## [求助][SPOJ MARIOGAM]-高斯消元(内含标程,数据等)

### 易错数据:

1 4
$#99 1 4 A5a$
2 3
$aA 1## 3 3 4A# ##$
1a!

### 大数据:

15 15
$A............. aaaaaaaaaaaaaa. .........#!1... .aaaaaaaaaaaaaa ............... aaaaaaaaaaaaaa. ............... .aaaaaaaaaaaaaa ............... aaaaaaaaaaaaaa. ............... .aaaaaaaaaaaaaa ............... aaaaaaaaaaaaaa. ............... 答案为:12.00000 15 15 .......#....... ........#.3.... ...$.....#..#..
..........#..#.
..........#.#..
...........a...
##########.#.##
Z!.......#...#.
!.........###..
...............
..............b
###...3....###.
.z#........#...
..###.....#....
...B#....#...A.

### 我的错误程序

#include <cstdio>
#include <cctype>
#include <cstring>
#include <iostream>
#include <cmath>
#include <algorithm>
#include <utility>
#include <queue>
#include <vector>
#define F(i, j, k) for(int i = j; i <= k; ++i)
typedef long double val_t;
using std::queue;
using std::pair;
using std::cout;
#define mp std::make_pair
int n, m, N, cnt, sx, sy;
const int maxn = 20;
const val_t eps = 1e-7;
const int life = 3;
const int maxm = maxn * maxn * life;
char a[maxn][maxn];
val_t mat[maxm][maxm];
pair<int, int> coin[maxm], out[26];
std::vector<pair<int, int> > in[26];
bool vis[maxn][maxn], vis2[maxn][maxn];
int dx[] = {1, 0, -1, 0};
int dy[] = {0, 1, 0, -1};
inline bool ok(int x, int y) {
return (x >= 1 && x <= n && y >= 1 && y <= m && a[x][y] != '#');
}
inline int numb(int k, int i, int j) {
int x = n * m;
return (k - 1) * x + (i - 1) * m + j;
}
void pre() {
scanf("%d %d", &n, &m);
N = life * n * m;
F(i, 1, n) {
scanf("%s", a[i] + 1);
F(j, 1, m) {
if(a[i][j] == '$') sx = i, sy = j; if(a[i][j] >= 'A' && a[i][j] <= 'Z') out[a[i][j] - 'A'] = mp(i, j); if(a[i][j] >= 'a' && a[i][j] <= 'z') in[a[i][j] - 'a'].push_back(mp(i,j)); if(a[i][j] >= '0' && a[i][j] <= '9') coin[++cnt] = mp(i, j); } } } bool bfs(int x, int y) { if(!ok(x,y)) return false; queue<pair<int, int> > q; memset(vis2, 0, sizeof(vis2)); vis2[x][y] = 1; q.push(mp(x,y)); while(!q.empty()) { int u = q.front().first; int v = q.front().second; q.pop(); if(islower(a[u][v])) { if(!vis2[out[a[u][v] - 'a'].first][out[a[u][v] - 'a'].second]) { vis2[out[a[u][v] - 'a'].first][out[a[u][v] - 'a'].second] = 1; q.push(out[a[u][v] - 'a']); } continue; } if(isdigit(a[u][v])) return true; F(k, 0, 3) { int du = u + dx[k]; int dv = v + dy[k]; if(du >= 1 && du <= n && dv >= 1 && dv <= m && a[du][dv] != '#' && !vis2[du][dv]) { vis2[du][dv] = 1; q.push(mp(du, dv)); } } } return false; } void build_formula() { F(k, 1, life) F(i, 1, n) F(j, 1, m) if(!vis[i][j]) { mat[numb(k, i, j)][numb(k, i, j)] = 1; } else if(a[i][j] >= 'a' && a[i][j] <= 'z') { mat[numb(k, i, j)][numb(k, i, j)] = 1; mat[numb(k, i, j)][numb(k, out[a[i][j] - 'a'].first, out[a[i][j] - 'a'].second)] = -1; } else { if(a[i][j] >= '0' && a[i][j] <= '9') mat[numb(k, i, j)][N+1] = -(a[i][j] - '0'); mat[numb(k, i, j)][numb(k, i, j)] = -1; int p = 0; F(K, 0, 3) { int di = i + dx[K]; int dj = j + dy[K]; if(di >= 1 && di <= n && dj >= 1 && dj <= m && a[di][dj] != '#') p++; } F(K, 0, 3) { int di = i + dx[K]; int dj = j + dy[K]; if(di >= 1 && di <= n && dj >= 1 && dj <= m && a[di][dj] != '#'){ if(a[di][dj] != '!')mat[numb(k, i, j)][numb(k, di, dj)] = 1.0 / p; else if(k != 1) mat[numb(k,i,j)][numb(k-1,di,dj)] = 1.0 / p; } } } } void print() { printf("======================\n"); F(i, 1, N) { F(j, 1, N) printf("%5.2Lf ", mat[i][j]); printf("|"); printf("%5.2Lf\n", mat[i][N+1]); } printf("======================\n"); } bool fl[maxm]; val_t gauss() { F(i, 1, N) { int r = i; F(j, i + 1, N) if(fabsl(mat[j][i]) > fabsl(mat[r][i])) r = j; if(r != i) F(j, 1, N+1) std::swap(mat[r][j], mat[i][j]); F(j, i + 1, N) if(fabsl(mat[i][i]) > eps){ val_t t = 1.0 * mat[j][i] / mat[i][i]; F(k, 1, N+1) mat[j][k] -= mat[i][k] * t; } else fl[i] = 1; } for(int i = N; i >= 1; i--) { for(int j = N; j > i; j--) { if(mat[i][j] && !fl[j]) mat[i][N+1] -= mat[j][N+1] * mat[i][j]; else if(mat[i][j] && fl[j]) fl[i] = 1; } if(fabsl(mat[i][i]) > eps) mat[i][N+1] /= mat[i][i]; else fl[i] = 1; } if(fl[numb(life,sx,sy)]) return -1; return mat[numb(life,sx,sy)][N+1]; } int main() { #ifdef orz freopen("input", "r", stdin); #endif pre(); F(i, 1, n) { F(j, 1, m) { vis[i][j] = bfs(i, j); } } build_formula(); val_t ans = gauss(); if(ans != -1) printf("%.9Lf\n", ans); else printf("-1\n"); return 0; } ### 标程 #include <cstdio> #include <iostream> #include <cmath> #include <algorithm> #include <vector> #include <cstring> using namespace std; typedef long double real; const real eps = 1e-12; const char Empty = '.'; const char Monster = '!'; const char Wall = '#'; const char Mario = '$';
const int maxv = 800;
const int mx[4] = {0, 1, 0, -1};
const int my[4] = {-1, 0, 1, 0};

