洛谷P2447 [SDOI2010]外星千足虫(异或方程组)

题意

题目链接

Sol

异或高斯消元的板子题。

bitset优化一下，复杂度\(O(\frac{nm}{32})\)

找最优解可以考虑高斯消元的过程，因为异或的特殊性质，每次向下找的时候找到第一个1然后交换就行，这样显然是最优的

#include<bits/stdc++.h>
using namespace std;
const int MAXN = 2001;
inline int read() {
	char c = getchar(); int x = 0, f = 1;
	while(c < '0' || c > '9') {if(c == '-') f = -1; c = getchar();}
	while(c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
	return x * f;
}
int N, M;
bitset<MAXN> b[MAXN];
void Gauss() {
	int ans = 0;
	for(int i = 1; i <= N; i++) {
		int j = i;
		while(!b[j][i] && j < M + 1)
			j++;
		if(j == M + 1) {puts("Cannot Determine"); return ;}
		ans = max(ans, j);
		swap(b[i], b[j]);
		for(int j = 1; j <= M; j++) {
			if(i == j || !b[j][i]) continue;
			b[j] ^= b[i];
		}
	}
	printf("%d\n", ans);
	for(int i = 1; i <= N; i++)
		puts(!b[i][N + 1] ? "Earth" : "?y7M#");
}
int main() {
	N = read(); M = read();
	for(int i = 1; i <= M; i++) {
		string s; cin >> s;
		b[i][N + 1] = read();
		for(int j = 1; j <= N; j++) b[i][j] = (s[j - 1] == '0' ? 0 : 1);
	}
	Gauss();
	return 0;
}