大纲要求
•【1】算数运算:加、减、乘、除、整除、求余
•【1】关系运算:大于,大于等于,小于,小于等于,等于,不等于
•【1】逻辑运算:与(&&)、或(||)、非(!)
•【1】变量自增与自减运算
•【1】三目运算
•【3】位运算:与(&)、或(|)、非(~)、 异或(^)、左移、右移
数学基本知识
- 负数,
- 绝对值,
- 分数,,也可以这样写1 / 10
- 小数,
- 阶乘,
- 幂次,%22%20aria-hidden%3D%22true%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMATHI-61%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMATHI-62%22%20x%3D%22748%22%20y%3D%22583%22%3E%3C%2Fuse%3E%0A%3C%2Fg%3E%0A%3C%2Fsvg%3E#card=math&code=a%5Eb&id=WlCqb),数学上也可以这样写a^b
根号,sqrt(n),数学上是这样写的
三角形
- 长方形
- 勾股定理
- 圆
- 平面直角坐标系
两点之间距离(欧几里得距离,曼哈顿距离)
余数
- 约数
- 倍数
- 上取整
- 下取整
- 整数除法
- 最大公约数, ,欧几里得算法(辗转相除法)
最小公倍数,
素数、质数
- 等差数列,
- 等比数列,
- 斐波那契数列
【拓展内容】
- 分数裂项基本形式
%7D%20%3D%20%5Cfrac%7B1%7D%7Bn%7D%20-%20%5Cfrac%7B1%7D%7Bn%2B1%7D%3C%2Ftitle%3E%0A%3Cdefs%20aria-hidden%3D%22true%22%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMATHI-61%22%20d%3D%22M33%20157Q33%20258%20109%20349T280%20441Q331%20441%20370%20392Q386%20422%20416%20422Q429%20422%20439%20414T449%20394Q449%20381%20412%20234T374%2068Q374%2043%20381%2035T402%2026Q411%2027%20422%2035Q443%2055%20463%20131Q469%20151%20473%20152Q475%20153%20483%20153H487Q506%20153%20506%20144Q506%20138%20501%20117T481%2063T449%2013Q436%200%20417%20-8Q409%20-10%20393%20-10Q359%20-10%20336%205T306%2036L300%2051Q299%2052%20296%2050Q294%2048%20292%2046Q233%20-10%20172%20-10Q117%20-10%2075%2030T33%20157ZM351%20328Q351%20334%20346%20350T323%20385T277%20405Q242%20405%20210%20374T160%20293Q131%20214%20119%20129Q119%20126%20119%20118T118%20106Q118%2061%20136%2044T179%2026Q217%2026%20254%2059T298%20110Q300%20114%20325%20217T351%20328Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMATHI-6E%22%20d%3D%22M21%20287Q22%20293%2024%20303T36%20341T56%20388T89%20425T135%20442Q171%20442%20195%20424T225%20390T231%20369Q231%20367%20232%20367L243%20378Q304%20442%20382%20442Q436%20442%20469%20415T503%20336T465%20179T427%2052Q427%2026%20444%2026Q450%2026%20453%2027Q482%2032%20505%2065T540%20145Q542%20153%20560%20153Q580%20153%20580%20145Q580%20144%20576%20130Q568%20101%20554%2073T508%2017T439%20-10Q392%20-10%20371%2017T350%2073Q350%2092%20386%20193T423%20345Q423%20404%20379%20404H374Q288%20404%20229%20303L222%20291L189%20157Q156%2026%20151%2016Q138%20-11%20108%20-11Q95%20-11%2087%20-5T76%207T74%2017Q74%2030%20112%20180T152%20343Q153%20348%20153%20366Q153%20405%20129%20405Q91%20405%2066%20305Q60%20285%2060%20284Q58%20278%2041%20278H27Q21%20284%2021%20287Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-3D%22%20d%3D%22M56%20347Q56%20360%2070%20367H707Q722%20359%20722%20347Q722%20336%20708%20328L390%20327H72Q56%20332%2056%20347ZM56%20153Q56%20168%2072%20173H708Q722%20163%20722%20153Q722%20140%20707%20133H70Q56%20140%2056%20153Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-31%22%20d%3D%22M213%20578L200%20573Q186%20568%20160%20563T102%20556H83V602H102Q149%20604%20189%20617T245%20641T273%20663Q275%20666%20285%20666Q294%20666%20302%20660V361L303%2061Q310%2054%20315%2052T339%2048T401%2046H427V0H416Q395%203%20257%203Q121%203%20100%200H88V46H114Q136%2046%20152%2046T177%2047T193%2050T201%2052T207%2057T213%2061V578Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-28%22%20d%3D%22M94%20250Q94%20319%20104%20381T127%20488T164%20576T202%20643T244%20695T277%20729T302%20750H315H319Q333%20750%20333%20741Q333%20738%20316%20720T275%20667T226%20581T184%20443T167%20250T184%2058T225%20-81T274%20-167T316%20-220T333%20-241Q333%20-250%20318%20-250H315H302L274%20-226Q180%20-141