v1.0.3:增加了莫队、2-SAT和其他内容“

Author: lr580

README.md

@@ -1,4 +1,4 @@
-**当前最新普通版发布版本为 `v1.0.1`** ，  **最新打印版发布版本为 `v1.0.0` (总词数约7.7w(含代码))**
+**当前最新普通版发布版本为 `v1.0.3`** ，  **最新打印版发布版本为 `v1.0.0` (总词数约7.7w(含代码))**
 
 成品为 `template.pdf` (移步 [releases](https://github.com/lr580/algorithm_template/releases) 查看/下载)
 
@@ -46,6 +46,13 @@
 
 ## 更新日志
 
+- 22/05/17 - 22/05/25 (`v1.0.3`)
+
+  - 增加了stringstream
+  - 增加了普通莫队、带修莫队、树上莫队和回滚莫队算法
+  - 增加了set部分内容
+  - 增加了2-SAT算法
+  
 - 22/04/19 - 22/04/22 (`v1.0.2`)
 
   - 增加了KMP算法周期与border

code/at1219_mo_algo.cpp

@@ -0,0 +1,84 @@
+#include <bits/stdc++.h>
+using namespace std;
+#define sc(x) scanf("%lld", &x)
+typedef long long ll;
+#define mn 100010
+ll n, x[mn], t[mn], m, k, ans[mn], bin[mn], cnt[mn];
+ll sq, bn, bel[mn], lf[mn], rf[mn];
+struct query
+{
+    ll l, r, i;
+    bool operator<(const query &x) const
+    { //一定要这么排序
+        return bel[l] == bel[x.l] ? r < x.r : bel[l] < bel[x.l];
+    }
+} q[mn];
+void del(ll v) { --bin[v]; }
+void add(ll v, ll &tmp) { tmp = max(tmp, (++bin[v]) * t[v]); }
+signed main()
+{
+    sc(n), sc(m), sq = sqrt(n), bn = n / sq;
+    for (ll i = 1; i <= n; ++i)
+    {
+        sc(x[i]), t[i] = x[i];
+    }
+    for (ll i = 1; i <= m; ++i)
+    {
+        sc(q[i].l), sc(q[i].r), q[i].i = i;
+    }
+    for (ll i = 1; i <= bn; ++i) //一定要这么分块，不能/sq，不然会炸
+        lf[i] = (i - 1) * sq + 1, rf[i] = i * sq;
+    if (rf[bn] < n)
+        ++bn, lf[bn] = rf[bn - 1] + 1, rf[bn] = n;
+    for (ll i = 1; i <= bn; ++i)
+        for (ll j = lf[i]; j <= rf[i]; ++j)
+            bel[j] = i;
+    sort(q + 1, q + 1 + m);
+    sort(t + 1, t + 1 + n);
+    k = unique(t + 1, t + 1 + n) - (t + 1);
+    for (ll i = 1; i <= n; ++i)
+    { // x[i]是输入的a[i]排在第x[i]位,离散化压[1,1e9]到[1,1e5]
+        x[i] = lower_bound(t + 1, t + 1 + k, x[i]) - t;
+    }
+    ll l = 1, r = 0, la = 0, sum = 0, l2 = 0, sum2 = 0;
+    for (ll i = 1; i <= m; ++i)
+    {
+        if (bel[q[i].l] == bel[q[i].r])
+        { // 询问的左右端点同属于一个块则暴力扫描回答
+            for (ll j = q[i].l; j <= q[i].r; ++j)
+            {
+                ++cnt[x[j]]; //入桶
+            }
+            for (ll j = q[i].l; j <= q[i].r; ++j)
+            { //按题意计算
+                ans[q[i].i] = max(ans[q[i].i], t[x[j]] * cnt[x[j]]);
+            }
+            for (ll j = q[i].l; j <= q[i].r; ++j)
+            {
+                --cnt[x[j]]; //清理记忆
+            }
+            continue;
+        }
+        if (bel[q[i].l] != la) // 访问到了新的块则重新初始化莫队区间
+        {
+            while (r > rf[bel[q[i].l]])
+                del(x[r--]);
+            while (l < rf[bel[q[i].l]] + 1)
+                del(x[l++]);
+            sum = 0, la = bel[q[i].l];
+        }
+        while (r < q[i].r) // 扩展右端点
+            add(x[++r], sum);
+        l2 = l, sum2 = sum;
+        while (l2 > q[i].l) // 扩展左端点
+            add(x[--l2], sum2);
+        ans[q[i].i] = sum2;
+        while (l2 < l) // 回滚
+            del(x[l2++]);
+    }
+    for (ll i = 1; i <= m; ++i)
+    {
+        printf("%lld\n", ans[i]);
+    }
+    return 0;
+}

