Merge pull request #7 from LogSingleDog/master

update

4-数学.md

@@ -190,61 +190,143 @@ int cat(int n)
 ## 矩阵
 
 ```cpp
-class matrix
-{
-public:
-    int x[105][105];
-    int sz;
-    matrix(int n)
-    {
-        sz = n;
-        for (int i = 1; i <= sz; i++)
-        {
-            for (int j = 1; j <= sz; j++)
-            {
-                x[i][j] = 0;
+struct matrix{
+    ll n;
+    vector<vector<ll>> M;
+    matrix(ll nn){
+        n=nn;
+        M.resize(n+1,vector<ll>(n+1));
+        clear();
+    }
+    void clear(){
+        rep(i,0,n){
+            rep(j,0,n){
+                M[i][j]=0;
             }
         }
     }
-    matrix mul(matrix a, matrix b);
-    matrix qpow(matrix a, int n);
-    void tra(matrix a);
-};
-
-matrix matrix::mul(matrix a, matrix b)
-{
-    matrix c(a.sz);
-    for (int i = 1; i <= a.sz; i++)
-        for (int j = 1; j <= a.sz; j++)
-            for (int k = 1; k <= a.sz; k++)
-                c.x[i][j] = (c.x[i][j] % mod + (a.x[i][k] * b.x[k][j]) % mod) % mod;
-    return c;
-}
-matrix matrix::qpow(matrix a, int n)
-{
-    matrix res(a.sz);
-    for (int i = 1; i <= a.sz; i++)
-        res.x[i][i] = 1;
-    while (n > 0)
-    {
-        if (n & 1)
-            res = mul(res, a);
-        a = mul(a, a);
-        n >>= 1;
+    void reset(){
+        clear();
+        rep(i,0,n){
+            M[i][i]=1;
+        }
     }
-    return res;
-}
-void matrix::tra(matrix a)
-{
-    for (int i = 1; i <= a.sz; i++)
-    {
-        for (int j = 1; j <= a.sz; j++)
-        {
-            cout << a.x[i][j] << " ";
+    matrix operator+(matrix t){
+        matrix ans(n);
+        rep(i,1,n){
+            rep(j,1,n){
+                ans.M[i][j]=(M[i][j]+t.M[i][j])%mod;
+            }
         }
-        cout << endl;
+        return ans;
     }
-}
+    matrix operator-(matrix t){
+        matrix ans(n);
+        rep(i,1,n){
+            rep(j,1,n){
+                ans.M[i][j]=(M[i][j]-t.M[i][j]+mod)%mod;
+            }
+        }
+        return ans;
+    }
+    matrix operator*(matrix t){
+        matrix ans(n);
+        rep(i,1,n){
+            rep(j,1,n){
+                rep(k,1,n){
+                    ans.M[i][j]+=M[i][k]*t.M[k][j];
+                    ans.M[i][j]%=mod;
+                }
+            }
+        }
+        return ans;
+    }
+    matrix inv(bool &ret){//只做初等行变换是不会影响结果的
+        ll m=n*2;
+        matrix a(m);
+        rep(i,1,n){
+            rep(j,1,n){
+                a.M[i][j]=M[i][j];
+            }
+            a.M[i][i+n]=1;
+        }
+        matrix ans(n);
+        rep(i,1,n){
+            ll pos=i;
+            rep(j,i+1,n){
+                if(llabs(a.M[j][i])>llabs(a.M[pos][i])){
+                    pos=j;
+                }
+            }
+            //找最大防止这里是0
+            if(i!=pos){
+                swap(a.M[i],a.M[pos]);
+            }
+            if(a.M[i][i]==0){
+                ret=false;
+                return ans;
+            }
+            ll inv=fast(a.M[i][i],mod-2);
+            rep(j,i,m){
+                a.M[i][j]=a.M[i][j]*inv%mod;
+            }
+            rep(j,1,n){
+                if(j==i) continue;
+                ll b=a.M[j][i];
+                rep(k,i,m){
+                    a.M[j][k]=(a.M[j][k]-b*a.M[i][k]%mod+mod)%mod;
+                }
+            }
+        }
+        rep(i,1,n){
+            rep(j,1,n){
+                ans.M[i][j]=a.M[i][j+n];
+            }
+        }
+        return ans;
+    }
+    void print(){
+        rep(i,1,n){
+            rep(j,1,n){
+                cout<<M[i][j]<<" ";
+            }
+            cout<<endl;
+        }
+    }
+    ll fast(ll b,ll idx){
+        ll ans=1;
+        while(idx){
+            if(idx%2) ans=ans*b%mod;
+            b=b*b%mod;
+            idx/=2;
+        }
+        return ans;
+    }
+    friend matrix fast(matrix b,ll idx){
+        matrix ans(b.n);
+        ans.reset();
+        while(idx){
+            if(idx%2) ans=ans*b;
+            b=b*b;
+            idx/=2;
+        }
+        return ans;
+    }
+    //计算E+b+b^2+...+b^idx的矩阵等比数列之和
+    friend matrix sum(matrix b,ll idx){
+        matrix res(b.n),sum(b.n);
+        res.reset(),sum.reset();
+        while(idx){
+            if(idx%2){
+                res=sum+res*b;
+            }
+            sum=sum+sum*b;
+            b=b*b;
+            idx/=2;
+        }
+        return res;
+    }
+};
 ```
 
 ## 高斯消元

6-计算几何.md

@@ -30,8 +30,8 @@ double dis(pt a,pt b){
 ## 二维凸包
 
 ```cpp
-	pt pa[maxn];
-    ll st[maxn*2];
+    pt pa[maxn];
+    ll st[maxn];
 ll tubao(pt p[],ll n){
     sort(p+1,p+n+1);//先按横坐标排，再按纵坐标排
     ll tp=1;
@@ -76,8 +76,8 @@ int main(){
 
 ```cpp
 //一款基于凸包的求凸多边形直径的算法
-	ll st[maxn];
-	pt pb[maxn];
+    ll st[maxn];
+    pt pb[maxn];
 double getdia(pt p[],ll n){
     ll tp=tubao(pb,n);//凸包见上
     double ans=0;