题目

代码

#include <bits/stdc++.h>
using namespace std;
const double eps = 1e-8;
unordered_map<string, int> e;
int eidx, midx; //eidx 元素数， midx 物质数
double matrix[45][45];
int q;
bool check_alpha(char c)
{
    if(c >= 'a' && c <= 'z') return true;
    return false;
}
bool gauss(int n, int m)
{
    //if(n < m) return false;
    int c, r, t;
    for(c = 1, r = 1; c <= m; c++)
    {
        t = r;
        for(int i = r+1; i <= n; i++) //找主元
        {
            if(fabs(matrix[i][c]) > fabs(matrix[t][c])) t = i;
        }
        if(fabs(matrix[t][c]) < eps) continue;
        for(int i = c; i <= m+1; i++) //交换
        {
            swap(matrix[r][i], matrix[t][i]);
        }
        for(int i = m+1; i >= c; i--) //归一化
        {
            matrix[r][i] /= matrix[r][c];
        }
        for(int i = r+1; i <= n; i++) //上三角化
        {
            for(int j = m+1; j >= c; j--)
            {
                matrix[i][j] -= matrix[i][c] * matrix[r][j];
            }
        }
        r++;
    }
    if((r-1) < m) return true;
    else return false;
}
int main()
{
    cin >> q;
    while (q -- ){
        memset(matrix, 0, sizeof matrix);
        e.clear();
        eidx = 0;
        cin >> midx;
        
        for(int i = 1; i <= midx; i++)
        {
            string s;
            cin >> s;
            string name = "";
            for(int j = 0; s[j] != '\0'; j++)
            {
                if(!check_alpha(s[j]))
                {
                    string num = "";
                    num += s[j];
                    while(s[++j] != '\0' && !check_alpha(s[j]))
                    {
                        num += s[j];
                    }
                    j--;
                    if(!e.count(name)) e[name] = ++eidx;
                    matrix[e[name]][i] = stoi(num);
                    name = "";
                }
                else name += s[j];
            }
        }
        if(gauss(eidx, midx)) cout << "Y" << endl;
        else cout << "N" << endl;
    }
}