[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)

如果有同学看出了我程序的错误, 欢迎联系我:

mail:unrealgengchen@gmail.com

QQ:543249426