以下关于Python列表的描述中，错误的是______
答：列表的长度和内容都可以改变，但元素类型必须相同
Which of the following statements is NOT true about the word ‘typical’?
答：It means ‘nice’.
调节酸碱平衡最重要的器官
答：肾
《三国演义》中貂蝉最后的结局是什么?
答：下落不明
人们日常的最主要的表情语是指()。
答：目光和笑态
心流的状态只有顶级优秀的人物才能达成
答：错
心衰B段是指合并基础心血管疾病,如高血压、冠心病和糖尿病,具有发生心衰风险的患者
答：×
某企业计划投资10万元建一条生产线，预计投资后每年可获净利1.5万元，年折旧率为10%，则静态投资回收期为年
答：4
目前认为核被膜破裂是由于：
答：核纤层蛋白去磷酸化
患者女性，21岁，坠楼后额部着地，确诊为颅底骨折。首选治疗措施是
答：保守治疗
优学院: 如果在社会生活中，把一切都看作是必然的，就会导致命运决定一切的( )。
答：唯心主义宿命论
中国大学MOOC: Choose the correct phrases or sentences to complete the sentences. Nature’s recycling system can work well only if people work with the system, ____ against it.
答：rather than
《情书》的导演是____
答：岩井俊二
如果某商品富有需求的价格弹性，则该商品价格上升( )
答：会使该商品销售收益下降
营销渠道管理是企业内部的管理活动
答：×
维新运动及其历史意义和教训？
答：戊戌变法的历史意义\n(1)资产阶级改良运动,符合中国历史发展趋势,具有进步意义.\n(2)爱国救亡运动,激发了人民的爱国思想和民族意识.\n(3)近代中国第一次思想解放的潮流.在社会上起了思想启蒙作用,促进了中国人民的觉醒。\n教训：在当时的中国,改良主义的道路是走不通的,中国近代化的路程是漫长而又坎坷的.
在定值保险中，保险赔款与被保险人的实际损失的关系是
答：保险赔款可能超过实际损失
What is the musical form of Bolero?
答：One movement
通常母乳中含量不足的营养素是
答：铁
风险管理的基础是
答：风险识别
出头教育: In August 1977, a satellite\nto gather data about the 10 million black holes which are thought to be in the Milky Way.
答：was launched

题目描述

在一个二维数组中（每个一维数组的长度相同）
每一行都按照从左到右递增的顺序排序
每一列都按照从上到下递增的顺序排序。

请完成一个函数，输入这样的一个二维数组和一个整数，判断数组中是否含有该整数。
理解

什么是二维数组？

实际上python当中没有数组的概念, 而是列表(List), 二维列表相当于二维数组 。

python中创建二维数组

import numpy as np
array = np.array([[1,2,3],[4,5,6],[7,8,9]])

[[1 2 3]
 [4 5 6]
 [7 8 9]]


数组和矩阵的区别？

python基础–数组和矩阵区别

数组和矩阵区别

解题思路
思路1

直接循环遍历每一个元素，判断是否等于给定的整数，如果相等则输出存在，否则不存在
class Solution:
    # array 二维列表
    def Find(self, target, array):
        for i in range(len(array)):
            for j in range(len(array[0])):
                if array[i][j] == target:
                    return True
        return False

思路2

由于数组元素是分别按行按列递增的，故可以：

从最后一行第一列开始遍历

记给定的整数为target，数组元素为array[i][j]

如果 target < array[i][j] 则行数减1

如果 target > array[i][j] 则列数加1

如果 target == array[i][j] 则返还True

class Solution:
    # array 二维列表
    def Find(self, target, array):
        row = len(array) - 1 
        col = len(array[0]) - 1 
        i = row
        j = 0
        while i >= 0 and j <= col:
            if target < array[i][j]:
                i = i - 1
            elif target > array[i][j]:
                j = j + 1
            else:
                return True

