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杂项

STL

  • copy
template <class InputIterator, class OutputIterator>
  OutputIterator copy (InputIterator first, InputIterator last, OutputIterator result);
  • merge (如果相等，第一个优先)
template <class InputIterator1, class InputIterator2,
          class OutputIterator, class Compare>
  OutputIterator merge (InputIterator1 first1, InputIterator1 last1,
                        InputIterator2 first2, InputIterator2 last2,
                        OutputIterator result, Compare comp);
  • for_each
template <class InputIterator, class Function>
   Function for_each (InputIterator first, InputIterator last, Function fn);
  • transform
template <class InputIterator, class OutputIterator, class UnaryOperation>
  OutputIterator transform (InputIterator first1, InputIterator last1,
                            OutputIterator result, UnaryOperation op);
  • numeric_limits
template <class T> numeric_limits;
  • iota
template< class ForwardIterator, class T >
void iota( ForwardIterator first, ForwardIterator last, T value );

日期

// Routines for performing computations on dates.  In these routines,
// months are exprsesed as integers from 1 to 12, days are expressed
// as integers from 1 to 31, and years are expressed as 4-digit
// integers.

string dayOfWeek[] = {"Mo", "Tu", "We", "Th", "Fr", "Sa", "Su"};

// converts Gregorian date to integer (Julian day number)

int DateToInt (int m, int d, int y){  
  return 
    1461 * (y + 4800 + (m - 14) / 12) / 4 +
    367 * (m - 2 - (m - 14) / 12 * 12) / 12 - 
    3 * ((y + 4900 + (m - 14) / 12) / 100) / 4 + 
    d - 32075;
}

// converts integer (Julian day number) to Gregorian date: month/day/year

void IntToDate (int jd, int &m, int &d, int &y){
  int x, n, i, j;

  x = jd + 68569;
  n = 4 * x / 146097;
  x -= (146097 * n + 3) / 4;
  i = (4000 * (x + 1)) / 1461001;
  x -= 1461 * i / 4 - 31;
  j = 80 * x / 2447;
  d = x - 2447 * j / 80;
  x = j / 11;
  m = j + 2 - 12 * x;
  y = 100 * (n - 49) + i + x;
}

// converts integer (Julian day number) to day of week

string IntToDay (int jd){
  return dayOfWeek[jd % 7];
}

子集枚举

  • 枚举真子集
for (int s = (S - 1) & S; s; s = (s - 1) & S)
  • 枚举大小为 k 的子集
template<typename T>
void subset(int k, int n, T&& f) {
    int t = (1 << k) - 1;
    while (t < 1 << n) {
        f(t);
        int x = t & -t, y = t + x;
        t = ((t & ~y) / x >> 1) | y;
    }
}

数位 DP

LL dfs(LL base, LL pos, LL len, LL s, bool limit) {
    if (pos == -1) return s ? base : 1;
    if (!limit && dp[base][pos][len][s] != -1) return dp[base][pos][len][s];
    LL ret = 0;
    LL ed = limit ? a[pos] : base - 1;
    FOR (i, 0, ed + 1) {
        tmp[pos] = i;
        if (len == pos)
            ret += dfs(base, pos - 1, len - (i == 0), s, limit && i == a[pos]);
        else if (s &&pos < (len + 1) / 2)
            ret += dfs(base, pos - 1, len, tmp[len - pos] == i, limit && i == a[pos]);
        else
            ret += dfs(base, pos - 1, len, s, limit && i == a[pos]);
    }
    if (!limit) dp[base][pos][len][s] = ret;
    return ret;
}

LL solve(LL x, LL base) {
    LL sz = 0;
    while (x) {
        a[sz++] = x % base;
        x /= base;
    }
    return dfs(base, sz - 1, sz - 1, 1, true);
}

模拟退火

  • 最小覆盖圆
using LD = double;
const int N = 1E4 + 100;
int x[N], y[N], n;

LD eval(LD xx, LD yy) {
    LD r = 0;
    FOR (i, 0, n)
        r = max(r, sqrt(pow(xx - x[i], 2) + pow(yy - y[i], 2)));
    return r;
}

mt19937 mt(time(0));
auto rd = bind(uniform_real_distribution<LD>(-1, 1), mt);


