v1.1.1:增加了部分数论算法和修改了若干错误

Author: lr580

README.md

@@ -1,4 +1,4 @@
-**当前最新普通版发布版本为 `v1.1.0`** ，  **最新打印版发布版本为 `v1.1.0` (总词数约9.0w(含代码))**
+**当前最新普通版发布版本为 `v1.1.1`** ，  **最新打印版发布版本为 `v1.1.0` (总词数约9.0w(含代码))**
 
 成品为 `template.pdf` (移步 [releases](https://github.com/lr580/algorithm_template/releases) 查看/下载)
 
@@ -46,6 +46,23 @@
 
 ## 更新日志
 
+- 22/10/24 - 22/11/11 (`v1.1.1`)
+
+  - 添加了树上随机游走
+  - 添加了带权并查集例题
+  - 添加了负环输出方案模板
+  - 添加了最短路少量内容
+  - 修改了 STL priority\_queue 的错误描述
+  - 微调了 tarjan 模板代码
+  - 添加了高阶前缀和公式
+  - 添加了错位排列数少量内容
+  - 添加了 BSGS, exBSGS 和 exGCD 的另一种实现模板
+  - 添加了中国剩余定理少量内容
+  - 添加了矩阵快速幂常见建模例子
+  - 添加了 exLucas 模板
+  - 修改了同余一条性质的错误表述
+  - 添加了 STL multiset 部分内容
+  
 - 22/10/19 - 22/10/20 (`v1.1.0`)
 
   - 添加了哈密顿图结论

code/p2294_diff_constraints.cpp

@@ -0,0 +1,71 @@
+#include <bits/stdc++.h>
+using namespace std;
+using ll = long long;
+const ll mn = 1e2 + 10, inf = 1e9;
+ll n, d[mn], m, vis[mn], cnt[mn];
+vector<pair<ll, ll>> e[mn];
+void solve()
+{
+    cin >> n >> m;
+    for (ll i = 0; i <= n; ++i)
+    {
+        e[i].clear();
+    }
+    for (ll i = 1, a, b, c; i <= m; ++i)
+    {
+        cin >> a >> b >> c;
+        e[b].push_back({a - 1, -c});
+        e[a - 1].push_back({b, c});
+    }
+    fill_n(d, n + 3, inf), fill_n(vis, n + 3, 0), fill_n(cnt, n + 3, 0);
+    auto spfa = [&](ll s)
+    {
+        d[s] = 0, vis[s] = true;
+        queue<ll> q;
+        q.push(s);
+        while (!q.empty())
+        {
+            ll u = q.front();
+            vis[u] = false;
+            q.pop();
+            for (auto pr : e[u])
+            {
+                ll v = pr.first, w = pr.second;
+                if (d[v] > d[u] + w)
+                {
+                    d[v] = d[u] + w;
+                    if (!vis[v])
+                    {
+                        if (++cnt[v] >= n + 1)
+                        {
+                            return false;
+                        }
+                        vis[v] = true;
+                        q.push(v);
+                    }
+                }
+            }
+        }
+        return true;
+    };
+    bool fail = false;
+    for (ll i = 0; i <= n; ++i)
+    {
+        if (!cnt[i])
+        {
+            fail |= spfa(i) == false;
+        }
+    }
+    cout << (fail ? "false\n" : "true\n");
+}
+signed main()
+{
+    cin.tie(0)->ios::sync_with_stdio(false);
+    ll t;
+    cin >> t;
+    while (t--)
+    {
+        solve();
+    }
+    return 0;
+}

code/p2294_disjoint_set.cpp

@@ -0,0 +1,41 @@
+#include<bits/stdc++.h>
+int fa[105],cha[105];  
+int find(int x)
+{  
+    if(x!=fa[x])
+    {
+        int t=find(fa[x]);
+        cha[x]+=cha[fa[x]];
+        fa[x]=t;  
+    }  
+    return fa[x];  
+}  
+int main()  
+{  
+    int T,n,m,i,x,y,z,flag;  
+    scanf("%d",&T);  
+    while (T--) 
+    {  
+        flag=0;  
+        scanf("%d%d",&n,&m);  
+        for(i=0;i<=n;i++)
+        {  
+            fa[i]=i;  
+            cha[i]=0;  
+        }  
+        for(i=1;i<=m;i++)  
+        {  
+            scanf("%d%d%d",&x,&y,&z);  
+            x--;  
+            if(find(x)!=find(y))  
+            {  
+                cha[fa[y]]=cha[x]-cha[y]-z;  
+                fa[fa[y]]=fa[x];
+            }  
+            else  
+            if(cha[x]-cha[y]!=z) flag=1;  
+        }  
+        if(flag==0) printf("true\n"); else printf("false\n");  
+    }  
+    return 0;  
+}