           ziplist和之前我解析过的adlist列表名字看上去的很像，但是作用却完全不同。之前的adlist主要针对的是普通的数据链表操作。而今天的ziplist指的是压缩链表，为什么叫压缩链表呢，因为链表中我们一般常用pre，next来指明当前的结点的前一个指针或当前的结点的下一个指针，这其实是在一定程度上占据了比较多的内存空间，ziplist采用了长度的表示方法，整个ziplist其实是超级长的字符串，通过里面各个结点的长度，上一个结点的长度等信息，通过快速定位实现相关操作，而且编写者，在长度上也做了动态分配字节的方法，表示长度，避免了一定的内存耗费，比如一个结点的字符串长度每个都很短，而你使用好几个字节表示字符串的长度，显然造成大量浪费，所以在长度表示方面，ziplist
 就做到了压缩，也体现了压缩的性能。ziplist 用在什么地方呢，ziplist 就是用在我们平常最常用的一个命令rpush,lpush等这些往链表添加数据的方法，这些数据就是存在ziplist 中的。之后我们会看到相应的实现方法。
     在学习ziplist的开始，一定要理解他的结构，关于这一点，必须花一定时间想想，要不然不太容易明白人家的设计。下面是我的理解，帮助大家理解：
/* The ziplist is a specially encoded dually linked list that is designed
 * to be very memory efficient. It stores both strings and integer values,
 * where integers are encoded as actual integers instead of a series of
 * characters. It allows push and pop operations on either side of the list
 * in O(1) time. However, because every operation requires a reallocation of
 * the memory used by the ziplist, the actual complexity is related to the
 * amount of memory used by the ziplist.
 *
 * ziplist是一个编码后的列表，特殊的设计使得内存操作非常有效率，此列表可以同时存放
 * 字符串和整数类型，列表可以在头尾各边支持推加和弹出操作在O(1)常量时间,但是，因为每次
 * 操作设计到内存的重新分配释放，所以加大了操作的复杂性
 * ----------------------------------------------------------------------------
 *
 * ziplist的结构组成：
 * ZIPLIST OVERALL LAYOUT:
 * The general layout of the ziplist is as follows:
 * <zlbytes><zltail><zllen><entry><entry><zlend>
 *
 * <zlbytes> is an unsigned integer to hold the number of bytes that the
 * ziplist occupies. This value needs to be stored to be able to resize the
 * entire structure without the need to traverse it first.
 * <zipbytes>代表着ziplist占有的字节数，这方便当重新调整大小的时候不需要重新从头遍历
 * 
 * <zltail> is the offset to the last entry in the list. This allows a pop
 * operation on the far side of the list without the need for full traversal.
 * <zltail>记录了最后一个entry的位置在列表中，可以方便快速在列表末尾弹出操作
 *
 * <zllen> is the number of entries.When this value is larger than 2**16-2,
 * we need to traverse the entire list to know how many items it holds.
 * <zllen>记录的是ziplist里面entry数据结点的总数
 *
 * <zlend> is a single byte special value, equal to 255, which indicates the
 * end of the list.
 * <zlend>代表的是结束标识别，用单字节表示，值是255，就是11111111
 *
 * ZIPLIST ENTRIES:
 * Every entry in the ziplist is prefixed by a header that contains two pieces
 * of information. First, the length of the previous entry is stored to be
 * able to traverse the list from back to front. Second, the encoding with an
 * optional string length of the entry itself is stored.
 * 每个entry数据结点主要包含2部分信息，第一个，上一个结点的长度，主要就可以可以从任意结点从后往前遍历整个列表
 * 第二个，编码字符串的方式的类型保存
 *
 * The length of the previous entry is encoded in the following way:
 * If this length is smaller than 254 bytes, it will only consume a single
 * byte that takes the length as value. When the length is greater than or
 * equal to 254, it will consume 5 bytes. The first byte is set to 254 to
 * indicate a larger value is following. The remaining 4 bytes take the
 * length of the previous entry as value.
 * 之前的数据结点的字符串长度的长度少于254个字节，他将消耗单个字节，一个字节8位，最大可表示长度为2的8次方
 * 当字符串的长度大于254个字节，则用5个字节表示，第一个字节被设置成254,其余的4个字节占据的长度为之前的数据结点的长度
 *
 * The other header field of the entry itself depends on the contents of the
 * entry. When the entry is a string, the first 2 bits of this header will hold
 * the type of encoding used to store the length of the string, followed by the
 * actual length of the string. When the entry is an integer the first 2 bits
 * are both set to 1. The following 2 bits are used to specify what kind of
 * integer will be stored after this header. An overview of the different
 * types and encodings is as follows:
 * 头部信息中的另一个值记录着编码的方式，当编码的是字符串，头部的前2位为00,01,10共3种
 * 如果编码的是整型数字的时候，则头部的前2位为11,代表的是整数编码，后面2位代表什么类型整型值将会在头部后面被编码
 * 00-int16_t, 01-int32_t, 10-int64_t, 11-24 bit signed，还有比较特殊的2个，11111110-8 bit signed,
 * 1111 0000 - 1111 1101,代表的是整型值0-12,头尾都已经存在，都不能使用，与传统的通过固定的指针表示长度，这么做的好处实现
 * 可以更合理的分配内存
 *
 * String字符串编码的3种形式
 * |00pppppp| - 1 byte
 *      String value with length less than or equal to 63 bytes (6 bits).
 * |01pppppp|qqqqqqqq| - 2 bytes
 *      String value with length less than or equal to 16383 bytes (14 bits).
 * |10______|qqqqqqqq|rrrrrrrr|ssssssss|tttttttt| - 5 bytes
 *      String value with length greater than or equal to 16384 bytes.
 * |11000000| - 1 byte
 *      Integer encoded as int16_t (2 bytes).
 * |11010000| - 1 byte
 *      Integer encoded as int32_t (4 bytes).
 * |11100000| - 1 byte
 *      Integer encoded as int64_t (8 bytes).
 * |11110000| - 1 byte
 *      Integer encoded as 24 bit signed (3 bytes).
 * |11111110| - 1 byte
 *      Integer encoded as 8 bit signed (1 byte).
 * |1111xxxx| - (with xxxx between 0000 and 1101) immediate 4 bit integer.
 *      Unsigned integer from 0 to 12. The encoded value is actually from
 *      1 to 13 because 0000 and 1111 can not be used, so 1 should be
 *      subtracted from the encoded 4 bit value to obtain the right value.
 * |11111111| - End of ziplist.
 *
 * All the integers are represented in little endian byte order.
 *
 * ----------------------------------------------------------------------------


