the first team and the strength of the second team if the captains of both teams will act optimally well.

Sample test(s)

input

2
2 1
2
p 1
p 2

output

1

input

6
6 4 5 4 5 5
4
b 2
p 1b 1p 2

output

0

input

4
1 2 3 4
4
p 2
b 2
p 1b 1

output

-2