补充了数论、高等数学、杂项；增加了博弈论、字符串、计算几何、线性代数和概率论、动态规划内容

Author: lr580

README.md

@@ -31,36 +31,30 @@
 - 22/03/24 
   - 开始模板编制工作
   - 增加部分数学公式、大部分 STL 内容
-  
 - 22/03/25
   - 补充 STL 内容
   - 增加排序、组合数学、快读快写、高精度、树
-  
 - 22/03/26
   - 补充树内容
   - 增加线段树、树状数组、平衡树等数据类型
-  
 - 22/03/28
   - 增加加权并查集内容
-  
 - 22/03/29
   - 增加整体二分、LIS、前缀和/差分内容
   - 增加了搜索、二分答案内容
-  
 - 22/03/30
   - 增加了zkw线段树、猫树、K-D Tree内容，修改了部分内容
   - 增加了图概念、最短路内容
-  
 - 22/03/31
   - 增加了拓扑排序、最小生成树、二分图匹配、网络流内容
-  
 - 22/04/01
-
   - 增加了图的连通性、组合数学、数学杂项内容
 
 - 22/04/02
-
   - 增加了数论主要内容、高等数学内容
 
-  
+- 22/04/03
+  - 补充了数论、高等数学、杂项内容
+  - 增加了博弈论、字符串、计算几何、线性代数和概率论、动态规划内容
+
 

code/kmp.cpp

@@ -0,0 +1,45 @@
+#include <bits/stdc++.h> //题目https://oj.socoding.cn/p/1713
+using namespace std;
+typedef long long ll;
+#define mn 2000010
+char s[mn], t[mn];
+ll kmp[mn], ns, nt, cnt;
+signed main()
+{
+    scanf("%s%s", s + 1, t + 1);
+    ns = strlen(s + 1), nt = strlen(t + 1);
+    for (ll i = 2, j = 0; i <= nt; ++i)
+    {
+        while (j > 0 && t[j + 1] != t[i])
+        {
+            j = kmp[j];
+        }
+        if (t[j + 1] == t[i])
+        {
+            ++j;
+        }
+        kmp[i] = j;
+    }
+    for (ll i = 1, j = 0; i <= ns; ++i)
+    {
+        while (j > 0 && t[j + 1] != s[i])
+        {
+            j = kmp[j];
+        }
+        if (t[j + 1] == s[i])
+        {
+            ++j;
+        }
+        if (j == nt)
+        {
+            ++cnt;
+            printf("%lld ", i - j + 1);
+            j = kmp[j];
+        }
+    }
+    if (cnt == 0)
+    {
+        printf("-1");
+    }
+    return 0;
+}

code/p1368_minimal_string.cpp

@@ -0,0 +1,23 @@
+#include <bits/stdc++.h>
+using namespace std;
+typedef long long ll;
+ll n, ans, a[300002], i, j = 1, k;
+signed main()
+{
+	scanf("%lld", &n);
+	for(ll i=0;i<n;++i) scanf("%lld", a + i);
+	while (i < n && j < n && k < n)
+	{
+		if (a[(i + k) % n] == a[(j + k) % n]) ++k;
+		else
+		{
+			if (a[(i + k) % n] > a[(j + k) % n]) i += k + 1;
+			else j += k + 1;
+			if (i == j) ++i; 
+			k = 0;
+		}
+	}
+	ans = min(i, j);
+	for(ll i=0;i<n;++i) printf("%lld ", a[(i + ans) % n]);
+	return 0;
+}

