​http://www.ifrog.cc/acm/problem/1137​

和差化积公式,

变成2 * sin((x + y) / 2) * cos((x - y) / 2) + sin(n - (x + y))

然后很重要的一个就是cos(x) = cos(-x)

这样,枚举x + y的取值i,当x + y取值是i的时候,x - y的取值也是有固定的规律,具体就是

i是偶数的时候,0、2、...、这样吧

i是奇数的时候,1、3......、这样吧

然后就要分情况取值,

当sin((x + y) / 2)小于0,就要取一个min去和它乘,否则娶个大的,

 

数组开大了TLE,不是很懂。

#include <bits/stdc++.h>
#define IOS ios::sync_with_stdio(false)
using namespace std;
#define inf (0x3f3f3f3f)
typedef long long int LL;
double dp[2][2];
void work() {
int n;
scanf("%d", &n);
dp[0][0] = dp[0][1] = 1;
dp[1][0] = dp[1][1] = cos(0.5);
double ans = -1.0;
for (int i = 2; i <= n - 1; ++i) {
double res = sin(i * 0.5);
if (res < 0) {
if (i & 1) {
ans = max(ans, 2 * res * dp[1][0] + sin(n - i));
} else ans = max(ans, 2 * res * dp[0][0] + sin(n - i));
} else {
if (i & 1) {
ans = max(ans, 2 * res * dp[1][1] + sin(n - i));
} else ans = max(ans, 2 * res * dp[0][1] + sin(n - i));
}
res = cos(i);
dp[0][0] = min(dp[0][0], res);
dp[0][1] = max(dp[0][1], res);
dp[1][0] = min(dp[1][0], res);
dp[1][1] = max(dp[1][1], res);
}
printf("%0.9f\n", ans);
}

int main() {
#ifdef local
freopen("data.txt", "r", stdin);
// freopen("data.txt", "w", stdout);
#endif
work();
return 0;
}

View Code

 

 

#include <bits/stdc++.h>
#define IOS ios::sync_with_stdio(false)
using namespace std;
#define inf (0x3f3f3f3f)
typedef long long int LL;
const int maxn = 3e6 + 20;
double dp[maxn][2];
void work() {
int n;
scanf("%d", &n);
dp[0][0] = dp[0][1] = cos(0);
dp[1][0] = dp[1][1] = cos(0.5);
// for (int i = 2; i <= n; ++i) {
// dp[i][0] = min(dp[i - 2][0], cos(i * 0.5));
// dp[i][1] = max(dp[i - 2][1], cos(i * 0.5));
// }
double ans = -1.0;
for (int i = 2; i <= n - 1; ++i) {
double res = sin(i * 0.5);
if (i & 1) {
ans = max(ans, 2 * res * dp[i - 2][0] + sin(n - i));
} else {
ans = max(ans, 2 * res * dp[i - 2][1] + sin(n - i));
}
res = cos(i * 0.5);
dp[i][0] = min(dp[i - 2][0], res);
dp[i][1] = max(dp[i - 2][1], res);
}
printf("%0.9f\n", ans);
}

int main() {
#ifdef local
freopen("data.txt", "r", stdin);
// freopen("data.txt", "w", stdout);
#endif
work();
return 0;
}

TLE code