Cpp算法-图论-Dijkstra

说明

n, m点数、边数

G[][]邻接矩阵存图

dist[]路径长度

pre[]路径

make()建图

实现

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const int maxn = 10010;
int n, m, G[maxn][maxn], dist[maxn], pre[maxn], s;

void make()
{
scanf("%d %d", &n, &m);
for (int i = 1; i <= n; ++i)
for (int j = 1; j <= n; ++j)
G[i][j] = INT_MAX;
for (int i = 1; i <= n; ++i) G[i][i] = 0;
for (int i = 1; i <= m; ++i)
{
int from, to, w;
scanf("%d %d %d", &from, &to, &w);
G[from][to] = w;
}
return;
}

void Dijkstra()
{
int k, min;
bool p[maxn];
for (int i = 1; i <= n; ++i)
{
p[i] = false;
if (i != s)
{
dist[i] = G[s][i];
pre[i] = s;
}
}
dist[s] = 0; p[s] = true;
for (int i = 1; i <= n - 1; ++i)
{
min = INT_MAX; k = 0;
for (int j = 1; j <= n; ++j)
{
if (!p[j] && dist[j] < min)
{
min = dist[j];
k = j;
}
}
if (k == 0) return;
p[k] = true;
for (int j = 1; j <= n; ++j)
{
if (!p[j] && G[k][j] != INT_MAX && dist[j] > dist[k] + G[k][j])
{
dist[j] = dist[k] + G[k][j];
pre[j] = k;
}
}
}
return;
}

堆优化(链式前向星)

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struct Edge
{
int to, nxt, t;
}edge[maxm << 1];
int head[maxn], cnt;
void add(int a, int b, int t)
{
edge[++cnt].to = b;
edge[cnt].nxt = head[a];
edge[cnt].t = t;
head[a] = cnt;
}

struct heap
{
int u, d;
bool operator < (const heap& a) const
{
return d > a.d;
}
};

void Dijkstra()
{
priority_queue<heap> q;
for (int i = 0; i <= n; ++i) dist[i] = INF;
dist[1] = 0;
q.push((heap){1, 0});
while (!q.empty())
{
heap top = q.top();
q.pop();
int tx = top.u;
int td = top.d;
if (td != dist[tx]) continue;
for (int i = head[tx]; i; i = edge[i].nxt)
{
int v = edge[i].to;
if (dist[v] > dist[tx] + edge[i].t)
{
dist[v] = dist[tx] + edge[i].t;
dy[v] = i;
dx[v] = tx; //记录路径
q.push((heap){v, dist[v]});
}
}
}
}
路径
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int q = n, p[maxm];
while (q != 1)
{
p[++tot] = dy[q];
q = dx[q];
}

Cpp算法-树状数组

树状数组

模板:洛谷P3374

说明

tree[]树状数组

lowbit(int)神奇的函数

add(int x, int k)第 $x$ 个数加上 $k$

sum(int x)前 $x$ 个数的和

实现

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int tree[2000010];

int lowbit(int k)
{
return k & -k;
}

void add(int x, int k)
{
while (x <= n)
{
tree[x] += k;
x += lowbit(x);
}
}

int sum(int x)
{
int ans = 0;
while (x != 0)
{
ans += tree[x];
x -= lowbit(x);
}
return ans;
}

Cpp算法-大整数类

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#include<string>
#include<iostream>
#include<iosfwd>
#include<cmath>
#include<cstring>
#include<stdlib.h>
#include<stdio.h>
#include<cstring>
using namespace std;

const int maxl = 5000;
#define max(a, b) a>b ? a : b
#define min(a, b) a<b ? a : b

class BigInteger
{
public:
int len, s[maxl];

BigInteger();
BigInteger(const char*);
BigInteger(int);
bool sign;
string toStr() const;
friend istream& operator>>(istream&, BigInteger&);
friend ostream& operator<<(ostream&, BigInteger&);

BigInteger operator=(const char*);
BigInteger operator=(int);
BigInteger operator=(const string);

bool operator>(const BigInteger&) const;
bool operator>=(const BigInteger&) const;
bool operator>(const BigInteger&) const;
bool operator>=(const BigInteger&) const;
bool operator==(const BigInteger&) const;
bool operator!=(const BigInteger&) const;