code/p2294_greedy.cpp

@@ -0,0 +1,72 @@
+#include<queue>
+#include<cmath>
+#include<cstdio>
+#include<cstring>
+#include<iostream>
+#include<algorithm>
+#define N 1100
+using namespace std;
+inline void read(int &x)
+{
+    x=0;
+    int p=1;
+    char c=getchar();
+    while(!isdigit(c)){if(c=='-')p=-1;c=getchar();}
+    while(isdigit(c)) {x=(x<<1)+(x<<3)+(c^'0');c=getchar();}
+    x*=p;
+
+}//快速读入
+
+int n,m;
+struct node
+{
+    int l,r,s;
+    bool operator < (const node &h)const
+    {
+        if(l!=h.l)return l>h.l;
+        return r>h.r;
+
+}//重载运算符，确定优先队列的优先级
+
+}tmp;
+priority_queue<node>q;
+int main()
+{
+    int t;
+    read(t);
+    while(t--)
+    {    
+        while (!q.empty()) q.pop();//多组数据清空
+        read(n);read(m);
+        if(m==1){printf("true\n");continue;}//其实没必要特判，只是优化一点点
+        for(int i=1;i<=m;i++)
+        {
+            int l,r,s;
+            read(tmp.l);read(tmp.r);read(tmp.s);
+            q.push(tmp);
+        }
+        tmp=q.top();//取出第一个
+        q.pop();
+        while(!q.empty())
+        {    
+            node tmp1;
+            tmp1=q.top();
+            q.pop();
+            if(tmp.l==tmp1.l)
+            {
+                if(tmp.r==tmp1.r)
+                {
+                    if(tmp.s!=tmp1.s)
+                    {printf("false\n");goto end;}//退出多重循环的小操作
+                }
+                else 
+                if(tmp.r<tmp1.r)
+                    q.push((node) {tmp.r+1, tmp1.r, tmp1.s - tmp.s});//将抵消后的部分放入队列
+            }
+            tmp = tmp1;//继续比
+        }
+        printf("true\n");
+        end:;
+    }
+    return 0;
+}

code/p3846_bsgs2.cpp

@@ -0,0 +1,39 @@
+#include <bits/stdc++.h>
+using namespace std;
+using ll = long long;
+ll bsgs(ll a, ll b, ll p)
+{ // min x of a^x%p=b
+    if (a % p == 0 && b)
+    {
+        return -1;
+    }
+    if (b == 1)
+    {
+        return 0;
+    }
+    map<ll, ll> h;
+    ll m = sqrt(p) + 1, s = 1;
+    for (ll i = 1; i <= m; ++i)
+    {
+        h[b] = i;
+        s = s * a % p, b = b * a % p;
+    }
+    a = s;
+    for (ll i = 1; i <= m; ++i)
+    {
+        if (h.count(a))
+        {
+            return i * m - h[a] + 1;
+        }
+        a = a * s % p;
+    }
+    return -1;
+}
+signed main()
+{
+    ll a, b, p;
+    cin >> p >> a >> b;
+    ll ans = bsgs(a, b, p);
+    cout << (ans == -1 ? "no solution" : to_string(ans));
+    return 0;
+}

code/p4195_exbsgs2.cpp

@@ -0,0 +1,76 @@
+#include <bits/stdc++.h>
+using namespace std;
+#define LL long long
+int read()
+{
+    register int x = 0;
+    register int y = 1;
+    register char c = getchar();
+    while (c < '0' || c > '9')
+    {
+        if (c == '-')
+            y = 0;
+        c = getchar();
+    }
+    while (c >= '0' && c <= '9')
+    {
+        x = x * 10 + (c ^ 48);
+        c = getchar();
+    }
+    return y ? x : -x;
+}
+unordered_map<int, int> mp;
+int gcd(int a, int b) { return b ? gcd(b, a % b) : a; }
+int BSGS(int a, int n, int p, int ad)
+{
+    mp.clear();
+    int m = ceil(sqrt(p));
+    int s = 1;
+    for (int i = 0; i < m; i++, s = 1ll * s * a % p)
+        mp[1ll * s * n % p] = i;
+    for (int i = 0, tmp = s, s = ad; i <= m; i++, s = 1ll * s * tmp % p)
+        if (mp.find(s) != mp.end())
+            if (1ll * i * m - mp[s] >= 0)
+                return 1ll * i * m - mp[s];
+    return -1;
+}
+int exBSGS(int a, int n, int p)
+{
+    a %= p;
+    n %= p;
+    if (n == 1 || p == 1)
+        return 0;
+    int cnt = 0;
+    int d, ad = 1;
+    while ((d = gcd(a, p)) ^ 1)
+    {
+        if (n % d)
+            return -1;
+        cnt++;
+        n /= d;
+        p /= d;
+        ad = (1ll * ad * a / d) % p;
+        if (ad == n)
+            return cnt;
+    }
+    LL ans = BSGS(a, n, p, ad);
+    if (ans == -1)
+        return -1;
+    return ans + cnt;
+}
+signed main()
+{
+    int a = read(), p = read(), n = read();
+    while (a || p || n)
+    {
+        int ans = exBSGS(a, n, p);
+        if (~ans)
+            printf("%d\n", ans);
+        else
+            puts("No Solution");
+        a = read();
+        p = read();
+        n = read();
+    }
+    return 0;
+}