希望大家能仔细反复阅读，理解作者的设计思路，下面给出的他的实际结构体的定义：
/* 实际存放数据的数据结点 */
typedef struct zlentry {
	//prevrawlen为上一个数据结点的长度，prevrawlensize为记录该长度数值所需要的字节数
    unsigned int prevrawlensize, prevrawlen;
    //len为当前数据结点的长度，lensize表示表示当前长度表示所需的字节数
    unsigned int lensize, len;
    //数据结点的头部信息长度的字节数
    unsigned int headersize;
    //编码的方式
    unsigned char encoding;
    //数据结点的数据(已包含头部等信息)，以字符串形式保存
    unsigned char *p;
} zlentry;
/* <zlentry>的结构图线表示 <pre_node_len>(上一结点的长度信息)<node_encode>(本结点的编码方式和编码数据的长度信息)<node>(本结点的编码数据) */


我们看一下里面比较核心的操作，插入操作，里面涉及指针的各种来回移动，这些都是内存地址的调整：
/* Insert item at "p". */
/* 插入操作的实现 */
static unsigned char *__ziplistInsert(unsigned char *zl, unsigned char *p, unsigned char *s, unsigned int slen) {
    size_t curlen = intrev32ifbe(ZIPLIST_BYTES(zl)), reqlen;
    unsigned int prevlensize, prevlen = 0;
    size_t offset;
    int nextdiff = 0;
    unsigned char encoding = 0;
    long long value = 123456789; /* initialized to avoid warning. Using a value
                                    that is easy to see if for some reason
                                    we use it uninitialized. */
    zlentry tail;

    /* Find out prevlen for the entry that is inserted. */
    //寻找插入的位置
    if (p[0] != ZIP_END) {
    	//定位到指定位置
        ZIP_DECODE_PREVLEN(p, prevlensize, prevlen);
    } else {
    	//如果插入的位置是尾结点，直接定位到尾结点，看第一个字节的就可以判断
        unsigned char *ptail = ZIPLIST_ENTRY_TAIL(zl);
        if (ptail[0] != ZIP_END) {
            prevlen = zipRawEntryLength(ptail);
        }
    }