BigInteger operator+(const BigInteger&) const;
BigInteger operator++();
BigInteger operator++(int);
BigInteger operator+=(const BigInteger&);
BigInteger operator-(const BigInteger&) const;
BigInteger operator--();
BigInteger operator--(int);
BigInteger operator-=(const BigInteger&);
BigInteger operator*(const BigInteger&) const;
BigInteger operator*(const int num) const;
BigInteger operator*=(const BigInteger&);
BigInteger operator/(const BigInteger&) const;
BigInteger operator/=(const BigInteger&);

BigInteger operator%(const BigInteger&) const;
BigInteger factorial() const;
BigInteger Sqrt() const;
BigInteger Pow(const BigInteger&) const;

void clean();
~BigInteger;
};


BigInteger::BigInteger()
{
memset(s, 0, sizeof(s));
len = 1;
sign = 1;
}

BigInteger::BigInteger(const char *num)
{
*this = num;
}

BigInteger::BigInteger(int num)
{
*this = num;
}

string BigInteger::toStr() const
{
string res;
res = "";
for (int i = 0; i < len; ++i)
res = (char)(s[i] + '0') + res;
if (res == "") res = "0";
if (!sign && res != "0") res = "-" + res;
return res;
}

istream& operator>>(istream& in, BigInteger& num)
{
string str;
in>>str;
num = str;
return in;
}

ostream& operator<<(ostream& out, BigInteger& num)
{
out<<num.toStr();
return out;
}

BigInteger BigInteger::operator=(const char* num)
{
memset(s, 0, sizeof(s));
char a[maxl] = "";
if (num[0] != "-")
strcpy(a, num);
else
for (int i = 1; i < strlen(num); ++i)
a[i - 1] = num[i];
sign = !(num[0] == "-");
len = strlen(a);
for (int i = 0; i < strlen(a); ++i)
s[i] = a[len - i - 1] - 48;
return *this;
}

BigInteger BigInteger::operator=(int num)
{
if (num < 0)
sign = 0, num = -num;
else
sign = 1;
char temp[MAX_L];
sprintf(temp, "%d", num);
*this = temp;
return *this;
}

BigInteger BigInteger::operator=(const string num)
{
const char* tmp;
tmp = num.c_str();
*this = tmp;
return *this;
}

bool BigInteger::operator<(const BigInteger& num) const
{
if (sign^num.sign)
return num.sign;
if (len != num.len)
return len < num.len;
for (int i = len - 1; i >= 0; --i)
if (s[i] != num.s[i])
return sign ? (s[i] < num.s[i]) : (s[i] > num.s[i])
return !sign;
}

bool BigInteger::operator>(const BigInteger& num) const
{
return num < *this;
}

bool BigInteger::operator<=(const BigInteger& num) const
{
return !(*this > num);
}

bool BigInteger::operator>=(const BigInteger& num) const
{
return !(*this < num);
}

bool BigInteger::operator!=(const BigInteger& num) const
{
return *this > num || *this < num;
}

bool BigInteger::operator==(const BigInteger& num) const
{
return !(num != *this);
}

BigInteger BigInteger::operator+(const BigInteger& num) const
{
if (sign^num.sign)
{
BigInteger tmp = sign ? num : *this;
tmp.sign = 1;
return sign ? *this - tmp : num - tmp;
}
BigInteger result;
result.len = 0;
int temp = 0;
for (int i = 0; temp || i < (max(len, num.len)); i++)
{
int t = s[i] + num.s[i] + temp;
result.s[result.len++] = t % 10;
temp = t / 10;
}
result.sign = sign;
return result;
}

BigInteger BigInteger::operator++()
{
*this = *this + 1;
return *this;
}

BigInteger BigInteger::operator++(int)
{
BigInteger old = *this;
++(*this);
return old;
}

BigInteger BigInteger::operator+=(const BigInteger& num)
{
*this = *this + num;
return *this;
}

BigInteger BigInteger::operator-(const BigInteger& num) const
{
BigInteger b = num, a = *this;
if (!num.sign && !sign)
{
b.sign = 1;
a.sign = 1;
return b - a;
}
if (!b.sign)
{
b.sign = 1;
return a + b;
}
if (!a.sign)
{
a.sign = 1;
b = BigInteger(0) - (a + b);
return b;
}
if (a < b)
{
BigInteger c = (b - a);
c.sign = false;
return c;
}
BigInteger result;
result.len = 0;
for (int i = 0, g = 0; i < a.len; i++)
{
int x = a.s[i] - g;
if (i < b.len) x -= b.s[i];
if (x >= 0) g = 0;
else
{
g = 1;
x += 10;
}
result.s[result.len++] = x;
}
result.clean();
return result;
}

