v1.0.2:增加和修改了若干内容，主要增添了部分随机化内容

Author: lr580

README.md

@@ -46,6 +46,16 @@
 
 ## 更新日志
 
+- 22/04/19 - 22/04/22 (`v1.0.2`)
+
+  - 增加了KMP算法周期与border
+  - 删除了凸包一节无关多余内容
+  - 增加了另一种写法的C语言快读
+  - 修正了计算几何判断线段相交的错误方法
+  - 增改了随机化的程序语法、公式和爬山算法及模拟退火例题
+  - 重制了珂朵莉树参考模板
+  - 微增了博弈论理论内容
+
 - 22/04/06 - 22/04/07 (`v1.0.1`)
 
   - 增加了位运算一节少量内容

code/hill_climbing.cpp

@@ -0,0 +1,34 @@
+#include <bits/stdc++.h> //SCNUOJ1679 http://10.191.65.243:5000/p/1679
+using namespace std;
+typedef long long ll;
+typedef double db;
+ll p, a, b, q;
+db k, t = 0.5, d, minx = 0.5, nowx = 0.5;
+db f(db x) // assume k=1
+{
+    return sqrt(p - a + x * x) + sqrt(p - b + (k - x) * (k - x));
+}
+signed main()
+{
+    scanf("%lld%lld%lld%lld", &p, &a, &b, &q);
+    while (q--)
+    {
+        scanf("%lf", &k);
+        minx = nowx = k / 2;
+        t = k / 2;
+        while (t > 1e-6) // t是温度参数
+        {
+            db x1 = nowx + t;
+            db x2 = nowx - t;
+            db newx = f(x1) < f(x2) ? x1 : x2;
+            nowx = newx;
+            if (f(newx) < f(minx))
+            {
+                minx = newx;
+            }
+            t *= 0.9; // 降温系数
+        }
+        printf("%lf %lf\n", minx, (k - minx));
+    }
+    return 0;
+}

code/odt.cpp

@@ -0,0 +1,72 @@
+#include <bits/stdc++.h> //SCNUOJ1731 https://oj.socoding.cn/p/1731
+using namespace std;
+#define sc(x) scanf("%lld", &x)
+typedef long long ll;
+ll n;
+struct node_t
+{
+    ll l, r;
+    mutable ll v; // mutable使得const可变(set元素是const)
+    node_t(const ll &il, const ll &ir, const ll &iv) : l(il), r(ir), v(iv) {}
+    inline bool operator<(const node_t &o) const { return l < o.l; }
+};
+set<node_t> odt; //建立一棵珂朵莉树
+auto split(ll x) //珂朵莉基操
+{
+    if (x > n)
+        return odt.end();
+    auto it = --odt.upper_bound(node_t{x, 0, 0});
+    if (it->l == x)
+        return it;
+    ll l = it->l, r = it->r, v = it->v;
+    odt.erase(it);
+    odt.insert(node_t(l, x - 1, v));
+    return odt.insert(node_t(x, r, v)).first;
+}
+void assign(ll l, ll r, ll v) //区间赋值为v, 均摊O(loglogn)
+{
+    auto itr = split(r + 1), itl = split(l);
+    odt.erase(itl, itr);
+    odt.insert(node_t(l, r, v));
+}
+void add(ll l, ll r, ll v) //区间增加v, 均摊O(loglogn)
+{
+    auto itr = split(r + 1), itl = split(l);
+    for (; itl != itr; ++itl) //枚举每个子区间
+    {
+        itl->v = itl->v + v;
+    }
+}
+ll query(ll l, ll r) //区间查询, 均摊O(loglogn)
+{
+    ll res = 0;
+    auto itr = split(r + 1), itl = split(l);
+    for (; itl != itr; ++itl)
+    { // itl->l, itl->r, itl->v 是当前子区间的左右端点和值
+        res += (itl->r - itl->l + 1) * (itl->v);
+    }
+    return res;
+}
+signed main()
+{
+    sc(n);
+    odt.insert({1, n, 1236895}); //初始化区间
+    ll m, cmd, l, r, x;
+    for (sc(m); m--;)
+    {
+        sc(cmd), sc(l), sc(r);
+        if (cmd == 1)
+        {
+            sc(x), assign(l, r, x);
+        }
+        else if (cmd == 2)
+        {
+            sc(x), add(l, r, x);
+        }
+        else
+        {
+            printf("%lld\n", query(l, r));
+        }
+    }
+    return 0;
+}

code/simulated_annealing.cpp

@@ -0,0 +1,61 @@
+#include <bits/stdc++.h> //SCNUOJ1730 https://oj.socoding.cn/p/1730
+using namespace std;
+#define sc(x) scanf("%lld", &x)
+typedef long long ll;
+typedef double db;
+ll a, b, c, d, e, l, r;
+db x, t, now, mx, ans = -6;
+db f(db x)
+{
+    return sin(x / a) + sin(x / b) + sin(x / c) + sin(x / d) + sin(x / e);
+}
+void solve()
+{
+    static ll rd = 1; //也可以用random_device生成种子
+    mt19937 mt(rd + time(0));
+    rd *= 2;
+    uniform_real_distribution<db> dist0(0, 1);
+    now = (l + r) / 2, t = r - l;
+    while (t > 1e-6)
+    {
+        uniform_real_distribution<db> dist(-t, t);
+        db newx = now + dist(mt);
+        newx = max(1. * l, min(1. * r, newx));
+        db fnow = f(now), fnew = f(newx);
+        db dt = (-fnew) - (-fnow);
+        if (fnow < fnew || exp(-dt / t) > dist0(mt))
+        {
+            now = newx;
+        }
+        if (ans < fnew)
+        {
+            ans = fnew;
+        }
+        t *= 0.999;
+    }
+    for (ll i = 0; i < 1000; ++i) //在终温随机多次
+    {                             //优化效果不明显
+        uniform_real_distribution<db> dist(-t, t);
+        db newx = now + dist(mt);
+        newx = max(1. * l, min(1. * r, newx));
+        db fnow = f(now), fnew = f(newx);
+        if (fnow < fnew)
+        {
+            now = newx;
+        }
+        if (ans < fnew)
+        {
+            ans = fnew;
+        }
+    }
+}
+signed main()
+{
+    sc(a), sc(b), sc(c), sc(d), sc(e), sc(l), sc(r);
+    for (ll i = 0; i < 20; ++i) //重要：多次退火
+    {
+        solve();
+    }
+    printf("%lf", ans);
+    return 0;
+}