code/p1903_mo_algo.cpp

@@ -0,0 +1,86 @@
+#include <bits/stdc++.h>
+using namespace std;
+#define sc(x) scanf("%lld", &x)
+typedef long long ll;
+#define mn 133340
+ll n, m, sq, a[mn], a0[mn], ans[mn], m1, m2, sum, bin[1000010];
+struct query1
+{
+    ll l, r, i, c;
+    bool operator<(const query1 &x) const
+    {
+        if (l / sq == x.l / sq)
+        {
+            return r / sq == x.r / sq ? i < x.i : r < x.r;
+        }
+        return l < x.l;
+    }
+} q1[mn];
+struct query2
+{
+    ll i, f, t;
+} q2[mn];
+void add(ll i)
+{
+    sum += bin[i]++ == 0;
+}
+void del(ll i)
+{
+    sum -= --bin[i] == 0;
+}
+ll l = 1, r;
+void addt(ll t)
+{
+    if (l <= q2[t].i && q2[t].i <= r)
+        del(q2[t].f), add(q2[t].t);
+    a0[q2[t].i] = q2[t].t;
+}
+void delt(ll t)
+{
+    if (l <= q2[t].i && q2[t].i <= r)
+        del(q2[t].t), add(q2[t].f);
+    a0[q2[t].i] = q2[t].f;
+}
+signed main()
+{
+    sc(n), sc(m), sq = pow(n, 2. / 3);
+    for (ll i = 1; i <= n; ++i)
+    {
+        sc(a[i]), a0[i] = a[i];
+    }
+    char ch[5] = {};
+    for (ll i = 1, x, y; i <= m; ++i)
+    {
+        scanf("%s%lld%lld", ch, &x, &y);
+        if (ch[0] == 'Q')
+        {
+            ++m1, q1[m1] = {x, y, m1, m2 + 1};
+        }
+        else
+        {
+            ++m2, q2[m2] = {x, a[x], y}, a[x] = y;
+        }
+    }
+    sort(q1 + 1, q1 + 1 + m1);
+    for (ll i = 1, t = 1; i <= m1; ++i)
+    {
+        while (t < q1[i].c)
+            addt(t++);
+        while (t > q1[i].c)
+            delt(--t);
+        while (l > q1[i].l)
+            add(a0[--l]);
+        while (r < q1[i].r)
+            add(a0[++r]);
+        while (l < q1[i].l)
+            del(a0[l++]);
+        while (r > q1[i].r)
+            del(a0[r--]);
+        ans[q1[i].i] = sum;
+    }
+    for (ll i = 1; i <= m1; ++i)
+    {
+        printf("%lld\n", ans[i]);
+    }
+    return 0;
+}

