[HNOI2013]游走

一看就是高斯消元。

但没想到边的期望经过次数=点的期望 / 点的度数

官方数据有误。

我的代码在gcc (Ubuntu/Linaro 4.4.4-14ubuntu5) 4.4.5 下可以过。

在 gcc 4.6.3 g++ Main.cc -o Main -Wall -lm --static -DONLINE_JUDGE 下可以过 （去掉-O2）

/**

 * Problem:HNOI2013-d2p2

 * Author:Shun Yao

 * Time:2013.5.28

 * Result:Accepted

 * Memo:DP, greedy, guass

 */



#include <cstring>

#include <cstdlib>

#include <cstdio>

#include <cmath>

#include <algorithm>



const long Maxn = 505;



long n, m, d[Maxn];

double a[Maxn][Maxn], w[Maxn];



class lnode {

public:

	long u, v;

	lnode() {}

	~lnode() {}

} line[Maxn * Maxn >> 1];



bool cmpa(double x, double y) {

	return x > y;

}



int main() {

	freopen("d2p2.in", "r", stdin);

	freopen("d2p2.out", "w", stdout);

	scanf("%ld%ld", &n, &m);

	memset(d, 0, sizeof d);

	for (long i = 1; i <= m; ++i) {

		scanf("%ld%ld", &line[i].u, &line[i].v);

		++d[line[i].u];

		++d[line[i].v];

	}

	for (long i = 1; i < n; ++i)

		a[i][i] = 1.0;

	a[1][0] = 1.0;

	for (long i = 1; i <= m; ++i) {

		if (line[i].u == n || line[i].v == n)

			continue;

		a[line[i].u][line[i].v] -= 1.0 / d[line[i].v];

		a[line[i].v][line[i].u] -= 1.0 / d[line[i].u];

	}

	for (long i = 1; i < n; ++i) {

		long pos;

		for (long j = i; j < n; ++j) {

			if (fabs(a[j][i]) > 1e-16) {

				pos = j;

				break;

			}

		}

		if (pos != i) {

			std::swap(a[pos][0], a[i][0]);

			for (long j = i; j < n; ++j)

				std::swap(a[pos][j], a[i][j]);

		}

		for (long j = i + 1; j < n; ++j)

			if (fabs(a[j][i]) > 1e-16) {

				double x = a[j][i] / a[i][i];

				a[j][0] -= a[i][0] * x;

				for (long k = i; k < n; ++k)

					a[j][k] -= a[i][k] * x;

			}

	}

	for (long i = n - 1; i; --i) {

		for (long j = i + 1; j < n; ++j)

			a[i][0] -= a[i][j] * a[j][0];

		a[i][0] /= a[i][i];

	}

	for (long i = 1; i <= m; ++i)

		w[i] = a[line[i].u][0] / d[line[i].u] + a[line[i].v][0] / d[line[i].v];

	std::sort(w + 1, w + m + 1, cmpa);

	double ans = 0.0;

	for (long i = 1; i <= m; ++i)

		ans += i * w[i];

	printf("%.3lf", ans);

	fclose(stdin);

	fclose(stdout);

	return 0;

}