BigInteger BigInteger::operator--()
{
*this = *this - 1;
return *this;
}

BigInteger BigInteger::operator--(int)
{
BigInteger old = *this;
--(*this);
return old;
}

BigInteger BigInteger::operator-=(const BigInteger& num)
{
*this = *this - num;
return *this;
}

BigInteger BigInteger::operator*(const BigInteger& num) const
{
BigInteger result;
result.len = len + num.len;
for (int i = 0; i < len; i++)
for (int j = 0; j < num.len; j++)
result.s[i + j] += s[i] * num.s[j];
for (int i = 0; i < result.len; i++)
{
result.s[i + 1] += result.s[i] / 10;
result.s[i] %= 10;
}
result.clean();
result.sign = !(sign^num.sign);
return result;
}

BigInteger BigInteger::operator*(const int num) const
{
BigInteger x = num;
BigInteger z = *this;
return *this;
}

BigInteger BigInteger::operator/(const BigInteger& num) const
{
BigInteger ans;
ans.len = len - num.len + 1;
if (ans.len < 0)
{
ans.len = 1;
return ans;
}
BigInteger divisor = *this, divid = num;
divisor.sign = divid.sign = 1;
int k = ans.len - 1;
int j = len - 1;
while (k >= 0)
{
while (divisor.s[j] == 0) j--;
if (k > j) k = j;
char z[MAX_L];
memset(z, 0, sizeof(z));
for (int i = j; i >= k; i--)
z[j - i] = divisor.s[i] + '0';
BigInteger dividend = z;
if (dividend < divid) { k--; continue; }
int key = 0;
while (divid*key <= dividend) key++;
key--;
ans.s[k] = key;
BigInteger temp = divid*key;
for (int i = 0; i < k; i++)
temp = temp * 10;
divisor = divisor - temp;
k--;
}
ans.clean();
ans.sign = !(sign^num.sign);
return ans;
}

BigInteger BigInteger::operator/=(const BigInteger& num)
{
*this = *this / num;
return *this;
}

BigInteger BigInteger::operator%(const BigInteger& num) const
{
BigInteger a = *this, b = num;
a.sign = b.sign = 1;
BigInteger result, temp = a / b*b;
result = a - temp;
result.sign = sign;
return result;
}

BigInteger BigInteger::Pow(const BigInteger& num) const
{
BigInteger result = 1;
for (BigInteger i = 0; i < num; i++)
result = result * (*this);
return result;
}

BigInteger BigInteger::factorial() const
{
BigInteger result = 1;
for (BigInteger i = 1; i <= *this; i++)
result *= i;
return result;
}

void BigInteger::clean()
{
if (len == 0) len++;
while (len > 1 && s[len - 1] == '\0')
len--;
}

BigInteger BigInteger::Sqrt() const
{
if(*this < 0) return - 1;
if(*this <= 1)return *this;
BigInteger l = 0, r = *this, mid;
while(r - l > 1)
{
mid = (l + r) / 2;
if(mid * mid > *this)
r = mid;
else
l = mid;
}
return l;
}

BigInteger::~BigInteger()
{

}

Cpp算法-BFS

说明

本文实现只是框架,应当灵活运用,bfs()函数内部根据情况灵活更改
广搜算法基于树、队列实现,具体思路: 将当前点的子节点入队,当前点出队,如果子节点满足条件则记录并重复此过程

框架

数组模拟队列

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void bfs()
{
int head = 1, tail = 2;
vis[start_x][start_y] = true; //标记起始点
que[head][0] = start_x;
que[head][1] = start_y; //起始点入队
while(head < tail) //队不为空
{
int x = que[head][0], y = que[head][1] //获取队首点
for (int i = 0; i < 子节点数; ++i)
{
int x2 = x子节点, y2 = y子节点;
if (x2, y2满足条件 && !vis[x2][y2])
{
记录结果;
vis[x2][y2] = true;
que[tail][0] = x2;
que[tail][0] = y2;
tail++; //入队
}
}
head++; //队首出队
}
return
}

STL-queue

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struct Node
{
int x, y;
}node, top;

queue<Node> que;

void bfs()
{
vis[sx][sy] = true;
node.x = sx;
node.y = sy;
que.push(node);
ans[sx][sy] = 0;
while(!que.empty())
{
top = que.front();
for (int i = 0; i < 8; ++i)
{
int x2 = ..., y2 = ...;
if (x2, y2满足条件 && !vis[x2][y2])
{
记录结果;
vis[x2][y2] = true;
node.x = x2;
node.y = y2;
que.push(node);
}
}
que.pop();
}
return;
}