    /* See if the entry can be encoded */
    if (zipTryEncoding(s,slen,&value,&encoding)) {
        /* 'encoding' is set to the appropriate integer encoding */
        reqlen = zipIntSize(encoding);
    } else {
        /* 'encoding' is untouched, however zipEncodeLength will use the
         * string length to figure out how to encode it. */
        reqlen = slen;
    }
    /* We need space for both the length of the previous entry and
     * the length of the payload. */
    reqlen += zipPrevEncodeLength(NULL,prevlen);
    reqlen += zipEncodeLength(NULL,encoding,slen);

    /* When the insert position is not equal to the tail, we need to
     * make sure that the next entry can hold this entry's length in
     * its prevlen field. */
    nextdiff = (p[0] != ZIP_END) ? zipPrevLenByteDiff(p,reqlen) : 0;

    /* Store offset because a realloc may change the address of zl. */
    //调整大小，为新结点的插入预留空间
    offset = p-zl;
    zl = ziplistResize(zl,curlen+reqlen+nextdiff);
    p = zl+offset;

    /* Apply memory move when necessary and update tail offset. */
    if (p[0] != ZIP_END) {
        /* Subtract one because of the ZIP_END bytes */
        //如果插入的位置不是尾结点，则挪动位置
        memmove(p+reqlen,p-nextdiff,curlen-offset-1+nextdiff);

        /* Encode this entry's raw length in the next entry. */
        zipPrevEncodeLength(p+reqlen,reqlen);

        /* Update offset for tail */
        ZIPLIST_TAIL_OFFSET(zl) =
            intrev32ifbe(intrev32ifbe(ZIPLIST_TAIL_OFFSET(zl))+reqlen);

        /* When the tail contains more than one entry, we need to take
         * "nextdiff" in account as well. Otherwise, a change in the
         * size of prevlen doesn't have an effect on the *tail* offset. */
        tail = zipEntry(p+reqlen);
        if (p[reqlen+tail.headersize+tail.len] != ZIP_END) {
            ZIPLIST_TAIL_OFFSET(zl) =
                intrev32ifbe(intrev32ifbe(ZIPLIST_TAIL_OFFSET(zl))+nextdiff);
        }
    } else {
    	//如果是尾结点，直接设置新尾结点
        /* This element will be the new tail. */
        ZIPLIST_TAIL_OFFSET(zl) = intrev32ifbe(p-zl);
    }

    /* When nextdiff != 0, the raw length of the next entry has changed, so
     * we need to cascade the update throughout the ziplist */
    if (nextdiff != 0) {
        offset = p-zl;
        zl = __ziplistCascadeUpdate(zl,p+reqlen);
        p = zl+offset;
    }

    /* Write the entry */
    //写入新的数据结点信息
    p += zipPrevEncodeLength(p,prevlen);
    p += zipEncodeLength(p,encoding,slen);
    if (ZIP_IS_STR(encoding)) {
        memcpy(p,s,slen);
    } else {
        zipSaveInteger(p,value,encoding);
    }
    
    //更新列表的长度加1
    ZIPLIST_INCR_LENGTH(zl,1);
    return zl;
}


下面是删除操作：
/* Delete "num" entries, starting at "p". Returns pointer to the ziplist. */
/* 删除方法涉及p指针的滑动，后面的地址内容都需要滑动 */
static unsigned char *__ziplistDelete(unsigned char *zl, unsigned char *p, unsigned int num) {
    unsigned int i, totlen, deleted = 0;
    size_t offset;
    int nextdiff = 0;
    zlentry first, tail;

    first = zipEntry(p);
    for (i = 0; p[0] != ZIP_END && i < num; i++) {
        p += zipRawEntryLength(p);
        deleted++;
    }

    totlen = p-first.p;
    if (totlen > 0) {
        if (p[0] != ZIP_END) {
            /* Storing `prevrawlen` in this entry may increase or decrease the
             * number of bytes required compare to the current `prevrawlen`.
             * There always is room to store this, because it was previously
             * stored by an entry that is now being deleted. */
            nextdiff = zipPrevLenByteDiff(p,first.prevrawlen);
            p -= nextdiff;
            zipPrevEncodeLength(p,first.prevrawlen);