int main() {
    int X, Y;
    while (cin >> X >> Y >> n) {
        FOR (i, 0, n) scanf("%d%d", &x[i], &y[i]);
        pair<LD, LD> ans;
        LD M = 1e9;
        FOR (_, 0, 100) {
            LD cur_x = X / 2.0, cur_y = Y / 2.0, T = max(X, Y);
            while (T > 1e-3) {
                LD best_ans = eval(cur_x, cur_y);
                LD best_x = cur_x, best_y = cur_y;
                FOR (___, 0, 20) {
                    LD nxt_x = cur_x + rd() * T, nxt_y = cur_y + rd() * T;
                    LD nxt_ans = eval(nxt_x, nxt_y);
                    if (nxt_ans < best_ans) {
                        best_x = nxt_x; best_y = nxt_y;
                        best_ans = nxt_ans;
                    }
                }
                cur_x = best_x; cur_y = best_y;
                T *= .9;
            }
            if (eval(cur_x, cur_y) < M) {
                ans = {cur_x, cur_y}; M = eval(cur_x, cur_y); 
            }
        }
        printf("(%.1f,%.1f).\n%.1f\n", ans.first, ans.second, eval(ans.first, ans.second));
    }
}

土制 bitset

  • 可以用 auto p = reinterpret_cast<unsigned*>(&x); （p[0] 的最低位就是 bitset 的最低位）
// M 要开大至少 1 个 64
const int M = (1E4 + 200) / 64;
typedef unsigned long long ULL;
const ULL ONE = 1;

struct Bitset {
    ULL a[M];
    void go(int x) {
        int offset = x / 64; x %= 64;
        for (int i = offset, j = 0; i + 1 < M; ++i, ++j) {
            a[j] |= a[i] >> x;
            if (x) a[j] |= a[i + 1] << (64 - x); // 不能左移 64 位
        }
    }
    void init() { memset(a, 0, sizeof a); }
    void set(int x) {
        int offset = x / 64; x %= 64;
        a[offset] |= (ONE << x);
    }
    void prt() {
        FOR (i, 0, M) FOR (j, 0, 64) putchar((a[i] & (ONE << j)) ? '1' : '0');
        puts("");
    }
    int lowbit() {
        FOR (i, 0, M) if (a[i]) return i * 64 + __builtin_ctzll(a[i]);
        assert (0);
    }
    int highbit(int x) {
        // [0,x) 的最高位
        int offset = x / 64; x %= 64;
        FORD (i, offset, -1) {
            if (!a[i]) continue;
            if (i == offset) {
                FORD (j, x - 1, -1) if ((ONE << j) & a[i]) { return i * 64 + j; }
            } else return i * 64 + 63 - __builtin_clzll(a[i]);
        }
        assert (0);
    }
};

随机

  • 不要使用 rand()。
  • chrono::steady_clock::now().time_since_epoch().count() 可用于计时。
  • 64 位可以使用 mt19937_64。
int main() {
    mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
    vector<int> permutation(N);

    for (int i = 0; i < N; i++)
        permutation[i] = i;
    shuffle(permutation.begin(), permutation.end(), rng);

    for (int i = 0; i < N; i++)
        permutation[i] = i;
    for (int i = 1; i < N; i++)
        swap(permutation[i], permutation[uniform_int_distribution<int>(0, i)(rng)]);

伪随机数

unsigned rnd() {
    static unsigned A = 1 << 16 | 3, B = 33333331, C = 2341;
    return C = A * C + B;
}

真实随机数

mt19937 mt(time(0));
auto rd = bind(uniform_real_distribution<double>(0, 1), mt);
auto rd2 = bind(uniform_int_distribution<int>(1, 6), mt);

随机素数表

42737, 46411, 50101, 52627, 54577, 191677, 194869, 210407, 221831, 241337, 578603, 625409, 713569, 788813, 862481, 2174729, 2326673, 2688877, 2779417, 3133583, 4489747, 6697841, 6791471, 6878533, 7883129, 9124553, 10415371, 11134633, 12214801, 15589333, 17148757, 17997457, 20278487, 27256133, 28678757, 38206199, 41337119, 47422547, 48543479, 52834961, 76993291, 85852231, 95217823, 108755593, 132972461, 171863609, 173629837, 176939899, 207808351, 227218703, 306112619, 311809637, 322711981, 330806107, 345593317, 345887293, 362838523, 373523729, 394207349, 409580177, 437359931, 483577261, 490845269, 512059357, 534387017, 698987533, 764016151, 906097321, 914067307, 954169327

1572869, 3145739, 6291469, 12582917, 25165843, 50331653 （适合哈希的素数）

from random import randint

def is_prime(num, test_count):
    if num == 1:
        return False
    if test_count >= num:
        test_count = num - 1
    for x in range(test_count):
        val = randint(1, num - 1)
        if pow(val, num-1, num) != 1:
            return False
    return True

def generate_big_prime(n):
    found_prime = False
    while not found_prime:
        p = randint(2**(n-1), 2**n)
        if is_prime(p, 1000):
            return p