洛谷P1443

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#include<bits/stdc++.h>
using namespace std;

int n, m, sx, sy, vis[210][210], ans[210][210];
int gox[8] = {-2, -1, 1, 2, 2, 1, -1, -2};
int goy[8] = {1, 2, 2, 1, -1, -2, -2, -1};

struct horse
{
int x, y;
}node, top;

queue<horse> que;

void bfs()
{
vis[sx][sy] = 1;
node.x = sx;
node.y = sy;
que.push(node);
ans[sx][sy] = 0;
while(!que.empty())
{
top = que.front();
for (int i = 0; i < 8; ++i)
{
int x2 = top.x + gox[i];
int y2 = top.y + goy[i];
if (x2 >= 1 && x2 <= n && y2 >= 1 && y2 <= m && !vis[x2][y2])
{
ans[x2][y2] = ans[top.x][top.y] + 1;
vis[x2][y2] = 1;
node.x = x2;
node.y = y2;
que.push(node);
}
}
que.pop();
}
return;
}

int main()
{
scanf("%d %d %d %d", &n, &m, &sx, &sy);
memset(ans, -1, sizeof(ans));
bfs();
for (int i = 1; i <= n; ++i)
{
for (int j = 1; j <= m; ++j)
printf("%-5d", ans[i][j]);
printf("\n");
}
return 0;
}
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#include<bits/stdc++.h>
using namespace std;

int n, m, sx, sy, vis[210][210], que[50000][2], ans[210][210];
int gox[8] = {-2, -1, 1, 2, 2, 1, -1, -2};
int goy[8] = {1, 2, 2, 1, -1, -2, -2, -1};

void bfs()
{
int head = 1, tail = 2;
vis[sx][sy] = 1;
que[head][0] = sx;
que[head][1] = sy;
ans[sx][sy] = 0;
while (head < tail)
{
int x, x2, y, y2;
x = que[head][0];
y = que[head][1];
for (int i = 0; i < 8; ++i)
{
x2 = x + gox[i];
y2 = y + goy[i];
if (x2 >= 1 && x2 <= n && y2 >= 1 && y2 <= m && !vis[x2][y2])
{
ans[x2][y2] = ans[x][y] + 1;
vis[x2][y2] = 1;
que[tail][0] = x2;
que[tail][1] = y2;
tail++;
}
}
head++;
}
return;
}

int main()
{
scanf("%d %d %d %d", &n, &m, &sx, &sy);
memset(ans, -1, sizeof(ans));
bfs();
for (int i = 1; i <= n; ++i)
{
for (int j = 1; j <= m; ++j)
printf("%-5d", ans[i][j]);
printf("\n");
}
return 0;
}

Cpp算法-DFS

说明

本文实现只是框架,应当灵活运用,dfs(…)函数返回值类型、参数列表根据情况灵活更改

框架

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void dfs(参数列表)
{
if (到达目的地) 输出结果;
else
{
for (int i = 0; i < 行动方法数; ++i)
{
if (下一步可行)
{
记录此步;
dfs(改动后的参数列表);
取消记录此步;
}
}
}
return;
}

洛谷P1605

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#include<bits/stdc++.h>
using namespace std;

int n, m, t, sx, sy, fx, fy, ans;
int mg[6][6], now[6][6];
int go[4][2] = {{-1, 0}, {0, 1}, {1, 0}, {0, -1}};

void dfs(int x, int y)
{
int x2, y2;
if (x == fx && y == fy) ans++;
else
{
for (int i = 0; i < 4; ++i)
{
x2 = x + go[i][0];
y2 = y + go[i][1];
if (x2 > 0 && x2 <= n && y2 > 0 && y2 <= m && mg[x2][y2] == 0 && now[x2][y2] == 0)

{
now[x2][y2] = 1;
dfs(x2, y2);
now[x2][y2] = 0;
}
}
}
return;
}

int main()
{
memset(mg, 0, sizeof(mg));
scanf("%d %d %d", &n, &m, &t);
scanf("%d %d %d %d", &sx, &sy, &fx, &fy);
for (int i = 1; i <= t; ++i)
{
int x, y;
scanf("%d %d", &x, &y);
mg[x][y] = 1;
}
now[sx][sy] = 1;
ans = 0;
dfs(sx, sy);
printf("%d", ans);
return 0;
}

