高斯消元与求秩（实数）

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
#include<bits/stdc++.h>
using namespace std;
using i64 = long long;
const int INF  =  1e9;
const i64 INFL = 1e18;
const int MAXN = 100 + 3;
const double EPS = 1e-9;
struct Mat{
    int n, m;
    double W[MAXN][MAXN];
    Mat(int _n = 0, int _m = 0){
        n = _n;
        m = _m;
        for(int i = 1;i <= n;++ i)
            for(int j = 1;j <= m;++ j)
                W[i][j] = 0;
    }
};
bool zero(double f){
    return fabs(f) < EPS;
}
int mat_rank(Mat &a){
    const int &n = a.n;
    const int &m = a.m;
    int cnt = 0;
    for(int i = 1;i <= m;++ i){
        int p = cnt + 1;
        int f = -1;
        for(int j = p;j <= n;++ j){
            if(!zero(a.W[j][i])){
                f = j;
                break;
            }
        }
        if(f == -1)
            continue;
        if(f != p){
            for(int j = 1;j <= m;++ j)
                swap(a.W[p][j], a.W[f][j]);
        }
        ++ cnt;
        for(int j = p + 1;j <= n;++ j){
            double rate = a.W[j][i] / a.W[p][i];
            for(int k = 1;k <= m;++ k){
                a.W[j][k] -= rate * a.W[p][k];
            }
        }
    }
    return cnt;
}
double X[MAXN];
int main(){
    int n;
    cin >> n;
    Mat A(n, n);
    Mat T(n, n + 1);
    for(int i = 1;i <= n;++ i){
        for(int j = 1;j <= n;++ j)
            cin >> A.W[i][j];
        for(int j = 1;j <= n;++ j)
            T.W[i][j] = A.W[i][j];
        cin >> T.W[i][n + 1];
    }
    int res1 = mat_rank(A);
    int res2 = mat_rank(T);
    if(res1 != res2)
        cout << -1 << endl;
    else
    if(res2 <  n)
        cout << 0 << endl;
    else {
        for(int i = n;i >= 1;-- i){
            X[i] = T.W[i][n + 1] / T.W[i][i];
            for(int j = i - 1;j >= 1;-- j){
                double rate = T.W[j][i] / T.W[i][i];
                T.W[j][    i] -= rate * T.W[i][    i];
                T.W[j][n + 1] -= rate * T.W[i][n + 1];
            }
        }
        for(int i = 1;i <= n;++ i)
            cout << "x" << i << "=" << fixed << setprecision(2) << X[i] << endl;
    }
    return 0;
}