NTT 素数表

$p= r2^k+1$，原根是 $g$。

3, 1, 1, 2; 5, 1, 2, 2; 17, 1, 4, 3; 97, 3, 5, 5; 193, 3, 6, 5; 257, 1, 8, 3; 7681, 15, 9, 17; 12289, 3, 12, 11; 40961, 5, 13, 3; 65537, 1, 16, 3; 786433, 3, 18, 10; 5767169, 11, 19, 3; 7340033, 7, 20, 3; 23068673, 11, 21, 3; 104857601, 25, 22, 3; 167772161, 5, 25, 3; 469762049, 7, 26, 3; 1004535809, 479, 21, 3; 2013265921, 15, 27, 31; 2281701377, 17, 27, 3; 3221225473, 3, 30, 5; 75161927681, 35, 31, 3; 77309411329, 9, 33, 7; 206158430209, 3, 36, 22; 2061584302081, 15, 37, 7; 2748779069441, 5, 39, 3; 6597069766657, 3, 41, 5; 39582418599937, 9, 42, 5; 79164837199873, 9, 43, 5; 263882790666241, 15, 44, 7; 1231453023109121, 35, 45, 3; 1337006139375617, 19, 46, 3; 3799912185593857, 27, 47, 5; 4222124650659841, 15, 48, 19; 7881299347898369, 7, 50, 6; 31525197391593473, 7, 52, 3; 180143985094819841, 5, 55, 6; 1945555039024054273, 27, 56, 5; 4179340454199820289, 29, 57, 3.

Java

Regex

// Code which demonstrates the use of Java's regular expression libraries.
// This is a solution for 
//
//   Loglan: a logical language
//   http://acm.uva.es/p/v1/134.html

import java.util.*;
import java.util.regex.*;

public class LogLan {

    public static void main(String args[]) {

        String regex = BuildRegex();
        Pattern pattern = Pattern.compile(regex);

        Scanner s = new Scanner(System.in);
        while (true) {

            // In this problem, each sentence consists of multiple lines, where the last 
            // line is terminated by a period.  The code below reads lines until
            // encountering a line whose final character is a '.'.  Note the use of
            //
            //    s.length() to get length of string
            //    s.charAt() to extract characters from a Java string
            //    s.trim() to remove whitespace from the beginning and end of Java string
            //
            // Other useful String manipulation methods include
            //
            //    s.compareTo(t) < 0 if s < t, lexicographically
            //    s.indexOf("apple") returns index of first occurrence of "apple" in s
            //    s.lastIndexOf("apple") returns index of last occurrence of "apple" in s
            //    s.replace(c,d) replaces occurrences of character c with d
            //    s.startsWith("apple) returns (s.indexOf("apple") == 0)
            //    s.toLowerCase() / s.toUpperCase() returns a new lower/uppercased string
            //
            //    Integer.parseInt(s) converts s to an integer (32-bit)
            //    Long.parseLong(s) converts s to a long (64-bit)
            //    Double.parseDouble(s) converts s to a double

            String sentence = "";
            while (true) {
                sentence = (sentence + " " + s.nextLine()).trim();
                if (sentence.equals("#")) return;
                if (sentence.charAt(sentence.length() - 1) == '.') break;
            }

            // now, we remove the period, and match the regular expression

            String removed_period = sentence.substring(0, sentence.length() - 1).trim();
            if (pattern.matcher(removed_period).find()) {
                System.out.println("Good");
            } else {
                System.out.println("Bad!");
            }
        }
    }
}

Decimal Format

// examples for printing floating point numbers

import java.util.*;
import java.io.*;
import java.text.DecimalFormat;

public class DecFormat {
    public static void main(String[] args) {
        DecimalFormat fmt;

        // round to at most 2 digits, leave of digits if not needed
        fmt = new DecimalFormat("#.##");
        System.out.println(fmt.format(12345.6789)); // produces 12345.68
        System.out.println(fmt.format(12345.0)); // produces 12345
        System.out.println(fmt.format(0.0)); // produces 0
        System.out.println(fmt.format(0.01)); // produces .1

        // round to precisely 2 digits
        fmt = new DecimalFormat("#.00");
        System.out.println(fmt.format(12345.6789)); // produces 12345.68
        System.out.println(fmt.format(12345.0)); // produces 12345.00
        System.out.println(fmt.format(0.0)); // produces .00

        // round to precisely 2 digits, force leading zero
        fmt = new DecimalFormat("0.00");
        System.out.println(fmt.format(12345.6789)); // produces 12345.68
        System.out.println(fmt.format(12345.0)); // produces 12345.00
        System.out.println(fmt.format(0.0)); // produces 0.00