int extX[27], extY[27];
char map[17][17];
int n, m, sx, sy, tmp;

int isbegin(char s) {
if((s >= 'a') && (s <= 'z')) return s - 'a' + 1;
return 0;
}

int isend(char s) {
if((s >= 'A') && (s <= 'Z')) return s - 'A' + 1;
return 0;
}

int money(char s) {
if((s >= '0') && (s <= '9')) return s - '0';
return 0;
}

void init() {
char s[100];
scanf("%d%d\n", &n, &m);
memset(map, '#', sizeof(map));

int i, j, k;
for(i = 1; i <= n; i++) {
scanf("%s", s);
for(j = 1; j <= m; j++) {
if( (map[i][j] = s[j-1]) == Mario) {
sx = i;
sy = j;
}
if(k = isend(s[j-1])) {
extX[k] = i;
extY[k] = j;
}
}
}
}

int qx[maxv], qy[maxv], ql[maxv];
int isvisit[16][16][3];
int l, r;

int go[maxv][4], gd[maxv], cango[maxv];
vector<int> reach[maxv];

int Queue_Insert(int x, int y, int life) {
if( map[x][y] == Wall ) return 0;
if( map[x][y] == Monster) life--;
if(life < 0) return 0;
if(tmp = isbegin(map[x][y])) {
x = extX[tmp];
y = extY[tmp];
}

if(isvisit[x][y][life] == 0) {
r++;
qx[r] = x;
qy[r] = y;
ql[r] = life;
isvisit[x][y][life] = r;
}

return isvisit[x][y][life];
}

void bfs() {
l = r = 0;
Queue_Insert(sx, sy, 2);
int nx, ny, nl;
int d;

while(l < r) {
l++;
nx = qx[l];
ny = qy[l];
nl = ql[l];
for(d = 0; d < 4; d++) if(map[nx + mx[d]][ny + my[d]] != Wall) {
cango[l]++;
tmp = Queue_Insert(nx + mx[d], ny + my[d], nl);
if(tmp) go[l][gd[l]++] = tmp, reach[tmp].push_back(l);
}
}
}

