题目链接:
题目分析:
显然可以把过程分成以下几个过程
- 往前把能走的走完
- 向后转最接近(180°)的度数
- 向后把能走的走完
- 原地转完剩下的旋转操作
最后一步可以不用管,因为反正没有产生位移
需要操作一下的就是向后转的动作,用类似(0/1)背包的思想(DP)一下,然后余弦定理一下即可
代码:
#include<bits/stdc++.h>
using namespace std;
inline int read() {
int cnt = 0, f = 1; char c = getchar();
while (!isdigit(c)) {if (c == '-') f = -f; c = getchar();}
while (isdigit(c)) {cnt = (cnt << 3) + (cnt << 1) + (c ^ 48); c = getchar();}
return cnt * f;
}
int n, x, f, b, p = 1e3;
const double PI = 3.1415926535;
int trn[55], cnt;
double ans;
bool dp[55][361];
char c[10];
int main() {
n = read();
for (register int i = 1; i <= n; ++i) {
scanf("%s", c + 1), x = read();
if (c[1] == 'f') f += x;
if (c[1] == 'b') b += x;
if (c[1] == 'r') trn[++cnt] = -x;
if (c[1] == 'l') trn[++cnt] = x;
}
ans += f;
dp[0][0] = 1;
for (register int i = 1; i <= cnt; ++i)
for (register int j = 0; j < 360; ++j)
if (dp[i - 1][j] == 1)
dp[i][j] = 1, dp[i][(j + trn[i] + 360 * 10) % 360] = 1;
for (register int i = 0; i < 360; ++i)
if (dp[cnt][i] == 1) p = min(p, abs(i - 180));
ans = sqrt(f * f + b * b + 2 * b * f * cos(p * PI / 180));
printf("%.6lf", ans);
return 0;
}