1. 高斯消元
求矩阵逆, 增广单位阵然后消元
求行列式, 先消元后对角线乘积即为行列式
求代数余子式$A_{xy}$, 先求出伴随矩阵$A^*=|A|A^{-1}$, 然后$A_{xy}=A^*[y][x]$
https://codeforces.com/contest/832/submission/61763466
https://codeforces.com/contest/1344/submission/84584146
void Gauss(int A[N][N], int n, int m, int q) {
//A为n行m+q列矩阵, n为方程数, m为变量数
//q为增广的列数, r为矩阵秩
int r = 0;
REP(i,1,m) {
int p = r;
while (!A[p][i]&&p<=n) ++p;
if (p>n) continue;
if (p!=r) REP(j,1,m+q) swap(A[p][j],A[r][j]);
REP(j,1,n) if (j!=r&&A[j][i]) {
ll t = A[j][i]*inv(A[r][i])%P;
REP(k,1,m+q) A[j][k]=(A[j][k]-t*A[r][k]%P+P)%P;
}
++r;
}
}
2. exgcd
ll exgcd(ll a, ll b, ll &x, ll &y) {
ll d = a;
if (!b) return x=1,y=0,d;
return d=exgcd(b,a%b,y,x),y-=a/b*x,d;
}
3. excrt
4. 极角排序
5. splay