real mat[maxv][maxv];
real matans[maxv];
real res[maxv];
int Mnum[maxv];

bool solve(int n) {
int i, j, k;
real tmp;
for(i = 1; i <= n; i++) {
j = i;
for(k = i + 1; k <= n; k++) if(fabs(mat[k][i]) > fabs(mat[j][i])) j = k;
if(fabs(mat[j][i]) < eps) return false;
for(k = i; k <= n+1; k++) swap(mat[i][k], mat[j][k]);
for(j = i + 1; j <= n; j++) if(fabs(mat[j][i]) > eps) {
tmp = mat[j][i] / mat[i][i];
for(k = i; k <= n+1; k++) mat[j][k] -= tmp * mat[i][k];
}
}

for(i = n; i; i--) {
matans[i] = -mat[i][n+1];
for(j = i + 1; j <= n; j++) matans[i] -= mat[i][j] * matans[j];
matans[i] /= mat[i][i];
}
return true;
}

bool will[maxv];
void dfs(int x) {
if(will[x]) return;
will[x] = true;
for(int i = 0; i < reach[x].size(); i++) dfs(reach[x][i]);
}
void work() {
int tot, i, j, k, x;
for(i = 1; i <= r; i++) if(money(map[qx[i]][qy[i]])) dfs(i);
for(int ll = 0; ll <= 2; ll++) {
tot = 0;
for(i = 1; i <= r; i++) if((ql[i] == ll) && (will[i])) Mnum[i] = ++tot;

for(i = 1; i <= tot; i++)
for(j = 1; j <= tot+1; j++) mat[i][j] = 0;
k = 0;
for(i = 1; i <= r; i++) if((ql[i] == ll) && (will[i])) {
k++;
mat[k][k] = -cango[i];
mat[k][tot+1] = money(map[qx[i]][qy[i]])* cango[i];
for(j = 0; j < gd[i]; j++) {
x = go[i][j];
if( (ql[x] != ll) || (!will[x])) mat[k][tot+1] += res[x];
else mat[k][Mnum[x]]++;
}
}

if(!solve(tot)) {
printf("-1\n");
return;
}
for(int i = 1; i <= r;i++) if(ql[i] == ll) res[i] = matans[Mnum[i]];
}
cout << res[1] << endl;
}
int main() {
#ifdef orz
freopen("input", "r", stdin);
#endif
cout.setf(ios::fixed);
cout.precision(10);
init();
bfs();
work();
return 0;
}

### 数据生成器

#include <cstdio>
#include <algorithm>
#include <ctime>
#include <cstdlib>
#include <cstring>
#define random(x) (rand() % x) + 1
int vis[27], color;
int main() {
memset(vis, 0, sizeof(vis));
srand(time(NULL));
int n = 15, m = 15;
color = 2;
int sx = random(n);
int sy = random(m);
printf("%d %d\n", n, m);
for(int i = 1; i <= n; i++) {
for(int j =1;  j<=m; j++) {
if(i == sx && j == sy) {
printf("%c",'\$');
continue;
}
int k = random(6);
here:
if(k == 1) printf("%c", '#');
if(k == 2) {
int x = random(color);
int cnt = 0;
while(vis[x]) {
x = random(color);
cnt++;
if(cnt > color) {
k = random(6);
goto here;
}
}
vis[x] = 1;
printf("%c", 'A' + x - 1);
}
if(k == 3) {
int x = random(3);
int cnt = 0;
while(!vis[x]){
x = random(color);
cnt++;
if(cnt > color) {
k = random(6);
goto here;
}
}
printf("%c", 'a' + x - 1);
}
if(k == 4) printf("%c", '!');
if(k == 5) printf(".");
if(k == 6) printf("%d", random(9));
}
printf("\n");
}
return 0;
}

### 对拍器

from math import *
import time
import os
n = input()
for i in range(1,int(n)+1):
os.system('./r > input')
if(os.system('./a < input > output.a') != 0):
break
os.system('./b < input > output.b')
f1 = open('output.a', 'r')
f2 = open('output.b', 'r')
flag = 0
if(fabs(x1 - x2) > 1e-6):
flag = fabs(x1 - x2)
if flag > 0:
print('Incorrect:{}'.format(flag))
break
else:
print('Correct {}/{}: my answer is {}, his answer is {}'.format(i, n, x1, x2))
#time.sleep(1)

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posted on 2017-08-13 11:42  蒟蒻konjac  阅读(...)  评论(...编辑  收藏

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