[luoguP2447] [SDOI2010]外星千足虫（高斯消元 + bitset）

Posted 2020-10-06 蒟蒻zht的博客

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用bitset优化，要不然n^3肯定超时

消元过程中有几点需要注意，找到最大元后break，保证题目中所说的K最小

如果有自由元说明解很多，直接返回

 

#include <bitset>
#include <cstdio>
#define N 2050
#define max(x, y) ((x) > (y) ? (x) : (y))

int n, m, ans;
std::bitset <N> s[N];
char S[N][N];

inline int read()
{
	int x = 0, f = 1;
	char ch = getchar();
	for(; !isdigit(ch); ch = getchar()) if(ch == ‘-‘) f = -1;
	for(; isdigit(ch); ch = getchar()) x = (x << 1) + (x << 3) + ch - ‘0‘;
	return x * f;
}

inline bool Gauss()
{
	int i, j, k;
	for(j = 1; j <= n; j++)
	{
		k = j;
		for(i = j; i <= m; i++)
			if(s[i][j])
			{
				k = i;
				ans = max(ans, i);
				break;
			}
		if(!s[k][j]) return 0;
		if(k != j) swap(s[k], s[j]);
		for(i = j + 1; i <= m; i++)
			if(s[i][j])
				s[i] ^= s[j];
	}
	for(i = n; i >= 1; i--)
		for(j = i + 1; j <= n; j++)
			s[i][n + 1] = s[i][n + 1] ^ (s[i][j] * s[j][n + 1]);
}

int main()
{
	int i, j, x;
	n = read();
	m = read();
	for(i = 1; i <= m; i++)
	{
		scanf("%s", S[i] + 1);
		for(j = 1; j <= n; j++)
			s[i][j] = S[i][j] - ‘0‘;
		s[i][n + 1] = read();
	}
	if(Gauss())
	{
		printf("%d\n", ans);
		for(i = 1; i <= n; i++)
			if(s[i][n + 1]) puts("?y7M#");
			else puts("Earth");
	}
	else puts("Cannot Determine");
	return 0;
}