Linux美化方案

I. 初步系统优化


  • 更改系统时间
  • 安装python
    sudo apt install python
  • 安装git并添加ssh密钥
    sudo apt install git
    git config --global user.name "your_name"
    git config --global user.email "you@example.com"
    ssh-keygen -t rsa -C "your_email@youremail.com"一路回车
    cat ~/.ssh/id_rsa.pub并复制粘贴到github上
    ssh -T git@github.com测试
    git clone https://github.com/Tony031218/Beautiful_Linux.git克隆下本仓库
  • 添加语言
      settings -> Region&Language -> manage installed language -> install/remove languages
                                  -> input sources
    
  • 软件更新
    sudo apt update
    sudo apt upgrade
  • 安装GDebi
    sudo apt install gdebi
  • 卸载libreoffice 安装 WPS(可选)
    sudo apt remove libreoffice-common
    http://www.wps.cn/product/wpslinux/ 上下载WPS
    sudo dpkg -i wps-office_10.1.0.6757_amd64.deb
  • 卸载firefox 安装 Chrome(可选)
    sudo apt remove firefox
    wget https://dl.google.com/linux/direct/google-chrome-stable_current_amd64.deb
    sudo dpkg -i google-chrome*
    sudo apt -f install
  • 更换更新源
    左下角 -> all -> Software&Updates
    sudo apt update
  • 安装vim
    sudo apt install vim
  • 菜单栏位置
    gsettings set com.canonical.Unity.Launcher launcher-position Bottom底部
    gsettings set com.canonical.Unity.Launcher launcher-position Left左侧

II. 主题配置


  • 安装 Unity-tweak-tool
    sudo apt install unity-tweak-tool
    如果出现报错需要安装缺失的包

  • 安装 Flatabulous 主题
    sudo add-apt-repository ppa:noobslab/themes
    sudo apt update
    sudo apt install flatabulous-theme主题
    sudo add-apt-repository ppa:noobslab/icons
    sudo apt update
    sudo apt install ultra-flat-icons图标
    unity-tweak-tool -> 主题/图标

  • 字体
    Monaco Powerline 也可以选择其他字体,但一定要支持Powerline的,否则后文会出现乱码

III. 终端Terminal美化


  • Terminal zsh
    sudo apt install zsh
    git clone https://github.com/robbyrussell/oh-my-zsh.git
    cd oh-my-zsh/tools
    ./install.sh
  • 更换默认shell
    chsh按步骤来输入zsh地址
  • zsh插件
    • 自动补全
      git clone https://github.com/zsh-users/zsh-autosuggestions $ZSH_CUSTOM/plugins/zsh-autosuggestions
    • 快速跳转
      git clone https://github.com/joelthelion/autojump.git
      cd autojump
      ./install.py按要求把代码填写到~/.zshrc文件尾
    • 配置
      vim ~/.zshrc
      修改60行左右的pluginsplugins=(git autojump zsh-suggestions)
    • 修改皮肤
      ~/.zshrc中的ZSH_THEME="robbyrussell"更改

IV. vim美化


  • molokai
    mkdir ~/.vim/colors
    将本仓库中的molokai.vim复制到~/.vim/colors/
  • Powerline
    sudo apt install python-pip
    pip install git+git://github.com/powerline/powerline
    pip show powerline-status
    按照具体位置更改~/.vimrc中的set rtp+=...一行(后文)
  • 插件
    • pathogen插件管理
      mkdir -p ~/.vim/autoload ~/.vim/bundle
      curl -LSso ~/.vim/autoload/pathogen.vim https://tpo.pe/pathogen.vim
    • nerdtree文件浏览器
      cd ~/.vim/bundle
      git clone https://github.com/scrooloose/nerdtree.git
    • taglist大纲界面
      taglist官网
      下载后解压到~/.vim/bundle/
  • vimrc
    将本仓库中的vimrc.txt复制到~/.vimrc
    内包含括号匹配,html标签匹配,powerline配置(可能需要改动),cpp.sh.java.py的文件头自动输入,插件的配置(F3打开nerdtree,F4打开taglist)

参考


CSDN博客
powerline
vim插件
monaco powerline字体
monokai主题
WPS

Git简单用法

Git是一款版本控制软件,配合GitHub可以更好的控制代码

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Markdown语法

Markdown是一款简洁实用的文本标记语言,可以在mkdocs,hexo中使用

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MkDocs使用方法

mkdocs是一款基于python markdown的项目文档工具,可以用来编写一个网站

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