code/p1495_CRT.cpp

@@ -0,0 +1,29 @@
+#include <bits/stdc++.h>
+using namespace std;
+typedef long long ll;
+#define mn 13
+ll n, a[mn], b[mn], pd = 1, c, ci, z, ans;
+void exgcd(ll a, ll b, ll &x, ll &y)
+{
+    if (!b)
+        x = 1, y = 0;
+    else
+        exgcd(b, a % b, y, x), y -= a / b * x;
+}
+signed main()
+{
+    scanf("%lld", &n);
+    for (ll i = 1; i <= n; ++i)
+    {
+        scanf("%lld%lld", &a[i], &b[i]);
+        pd *= a[i];
+    }
+    for (ll i = 1; i <= n; ++i)
+    {
+        c = pd / a[i], z = 0, ci = 0;
+        exgcd(c, a[i], ci, z);
+        ans += b[i] * c * ((ci + a[i]) % a[i]);
+    }
+    printf("%lld", ans % pd);
+    return 0;
+}

code/p3803_fft.cpp

@@ -0,0 +1,73 @@
+#include <bits/stdc++.h>
+using namespace std;
+typedef long long ll;
+typedef double db;
+#define mn ((1 << 21) + 1)
+ll n1, n2, rev[mn], ans[mn], k, s = 1, len, n;
+db pi = acos(-1), v;
+typedef complex<db> cp;
+cp a[mn], b[mn];
+void fft(cp *a, ll n, ll flag)
+{
+    for (ll i = 0; i < n; ++i)
+    {
+        if (i < rev[i])
+        {
+            swap(a[i], a[rev[i]]);
+        }
+    }
+    for (ll h = 1; h < n; h <<= 1)
+    {
+        cp wn = exp(cp(0, flag * pi / h));
+        for (ll j = 0; j < n; j += h << 1)
+        {
+            cp w(1, 0);
+            for (ll k = j; k < j + h; ++k)
+            {
+                cp x = a[k], y = w * a[k + h];
+                a[k] = x + y;
+                a[k + h] = x - y;
+                w *= wn;
+            }
+        }
+    }
+    if (flag == -1)
+    {
+        for (ll i = 0; i < n; ++i)
+        {
+            a[i] /= n;
+        }
+    }
+}
+#pragma GCC diagnostic ignored "-Wformat" //忽略db转complex警告
+signed main()
+{
+    scanf("%lld%lld", &n1, &n2), n = n1 + n2;
+    for (ll i = 0; i <= n1; ++i)
+    {
+        scanf("%lf", a + i);
+    }
+    for (ll i = 0; i <= n2; ++i)
+    {
+        scanf("%lf", b + i);
+    }
+    while (s <= n)
+    {
+        s <<= 1, ++k;
+    }
+    for (ll i = 0; i < s; ++i)
+    {
+        rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (k - 1));
+    }
+    fft(a, s, 1), fft(b, s, 1);
+    for (ll i = 0; i <= s; ++i)
+    {
+        a[i] *= b[i];
+    }
+    fft(a, s, -1);
+    for (ll i = 0; i <= n; ++i)
+    {
+        printf("%lld ", (ll)(a[i].real() + 0.5));
+    }
+    return 0;
+}

code/p3805_manacher.cpp

@@ -0,0 +1,31 @@
+#include <bits/stdc++.h>
+using namespace std;
+#define mn 22000010
+char s[mn], ch;
+int p[mn], n, ans, r, c;
+signed main()
+{
+    s[0] = '#', s[++n] = '#';
+    while (EOF != (ch = getchar()))
+    {
+        s[++n] = ch, s[++n] = '#';
+    }
+    for (int i = 1; i <= n; ++i)
+    {
+        if (i <= r)
+        {
+            p[i] = min(p[c * 2 - i], r - i + 1);
+        }
+        while (s[i + p[i]] == s[i - p[i]])
+        {
+            ++p[i];
+        }
+        if (i + p[i] > r)
+        {
+            r = p[i] + i - 1, c = i;
+        }
+        ans = max(ans, p[i]);
+    }
+    printf("%d", ans - 1);
+    return 0;
+}

