POJ 1222 EXTENDED LIGHTS OUT 高斯消元 异或方程 (水

题目链接：点击打开链接

题意：

给定5*6 的灯的目标状态（开始全暗），每按下一个灯就会把这个灯及这灯相邻的4个灯状态改变。

输出一个按灯的方案使得由全暗变成输入的状态。

思路：

每盏灯都作为一个变量，

a1&x1 + a2&x2 + a3&x3 ··· a30&x30 = input[1][1]

 能影响到某盏灯的系数是1，其他是0

实际上是

x4 + x5 + x3 + x10 = input[4]

但其他不相关的变量也要填充进方程，所以前面系数设置为0。

共5*6个变量，系数矩阵30*30,增广矩阵 30*31.

回代时注意是系数和变量之间的符号是&

#include<cstdio>#include<cstring>#include<cmath>#include<vector>#include<algorithm>template <class T>inline bool rd(T &ret) {char c; int sgn;if (c = getchar(), c == EOF) return 0;while (c != '-' && (c<'0' || c>'9')) c = getchar();sgn = (c == '-') ? -1 : 1;ret = (c == '-') ? 0 : (c - '0');while (c = getchar(), c >= '0'&&c <= '9') ret = ret * 10 + (c - '0');ret *= sgn;return 1;}template <class T>inline void pt(T x) {if (x <0) {putchar('-');x = -x;}if (x>9) pt(x / 10);putchar(x % 10 + '0');}const double eps = 1e-8;typedef long long ll;using namespace std;int step[5][2], id[5][6];int A[30][31], init[30][31];int ans[30];int Guass(int mat[][31], int row, int col){int r, c, i, j;for (r = c = 0; r < row && c < col; r++, c++){for (i = r; i < row; i++)if (mat[i][c]>0)break;if (i == row){ r--; continue; }if (i != r)for (j = c; j <= col; j++)swap(mat[i][j], mat[r][j]);for (i = r + 1; i < row; i++)if(mat[i][c]>0)for (j = c; j <= col; j++)mat[i][j] ^= mat[r][j];}for (i = r; i < row; i++) if (mat[i][col] > 0)return 0;for (i = r - 1; i >= 0; i--){ans[i] = mat[i][col];for (j = i + 1; j < col; j++)ans[i] ^= (mat[i][j] && ans[j]);}return 1;}int main() {step[0][0] = 0; step[0][1] = 0;step[1][0] = 1; step[1][1] = 0;step[2][0] = 0; step[2][1] = 1;step[3][0] = -1; step[3][1] = 0;step[4][0] = 0; step[4][1] = -1;int now = 0;for (int i = 0; i < 5; i++)for (int j = 0; j < 6; j++)id[i][j] = now++;memset(init, 0, sizeof init);for (int i = 0; i < 5; i++)for (int j = 0; j < 6; j++){for (int k = 0; k < 5; k++){int x = i + step[k][0], y = j + step[k][1];if (0 <= x&&x<5 && 0 <= y&&y<6)init[id[i][j]][id[x][y]] = 1;}}int T, Cas = 1; rd(T);while (T-->0){for (int i = 0; i < 30; i++)for (int j = 0; j < 30; j++)A[i][j] = init[i][j];for (int i = 0; i < 5; i++)for (int j = 0; j < 6; j++)rd(A[id[i][j]][now]);Guass(A, 30, 30);printf("PUZZLE #%d\n", Cas++);for (int i = 0, tmp = 0; i < 5; i++)for (int j = 0; j < 6; j++){pt(ans[tmp++]);if (j == 5)puts(""); else putchar(' ');}}return 0;}