            /* Update offset for tail */
            ZIPLIST_TAIL_OFFSET(zl) =
                intrev32ifbe(intrev32ifbe(ZIPLIST_TAIL_OFFSET(zl))-totlen);

            /* When the tail contains more than one entry, we need to take
             * "nextdiff" in account as well. Otherwise, a change in the
             * size of prevlen doesn't have an effect on the *tail* offset. */
            tail = zipEntry(p);
            if (p[tail.headersize+tail.len] != ZIP_END) {
                ZIPLIST_TAIL_OFFSET(zl) =
                   intrev32ifbe(intrev32ifbe(ZIPLIST_TAIL_OFFSET(zl))+nextdiff);
            }

            /* Move tail to the front of the ziplist */
            memmove(first.p,p,
                intrev32ifbe(ZIPLIST_BYTES(zl))-(p-zl)-1);
        } else {
            /* The entire tail was deleted. No need to move memory. */
            ZIPLIST_TAIL_OFFSET(zl) =
                intrev32ifbe((first.p-zl)-first.prevrawlen);
        }

        /* Resize and update length */
        //调整列表大小
        offset = first.p-zl;
        zl = ziplistResize(zl, intrev32ifbe(ZIPLIST_BYTES(zl))-totlen+nextdiff);
        ZIPLIST_INCR_LENGTH(zl,-deleted);
        p = zl+offset;

        /* When nextdiff != 0, the raw length of the next entry has changed, so
         * we need to cascade the update throughout the ziplist */
        if (nextdiff != 0)
            zl = __ziplistCascadeUpdate(zl,p);
    }
    return zl;
}


该方法的意思是从index索引对应的结点开始算起，删除num个结点，这是删除的最原始的方法，其他方法都是对此方法的包装。
下面我们看看我们在redis命令行中输入的lpush或rpush调用的是什么方法呢？调用的形式：
zl = ziplistPush(zl, (unsigned char*)"foo", 3, ZIPLIST_TAIL);
    zl = ziplistPush(zl, (unsigned char*)"quux", 4, ZIPLIST_TAIL);
    zl = ziplistPush(zl, (unsigned char*)"hello", 5, ZIPLIST_HEAD);

/* 在列表2边插入数据的方法 */
unsigned char *ziplistPush(unsigned char *zl, unsigned char *s, unsigned int slen, int where) {
    unsigned char *p;
    //这里开始直接定位
    p = (where == ZIPLIST_HEAD) ? ZIPLIST_ENTRY_HEAD(zl) : ZIPLIST_ENTRY_END(zl);
    //组后调用插入数据的insert方法
    return __ziplistInsert(zl,p,s,slen);
}


到最后还是调用了insert方法。在写之前看了一些别人分析的ziplist分析，感觉有些说的的都很粗略，还是自己仔细过一遍心里会清楚很多，建议大家多多阅读源码。每个人侧重点都是不一样的。最后给出头文件和比较关键的宏定义：
/* zip列表的末尾值 */
#define ZIP_END 255
/* zip列表的最大长度 */
#define ZIP_BIGLEN 254

/* Different encoding/length possibilities */
/* 不同的编码 */
#define ZIP_STR_MASK 0xc0
#define ZIP_INT_MASK 0x30
#define ZIP_STR_06B (0 << 6)
#define ZIP_STR_14B (1 << 6)
#define ZIP_STR_32B (2 << 6)
#define ZIP_INT_16B (0xc0 | 0<<4)
#define ZIP_INT_32B (0xc0 | 1<<4)
#define ZIP_INT_64B (0xc0 | 2<<4)
#define ZIP_INT_24B (0xc0 | 3<<4)
#define ZIP_INT_8B 0xfe

/* 4 bit integer immediate encoding */
#define ZIP_INT_IMM_MASK 0x0f    //后续的好多运算都需要与掩码进行位运算
#define ZIP_INT_IMM_MIN 0xf1    /* 11110001 */
#define ZIP_INT_IMM_MAX 0xfd    /* 11111101 */   //最大值不能为11111111，这跟最末尾的结点重复了
#define ZIP_INT_IMM_VAL(v) (v & ZIP_INT_IMM_MASK)

#define INT24_MAX 0x7fffff
#define INT24_MIN (-INT24_MAX - 1)