code/p3901_mo_algo.cpp

@@ -0,0 +1,56 @@
+#include <bits/stdc++.h>
+using namespace std;
+#define sc(x) scanf("%lld", &x)
+typedef long long ll;
+#define mn 100010
+ll n, m, x, bin[mn], ans[mn], sq, a[mn], sum;
+struct query
+{
+    ll l, r, i;
+    bool operator<(const query &x) const
+    {
+        if (l / sq != x.l / sq)
+            return l < x.l;
+        if (l / sq & 1)
+            return r < x.r;
+        return r > x.r;
+    }
+} q[mn];
+void add(ll i)
+{
+    sum += bin[a[i]]++ == 0;
+}
+void del(ll i)
+{
+    sum -= --bin[a[i]] == 0;
+}
+signed main()
+{
+    sc(n), sc(m), sq = sqrt(n);
+    for (ll i = 1; i <= n; ++i)
+    {
+        sc(a[i]);
+    }
+    for (ll i = 1; i <= m; ++i)
+    {
+        sc(q[i].l), sc(q[i].r), q[i].i = i;
+    }
+    sort(q + 1, q + 1 + m);
+    for (ll i = 1, l = 1, r = 0; i <= m; ++i)
+    {
+        while (l > q[i].l)
+            add(--l);
+        while (r < q[i].r)
+            add(++r);
+        while (l < q[i].l)
+            del(l++);
+        while (r > q[i].r)
+            del(r--);
+        ans[q[i].i] = sum == (q[i].r - q[i].l + 1);
+    }
+    for (ll i = 1; i <= m; ++i)
+    {
+        printf("%s\n", ans[i] ? "Yes" : "No");
+    }
+    return 0;
+}

code/p4782_2_sat.cpp

@@ -0,0 +1,88 @@
+#include <bits/stdc++.h>
+using namespace std;
+#define sc(x) scanf("%lld", &x)
+typedef long long ll;
+#define mn 2000010
+ll n, m, hd[mn], cnt, st, low[mn], dfn[mn], ins[mn], scc, c[mn];
+stack<ll> s;
+struct edge
+{
+    ll to, nx;
+} e[mn * 2];
+void tarjan(ll u)
+{
+    low[u] = dfn[u] = ++st, ins[u] = true;
+    s.push(u);
+    for (ll i = hd[u], v; i; i = e[i].nx)
+    {
+        v = e[i].to;
+        if (!dfn[v])
+        {
+            tarjan(v);
+            low[u] = min(low[u], low[v]);
+        }
+        else if (ins[v])
+        {
+            low[u] = min(low[u], dfn[v]);
+        }
+    }
+    if (low[u] == dfn[u])
+    {
+        ++scc;
+        do
+        {
+            c[u] = scc;
+            u = s.top();
+            s.pop();
+            ins[u] = false;
+        } while (low[u] != dfn[u]);
+    }
+}
+signed main()
+{
+    sc(n), sc(m);
+    auto adde = [&](ll u, ll v)
+    { e[++cnt] = {v, hd[u]}, hd[u] = cnt; };
+    for (ll i = 1, a, va, b, vb; i <= m; ++i)
+    {
+        sc(a), sc(va), sc(b), sc(vb);
+        if (va && vb)
+        {
+            adde(a + n, b), adde(b + n, a);
+        }
+        else if (!va && vb)
+        {
+            adde(a, b), adde(b + n, a + n);
+        }
+        else if (va && !vb)
+        {
+            adde(a + n, b + n), adde(b, a);
+        }
+        else if (!va && !vb)
+        {
+            adde(a, b + n), adde(b, a + n);
+        }
+        // i.e. adde(a+n*va,b+n*(vb^1)),adde(b+n*vb,a+n*(va^1))
+    }
+    for (ll i = 1; i <= 2 * n; ++i)
+    {
+        if (!dfn[i])
+        {
+            tarjan(i);
+        }
+    }
+    for (ll i = 1; i <= n; ++i)
+    {
+        if (c[i] == c[i + n])
+        {
+            printf("IMPOSSIBLE");
+            return 0;
+        }
+    }
+    printf("POSSIBLE\n");
+    for (ll i = 1; i <= n; ++i)
+    { // tarjan逆拓扑序
+        printf("%d ", c[i] < c[i + n]);
+    }
+    return 0;
+}