[求助][SPOJ MARIOGAM]-高斯消元(内含标程,数据等)
小蒟蒻开始做概率的题之后,遇到了这道题,然而,他发现自己的程序调试了无数次也无法通过,系统总是返回令人伤心的WA,
于是,他决定把这一天半的时间收集到的资料放在网上, 寻求大家的帮助, 也可以节省后来人的时间.
题目描述和题解就不写了.
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.
答案为:3.24303821
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
和标程对拍了5000组数据没有出错QAQ
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')
x1 = float(f1.readline())
x2 = float(f2.readline())
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)