%20137%20-14T94%20250Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-2B%22%20d%3D%22M56%20237T56%20250T70%20270H369V420L370%20570Q380%20583%20389%20583Q402%20583%20409%20568V270H707Q722%20262%20722%20250T707%20230H409V-68Q401%20-82%20391%20-82H389H387Q375%20-82%20369%20-68V230H70Q56%20237%2056%20250Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-29%22%20d%3D%22M60%20749L64%20750Q69%20750%2074%20750H86L114%20726Q208%20641%20251%20514T294%20250Q294%20182%20284%20119T261%2012T224%20-76T186%20-143T145%20-194T113%20-227T90%20-246Q87%20-249%2086%20-250H74Q66%20-250%2063%20-250T58%20-247T55%20-238Q56%20-237%2066%20-225Q221%20-64%20221%20250T66%20725Q56%20737%2055%20738Q55%20746%2060%20749Z%22%3E%3C%2Fpath%3E%0A%3Cpath%20stroke-width%3D%221%22%20id%3D%22E1-MJMAIN-2212%22%20d%3D%22M84%20237T84%20250T98%20270H679Q694%20262%20694%20250T679%20230H98Q84%20237%2084%20250Z%22%3E%3C%2Fpath%3E%0A%3C%2Fdefs%3E%0A%3Cg%20stroke%3D%22currentColor%22%20fill%3D%22currentColor%22%20stroke-width%3D%220%22%20transform%3D%22matrix(1%200%200%20-1%200%200)%22%20aria-hidden%3D%22true%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMATHI-61%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20transform%3D%22scale(0.707)%22%20xlink%3Ahref%3D%22%23E1-MJMATHI-6E%22%20x%3D%22748%22%20y%3D%22-213%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-3D%22%20x%3D%221331%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(2110%2C0)%22%3E%0A%3Cg%20transform%3D%22translate(397%2C0)%22%3E%0A%3Crect%20stroke%3D%22none%22%20width%3D%223823%22%20height%3D%2260%22%20x%3D%220%22%20y%3D%22220%22%3E%3C%2Frect%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-31%22%20x%3D%221661%22%20y%3D%22676%22%3E%3C%2Fuse%3E%0A%3Cg%20transform%3D%22translate(60%2C-771)%22%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMATHI-6E%22%20x%3D%220%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMAIN-28%22%20x%3D%22600%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3D%22%23E1-MJMATHI-6E%22%20x%3D%22990%22%20y%3D%220%22%3E%3C%2Fuse%3E%0A%20%3Cuse%20xlink%3Ahref%3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- 整数裂项基本形式
数制转换
- 基数、位权
- 二进制、十进制、八进制、十六进制之间的相互转换
- 短除法,一些性质,整数部分、小数部分
组合数学(复刷内容,初赛前掌握)
- 排列组合
- 特殊优先
- 捆绑与插空
- 隔板法
- 错位排列
- 抽屉原理
- Catlan数
- 补集思想(集合和子集,逆向思维)
- 容斥原理
- 简单的Nim游戏
逻辑运算
逻辑与 &&
逻辑或 ||
逻辑非 !
三目运算符
表达式 ? 表达式 : 表达式 ;
x < 0 ? y = 10 : z = 20;
if (x < 0) y = 10;
else z = 20;
赋值语句的示例
a = (x > 100) ? 0 : 1;
位运算
在C++中,位运算符,主要用于数值类型的二进制运算。
// if (x % 2 == 1) cout << "odd" << '\n';
if (x & 1) cout << "odd" << '\n';
else cout << "even" << '\n';
cout << (1 << 2) << '\n';
优先级 | 运算符 | 说明 | 结合性 |
---|---|---|---|
1 | :: | 范围解析 | 自左向右 |
2 | ++ — | 后缀自增/后缀自减 | |
() | 括号 | ||
[] | 数组下标 | ||
. | 成员选择(对象) | ||
−> | 成员选择(指针) | ||
3 | ++ — | 前缀自增/前缀自减 | 自右向左 |
+ − | 加/减 | ||
! ~ | 逻辑非/按位取反 | ||
(type) | 强制类型转换 | ||
* | 取指针指向的值 | ||
& | 某某的地址 | ||
sizeof | 某某的大小 | ||
new, new[] | 动态内存分配/动态数组内存分配 | ||
delete, delete[] | 动态内存释放/动态数组内存释放 | ||
4 | . -> | 成员对象选择/成员指针选择 | 自左向右 |
5 | * / % | 乘法/除法/取余 | |
6 | + − | 加号/减号 | |
7 | << >> | 位左移/位右移 | |
8 | < <= | 小于/小于等于 | |
> >= | 大于/大于等于 | ||
9 | == != | 等于/不等于 | |
10 | & | 按位与 | |
11 | ^ | 按位异或 | |
12 | | | 按位或 | |
13 | && | 与运算 | |
14 | || | 或运算 | |
15 | ?: | 三目运算符 | 自右向左 |
16 | = | 赋值 | |
+= −= | 相加后赋值/相减后赋值 | ||
*= /= %= | 相乘后赋值/相除后赋值/取余后赋值 | ||
<<= >>= | 位左移赋值/位右移赋值 | ||
&= ^= |= | 位与运算后赋值/位异或运算后赋值/位或运算后赋值 | ||
17 | throw | 抛出异常 | |
18 | , | 逗号 | 自左向右 |