import java.io.BufferedReader;import java.io.InputStreamReader;import java.io.PrintWriter;import java.math.BigInteger;import java.text.DecimalFormat;import java.util.ArrayDeque;import java.util.ArrayList;import java.util.Arrays;import java.util.Collection;import java.util.Collections;import java.util.Comparator;import java.util.Deque;import java.util.HashMap;import java.util.Iterator;import java.util.LinkedList;import java.util.Map;import java.util.PriorityQueue;import java.util.Scanner;import java.util.Stack;import java.util.StringTokenizer;import java.util.TreeMap;import java.util.TreeSet;import java.util.Queue;import java.io.File;import java.io.FileInputStream;import java.io.FileNotFoundException;import java.io.FileOutputStream;public class Main {int[][] step = new int[5][2], id = new int[N][N];int[][] A = new int[N][N], init = new int[N][N];int[] ans = new int[N];int Guass(int[][] mat, int row, int col){int r, c, i, j;for (r = c = 0; r < row && c < col; r++, c++){for (i = r; i < row; i++)if (mat[i][c]>0)break;if (i == row){ r--; continue; }if (i != r)for (j = c; j <= col; j++){int tmp = mat[i][j]; mat[i][j] = mat[r][j]; mat[r][j] = tmp;}for (i = r + 1; i < row; i++)if(mat[i][c]>0)for (j = c; j <= col; j++)mat[i][j] ^= mat[r][j];}for (i = r; i < row; i++) if (mat[i][col] > 0)return 0;for (i = r - 1; i >= 0; i--){ans[i] = mat[i][col];for (j = i + 1; j < col; j++)ans[i] ^= (mat[i][j] & ans[j]);}return 1;}void work() throws Exception {step[0][0] = 0; step[0][1] = 0;step[1][0] = 1; step[1][1] = 0;step[2][0] = 0; step[2][1] = 1;step[3][0] = -1; step[3][1] = 0;step[4][0] = 0; step[4][1] = -1;int now = 0;for(int i = 0; i < 5; i++)for(int j = 0; j < 6; j++)id[i][j] = now++;for(int i = 0; i < N; i++)for(int j = 0; j < N; j++)init[i][j] = 0;for(int i = 0; i < 5; i++)for(int j = 0; j < 6; j++){for(int k = 0; k < 5; k++){int x = i+step[k][0], y = j+step[k][1];if(0<=x&&x<5&&0<=y&&y<6)init[id[i][j]][id[x][y]] = 1;}}int T = Int(), Cas = 1;while (T-->0){for(int i = 0; i < N; i++)for(int j = 0; j < N; j++)A[i][j] = init[i][j];for(int i = 0; i < 5; i++)for(int j = 0; j < 6; j++)A[id[i][j]][now] = Int();Guass(A, now, now);out.println("PUZZLE #" + (Cas++));for(int i = 0, tmp = 0; i < 5; i++)for(int j = 0; j < 6; j++){out.print(ans[tmp++]);if(j==5)out.println(); else out.print(" ");}}}public static void main(String[] args) throws Exception {Main wo = new Main();        in = new BufferedReader(new InputStreamReader(System.in));          out = new PrintWriter(System.out);  // in = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));// out = new PrintWriter(new File("output.txt"));wo.work();out.close();}static int N = 56;static int M = N * 2;DecimalFormat df = new DecimalFormat("0.0000");static int inf = (int) 1e9;static long inf64 = (long) 1e18;static double eps = 1e-8;static double Pi = Math.PI;static int mod = (int) 1e9 + 7;private String Next() throws Exception {while (str == null || !str.hasMoreElements())str = new StringTokenizer(in.readLine());return str.nextToken();}private int Int() throws Exception {return Integer.parseInt(Next());}private long Long() throws Exception {return Long.parseLong(Next());}private double Double() throws Exception {return Double.parseDouble(Next());}StringTokenizer str;static Scanner cin = new Scanner(System.in);static BufferedReader in;static PrintWriter out;class Edge{int from, to, dis, nex;Edge(){} Edge(int from, int to, int dis, int nex){this.from = from; this.to = to; this.dis = dis; this.nex =nex; }} Edge[] edge = new Edge[M<<1]; int[] head = new int[N]; int edgenum; void init_edge(){ for(int i = 0; i < N; i++)head[i] = -1; edgenum = 0;} void add(int u, int v, int dis){ edge[edgenum] = new Edge(u, v, dis, head[u]); head[u] = edgenum++; } /* */int upper_bound(int[] A, int l, int r, int val) {// upper_bound(A+l,A+r,val)-A;int pos = r;r--;while (l <= r) {int mid = (l + r) >> 1;if (A[mid] <= val) {l = mid + 1;} else {pos = mid;r = mid - 1;}}return pos;}int lower_bound(int[] A, int l, int r, int val) {// upper_bound(A+l,A+r,val)-A;int pos = r;r--;while (l <= r) {int mid = (l + r) >> 1;if (A[mid] < val) {l = mid + 1;} else {pos = mid;r = mid - 1;}}return pos;}int Pow(int x, int y) {int ans = 1;while (y > 0) {if ((y & 1) > 0)ans *= x;y >>= 1;x = x * x;}return ans;}double Pow(double x, int y) {double ans = 1;while (y > 0) {if ((y & 1) > 0)ans *= x;y >>= 1;x = x * x;}return ans;}int Pow_Mod(int x, int y, int mod) {int ans = 1;while (y > 0) {if ((y & 1) > 0)ans *= x;ans %= mod;y >>= 1;x = x * x;x %= mod;}return ans;}long Pow(long x, long y) {long ans = 1;while (y > 0) {if ((y & 1) > 0)ans *= x;y >>= 1;x = x * x;}return ans;}long Pow_Mod(long x, long y, long mod) {long ans = 1;while (y > 0) {if ((y & 1) > 0)ans *= x;ans %= mod;y >>= 1;x = x * x;x %= mod;}return ans;}int gcd(int x, int y) {if (x > y) {int tmp = x;x = y;y = tmp;}while (x > 0) {y %= x;int tmp = x;x = y;y = tmp;}return y;}int max(int x, int y) {return x > y ? x : y;}int min(int x, int y) {return x < y ? x : y;}double max(double x, double y) {return x > y ? x : y;}double min(double x, double y) {return x < y ? x : y;}long max(long x, long y) {return x > y ? x : y;}long min(long x, long y) {return x < y ? x : y;}int abs(int x) {return x > 0 ? x : -x;}double abs(double x) {return x > 0 ? x : -x;}long abs(long x) {return x > 0 ? x : -x;}boolean zero(double x) {return abs(x) < eps;}double sin(double x) {return Math.sin(x);}double cos(double x) {return Math.cos(x);}double tan(double x) {return Math.tan(x);}double sqrt(double x) {return Math.sqrt(x);}double fabs(double x){return x>0?x:-x;}}