Room and Moor

11916: Room and Moor

时间限制: 6 Sec  内存限制: 256 MB
提交: 2  解决: 2
[提交] [状态] [命题人:外部导入]

题目描述

PM Room defines a sequence A = {A1, A2,..., AN}, each of which is either 0 or 1. In order to beat him, programmer Moor has to construct another sequence B = {B1, B2,... , BN} of the same length, which satisfies that:

 

输入

The input consists of multiple test cases. The number of test cases T(T<=100) occurs in the first line of input.

For each test case:
The first line contains a single integer N (1<=N<=100000), which denotes the length of A and B.
The second line consists of N integers, where the ith denotes Ai.

 

输出

Output the minimal f (A, B) when B is optimal and round it to 6 decimals.

 

样例输入

复制样例数据

4
9
1 1 1 1 1 0 0 1 1
9
1 1 0 0 1 1 1 1 1
4
0 0 1 1
4
0 1 1 1

样例输出

1.428571
1.000000
0.000000
0.000000

 

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
const int maxn = 3e5 + 10;
const ll mod = 1e9 + 7;
const double eps = 1e-7;
struct node {
    int cnt0, cnt1;
    double val;
} v[maxn];
int T, n, cnt;
int c[maxn];

int main() {
    //freopen("1.txt", "r", stdin);
    stack<node> sk;
    scanf("%d", &T);
    while (T--) {
        scanf("%d", &n);
        for (register int i = 1; i <= n; ++i)scanf("%d", c + i);
        int l = 1, r = n;
        while (c[l] == 0 && l <= n)l++;
        while (c[r] == 1 && r >= 1)r--;
        if (l > r) {
            printf("0.000000\n");
            continue;
        }
        cnt = 0;
        for (register int i = l; i <= r;) {
            int n0 = 0, n1 = 0;
            while (c[i] == 1 && i <= r)i++, n1++;
            while (c[i] == 0 && i <= r)i++, n0++;
            v[++cnt].cnt0 = n0;
            v[cnt].cnt1 = n1;
            v[cnt].val = 1.0 * n1 / (double) (n0 + n1);
            //sk.push(v[cnt]);
        }
        //while (!sk.empty())sk.pop();
        for (register int i = 1; i <= cnt; ++i) {
            if (sk.empty())sk.push(v[i]);
            else {
                node last = sk.top();
                if (last.val <= v[i].val) {
                    sk.push(v[i]);
                } else {
                    node cur = v[i];
                    while (true) {
                        last = sk.top();
                        if (cur.val < last.val) {
                            cur.cnt0 += last.cnt0;
                            cur.cnt1 += last.cnt1;
                            cur.val = 1.0 * cur.cnt1 / (double) (cur.cnt0 + cur.cnt1);
                            sk.pop();
                        } else {
                            sk.push(cur);
                            break;
                        }
                        if (sk.empty()) {
                            sk.push(cur);
                            break;
                        }
                    }
                }
            }
        }
        node o;
        double res = 0;
        while (!sk.empty()) {
            o = sk.top();
            //cout<<"debug o.val="<<o.val<<' '<<"debug o.cnt0="<<o.cnt0<<' '<<"debug o.cnt1="<<o.cnt1<<endl;
            sk.pop();
            res += o.val * o.val * o.cnt0 + (1.0 - o.val) * (1.0 - o.val) * o.cnt1;
        }
        printf("%.6f\n", res);
    }
    return 0;
}