        // round to precisely 2 digits, force leading zeros
        fmt = new DecimalFormat("000000000.00");
        System.out.println(fmt.format(12345.6789)); // produces 000012345.68
        System.out.println(fmt.format(12345.0)); // produces 000012345.00
        System.out.println(fmt.format(0.0)); // produces 000000000.00

        // force leading '+'
        fmt = new DecimalFormat("+0;-0");
        System.out.println(fmt.format(12345.6789)); // produces +12346
        System.out.println(fmt.format(-12345.6789)); // produces -12346
        System.out.println(fmt.format(0)); // produces +0

        // force leading positive/negative, pad to 2
        fmt = new DecimalFormat("positive 00;negative 0");
        System.out.println(fmt.format(1)); // produces "positive 01"
        System.out.println(fmt.format(-1)); // produces "negative 01"

        // qoute special chars (#)
        fmt = new DecimalFormat("text with '#' followed by #");
        System.out.println(fmt.format(12.34)); // produces "text with # followed by 12"

        // always show "."
        fmt = new DecimalFormat("#.#");
        fmt.setDecimalSeparatorAlwaysShown(true);
        System.out.println(fmt.format(12.34)); // produces "12.3"
        System.out.println(fmt.format(12)); // produces "12."
        System.out.println(fmt.format(0.34)); // produces "0.3"

        // different grouping distances:
        fmt = new DecimalFormat("#,####.###");
        System.out.println(fmt.format(123456789.123)); // produces "1,2345,6789.123"

        // scientific:
        fmt = new DecimalFormat("0.000E00");
        System.out.println(fmt.format(123456789.123)); // produces "1.235E08"
        System.out.println(fmt.format(-0.000234)); // produces "-2.34E-04"

        // using variable number of digits:
        fmt = new DecimalFormat("0");
        System.out.println(fmt.format(123.123)); // produces "123"
        fmt.setMinimumFractionDigits(8);
        System.out.println(fmt.format(123.123)); // produces "123.12300000"
        fmt.setMaximumFractionDigits(0);
        System.out.println(fmt.format(123.123)); // produces "123"

        // note: to pad with spaces, you need to do it yourself:
        // String out = fmt.format(...)
        // while (out.length() < targlength) out = " "+out;
    }
}

Sort

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;

public class Employee implements Comparable<Employee> {
    private int id;
    private String name;
    private int age;

    public Employee(int id, String name, int age) {
        this.id = id;
        this.name = name;
        this.age = age;
    }

    @Override
    public int compareTo(Employee o) {
        if (id > o.id) {
            return 1;
        } else if (id < o.id) {
            return -1;
        }
        return 0;
    }

    public static void main(String[] args) {
        List<Employee> list = new ArrayList<Employee>();
        list.add(new Employee(2, "Java", 20));
        list.add(new Employee(1, "C", 30));
        list.add(new Employee(3, "C#", 10));
        Collections.sort(list);
    }
}

扩栈（本地使用）

#include <sys/resource.h>
void init_stack(){
    const rlim_t kStackSize = 512 * 1024 * 1024;
    struct rlimit rl;
    int result;
    result = getrlimit(RLIMIT_STACK, &rl);
    if (result == 0) {
        if (rl.rlim_cur < kStackSize) {
            rl.rlim_cur = kStackSize;
            result = setrlimit(RLIMIT_STACK, &rl);
            if (result != 0) {
                fprintf(stderr, "setrlimit returned result = %d\n", result);
            }
        }
    }
}

心态崩了

  • (int)v.size()
  • 1LL << k
  • 递归函数用全局或者 static 变量要小心
  • 预处理组合数注意上限
  • 想清楚到底是要 multiset 还是 set
  • 提交之前看一下数据范围，测一下边界
  • 数据结构注意数组大小 （2倍，4倍）
  • 字符串注意字符集
  • 如果函数中使用了默认参数的话，注意调用时的参数个数。
  • 注意要读完
  • 构造参数无法使用自己
  • 树链剖分/dfs 序，初始化或者询问不要忘记 idx, ridx
  • 排序时注意结构体的所有属性是不是考虑了
  • 不要把 while 写成 if
  • 不要把 int 开成 char
  • 清零的时候全部用 0~n+1。
  • 模意义下不要用除法
  • 哈希不要自然溢出
  • 最短路不要 SPFA，乖乖写 Dijkstra
  • 上取整以及 GCD 小心负数
  • mid 用 l + (r - l) / 2 可以避免溢出和负数的问题
  • 小心模板自带的意料之外的隐式类型转换
  • 求最优解时不要忘记更新当前最优解
  • 图论问题一定要注意图不连通的问题
  • 处理强制在线的时候 lastans 负数也要记得矫正
  • 不要觉得编译器什么都能优化