题面
Sol
模拟退火
再做数列上的\(DP\)
# include <bits/stdc++.h>
# define RG register
# define IL inline
# define Fill(a, b) memset(a, b, sizeof(a))
using namespace std;
typedef long long ll;
const int _(1005);
IL int Input(){
RG int x = 0, z = 1; RG char c = getchar();
for(; c < '0' || c > '9'; c = getchar()) z = c == '-' ? -1 : 1;
for(; c >= '0' && c <= '9'; c = getchar()) x = (x << 1) + (x << 3) + (c ^ 48);
return x * z;
}
const double EPS(1e-15);
const double dt(0.9993);
double a[_], ans = 1e18, f[50][50], sum[_], ave;
int n, m;
# define Sqr(x) ((x) * (x))
IL double Calc(){
Fill(f, 127); f[0][0] = 0;
for(RG int i = 1; i <= n; ++i) sum[i] = sum[i - 1] + a[i];
for(RG int i = 1; i <= n; ++i)
for(RG int j = 1; j <= i && j <= m; ++j)
for(RG int k = 0; k < i; ++k)
f[i][j] = min(f[i][j], f[k][j - 1] + Sqr(sum[i] - sum[k] - ave));
return f[n][m];
}
IL double SA(RG double T){
RG double cnt = 1e18;
for(; T > EPS; T *= dt){
RG int x = 1, y = 1;
while(x == y) x = rand() % n + 1, y = rand() % n + 1;
swap(a[x], a[y]);
RG double ret = Calc();
ans = min(ans, ret);
if(ret < cnt || exp((ret - ans) / T) * RAND_MAX < rand()) cnt = ret;
else swap(a[x], a[y]);
}
}
int main(RG int argc, RG char* argv[]){
n = Input(); m = Input();
srand(19260817);
for(RG int i = 1; i <= n; ++i) a[i] = Input(), ave += a[i];
ave /= m;
SA(1000000);
printf("%.2lf\n", sqrt(ans / m));
return 0;
}