code/p3808_ac_automaton.cpp

@@ -0,0 +1,65 @@
+#include <bits/stdc++.h>
+using namespace std;
+typedef long long ll;
+#define sc(x) scanf("%lld", &x)
+#define mn 1000010
+int tr[mn][26], cnt, e[mn], fail[mn];
+ll n, ans;
+char s[mn];
+queue<int> q;
+signed main()
+{
+    sc(n);
+    for (ll i = 1; i <= n; ++i)
+    {
+        scanf("%s", s + 1);
+        int u = 0;
+        for (int i = 1; s[i]; ++i)
+        {
+            int a = s[i] - 'a';
+            if (!tr[u][a])
+            {
+                tr[u][a] = ++cnt;
+            }
+            u = tr[u][a];
+        }
+        ++e[u];
+    }
+    for (ll i = 0; i < 26; ++i)
+    {
+        if (tr[0][i])
+        {
+            q.push(tr[0][i]);
+        }
+    }
+    while (!q.empty())
+    {
+        int u = q.front();
+        q.pop();
+        for (int i = 0; i < 26; ++i)
+        {
+            if (tr[u][i])
+            {
+                fail[tr[u][i]] = tr[fail[u]][i];
+                q.push(tr[u][i]);
+            }
+            else
+            {
+                tr[u][i] = tr[fail[u]][i];
+            }
+        }
+    }
+    scanf("%s", s + 1);
+    int u = 0;
+    for (int i = 1; s[i]; ++i)
+    {
+        int a = s[i] - 'a';
+        u = tr[u][a];
+        for (int j = u; j && e[j] != -1; j = fail[j])
+        {
+            ans += e[j], e[j] = -1;
+        }
+    }
+    printf("%lld", ans);
+    return 0;
+}

code/p3809_suffix_array.cpp

@@ -0,0 +1,72 @@
+#include <bits/stdc++.h>
+using namespace std;
+typedef long long ll;
+#define mn 1000010
+char s[mn];
+ll n, sa[mn], rk[mn], oldrk[mn << 1], id[mn], px[mn], cnt[mn];
+bool cmp(ll x, ll y, ll w)
+{
+    return oldrk[x] == oldrk[y] && oldrk[x + w] == oldrk[y + w];
+}
+ll m = 300, i, p, w; //ASCII范围<300为计数排序值域,p是新值域
+signed main()
+{
+    scanf("%s", s + 1), n = strlen(s + 1);
+    for (ll i = 1; i <= n; ++i)
+    { //暂时以第一关键字为排序值，有很多同名并列
+        ++cnt[rk[i] = s[i]];
+    }
+    for (ll i = 1; i <= m; ++i)
+    {
+        cnt[i] += cnt[i - 1];
+    }
+    for (ll i = n; i >= 1; --i)
+    {
+        sa[cnt[rk[i]]--] = i;
+    }
+    for (w = 1;; w <<= 1, m = p)
+    {
+        for (p = 0, i = n; i > n - w; --i)
+        { //第二关键字排序；无穷小区域
+            id[++p] = i;
+        }
+        for (ll i = 1; i <= n; ++i)
+        {
+            if (sa[i] > w)
+            {
+                id[++p] = sa[i] - w;
+            }
+        }
+        memset(cnt, 0, sizeof cnt);
+        for (ll i = 1; i <= n; ++i) //第一关键字排序
+        {
+            ++cnt[px[i] = rk[id[i]]];
+        }
+        for (ll i = 1; i <= m; ++i)
+        {
+            cnt[i] += cnt[i - 1];
+        }
+        for (ll i = n; i >= 1; --i)
+        {
+            sa[cnt[px[i]]--] = id[i];
+        }
+        memcpy(oldrk, rk, sizeof rk);
+        for (p = 0, i = 1; i <= n; ++i)
+        {
+            rk[sa[i]] = cmp(sa[i], sa[i - 1], w) ? p : ++p;
+        }
+        if (p == n)
+        {
+            for (ll i = 1; i <= n; ++i)
+            {
+                sa[rk[i]] = i;
+            }
+            break;
+        }
+    }
+    for (ll i = 1; i <= n; ++i)
+    {
+        printf("%lld ", sa[i]);
+    }
+    return 0;
+}