UVA 1560 - Extended Lights Out(高斯消元)

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UVA 1560 - Extended Lights Out

題目連結

題意：給定一個矩陣，1代表開著燈，0代表關燈，沒按一個開關，周圍4個位置都會變化，問一個按的方法使得所有燈都變暗

思路：兩種做法：
1、枚舉遞推
這個比較簡單，就枚舉第一行，然後遞推過去，每次如果上一行是亮燈，則下一行開關必須按下去

2、高斯消元，
這個做法比較屌一些，每個位置對應上下左右中5個位置可以列出一個異或運算式，然後30個位置對應30個異或運算式，利用高斯消元法就能求出每個位置的解了

代碼：

高斯消元法：

#include <cstdio>#include <cstring>#include <algorithm>using namespace std;const int d[5][2] = {{0, 0}, {0, 1}, {0, -1}, {1, 0}, {-1, 0}};int t, a[31][31], out[6][6];void back() {    for (int i = 29; i >= 0; i--) {out[i / 6][i % 6] = a[i][30];for (int j = 0; j < i; j++) {    if (a[j][i])a[j][30] ^= a[i][30];}    }}void guess() {    for (int i = 0; i < 30; i++) {int k = i;for (; k < 30; k++)    if (a[k][i]) break;for (int j = 0; j <= 30; j++)    swap(a[i][j], a[k][j]);for (int j = i + 1; j < 30; j++) {    if (a[j][i]) {for (int k = i; k <= 30; k++)    a[j][k] ^= a[i][k];    }}    }    back();}int main() {    int cas = 0;    scanf("%d", &t);    while (t--) {memset(a, 0, sizeof(a));for (int i = 0; i < 30; i++)    scanf("%d", &a[i][30]);for (int i = 0; i < 30; i++) {    int x = i / 6, y = i % 6;    for (int j = 0; j < 5; j++) {int xx = x + d[j][0];int yy = y + d[j][1];if (xx < 0 || xx >= 5 || yy < 0 || yy >= 6) continue;a[i][xx * 6 + yy] = 1;    }}guess();printf("PUZZLE #%d\n", ++cas);for (int i = 0; i < 5; i++) {    for (int j = 0; j < 5; j++)printf("%d ", out[i][j]);    printf("%d\n", out[i][5]);}    }    return 0;}

枚舉遞推：

#include <cstdio>#include <cstring>#include <algorithm>using namespace std;const int d[5][2] = {{0, 0}, {1, 0}, {-1, 0}, {0, 1}, {0, -1}};const int N = 6;int t, g[N][N], tmp[N][N], out[N][N];bool judge(int s) {    memset(out, 0, sizeof(out));    for (int i = 0; i < 5; i++)for (int j = 0; j < 6; j++)    tmp[i][j] = g[i][j];    for (int i = 0; i < 6; i++) {if (s&(1<<i)) {    out[0][i] = 1;    for (int j = 0; j < 5; j++) {int xx = d[j][0];int yy = i + d[j][1];if (xx < 0 || yy < 0 || xx >= 5 || yy >= 6) continue;tmp[xx][yy] = (!tmp[xx][yy]);    }}    }    for (int i = 1; i < 5; i++) {for (int j = 0; j < 6; j++) {    if (tmp[i - 1][j]) {out[i][j] = 1;for (int k = 0; k < 5; k++) {    int xx = i + d[k][0];    int yy = j + d[k][1];    if (xx < 0 || yy < 0 || xx >= 5 || yy >= 6) continue;    tmp[xx][yy] = (!tmp[xx][yy]);}    }}    }    for (int i = 0; i < 6; i++)if (tmp[4][i]) return false;    return true;}void solve() {    for (int i = 0; i < (1<<6); i++)if (judge(i)) return;}int main() {    int cas = 0;    scanf("%d", &t);    while (t--) {for (int i = 0; i < 5; i++)    for (int j = 0; j < 6; j++)scanf("%d", &g[i][j]);solve();printf("PUZZLE #%d\n", ++cas);for (int i = 0; i < 5; i++) {    for (int j = 0; j < 5; j++)printf("%d ", out[i][j]);    printf("%d\n", out[i][5]);}    }    return 0;}