/* Macro to determine type */
#define ZIP_IS_STR(enc) (((enc) & ZIP_STR_MASK) < ZIP_STR_MASK)

/* Utility macros */
/* 下面是一些用来到时能够直接定位的数值偏移量 */
#define ZIPLIST_BYTES(zl)       (*((uint32_t*)(zl)))
#define ZIPLIST_TAIL_OFFSET(zl) (*((uint32_t*)((zl)+sizeof(uint32_t))))
#define ZIPLIST_LENGTH(zl)      (*((uint16_t*)((zl)+sizeof(uint32_t)*2)))
#define ZIPLIST_HEADER_SIZE     (sizeof(uint32_t)*2+sizeof(uint16_t))
#define ZIPLIST_ENTRY_HEAD(zl)  ((zl)+ZIPLIST_HEADER_SIZE)
#define ZIPLIST_ENTRY_TAIL(zl)  ((zl)+intrev32ifbe(ZIPLIST_TAIL_OFFSET(zl)))
#define ZIPLIST_ENTRY_END(zl)   ((zl)+intrev32ifbe(ZIPLIST_BYTES(zl))-1)
.h文件：
/*
 * Copyright (c) 2009-2012, Pieter Noordhuis <pcnoordhuis at gmail dot com>
 * Copyright (c) 2009-2012, Salvatore Sanfilippo <antirez at gmail dot com>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *
 *   * Redistributions of source code must retain the above copyright notice,
 *     this list of conditions and the following disclaimer.
 *   * Redistributions in binary form must reproduce the above copyright
 *     notice, this list of conditions and the following disclaimer in the
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/* 标记列表头节点和尾结点的标识 */
#define ZIPLIST_HEAD 0
#define ZIPLIST_TAIL 1

unsigned char *ziplistNew(void);    //创建新列表
unsigned char *ziplistPush(unsigned char *zl, unsigned char *s, unsigned int slen, int where);  //像列表中推入数据
unsigned char *ziplistIndex(unsigned char *zl, int index);   //索引定位到列表的某个位置
unsigned char *ziplistNext(unsigned char *zl, unsigned char *p);   //获取当前列表位置的下一个值
unsigned char *ziplistPrev(unsigned char *zl, unsigned char *p);   //获取当期列表位置的前一个值
unsigned int ziplistGet(unsigned char *p, unsigned char **sval, unsigned int *slen, long long *lval);   //获取列表的信息
unsigned char *ziplistInsert(unsigned char *zl, unsigned char *p, unsigned char *s, unsigned int slen); //向列表中插入数据
unsigned char *ziplistDelete(unsigned char *zl, unsigned char **p); //列表中删除某个结点
unsigned char *ziplistDeleteRange(unsigned char *zl, unsigned int index, unsigned int num);   //从index索引对应的结点开始算起，删除num个结点
unsigned int ziplistCompare(unsigned char *p, unsigned char *s, unsigned int slen);   //列表间的比较方法
unsigned char *ziplistFind(unsigned char *p, unsigned char *vstr, unsigned int vlen, unsigned int skip); //在列表中寻找某个结点
unsigned int ziplistLen(unsigned char *zl);   //返回列表的长度
size_t ziplistBlobLen(unsigned char *zl);   //返回列表的二进制长度，返回的是字节数

01-向量究竟是什么？

物理观点


向量是空间中的一个有向箭头
决定这个向量的是它的长度和所指的方向
因为长度+方向唯一地确定一个向量，因此物理学的观点中描述的向量是自由向量，可以自由平移一个向量且保持该向量不变。


CS观点


向量是有序的数字列表
在实际问题中我们往往会使用一串数字对问题进行描述和建模，且数字之间是严格有序的
向量其实就是列表的另一种表达，且向量的维度就是列表的长度


数学家观点


向量可以是任何事物，只要两个被定义为向量的事物的加法与数乘运算有意义。


线性代数对向量的抽象


每次讲述到向量及其相关概念时，先预想一个在坐标系中经过原点的带箭头的线段
有序列表——设想一个坐标系，原点则是所有向量的凝聚的核心，向量坐标就是有序列表，它是用来指导如何从原点到达箭头所在坐标点


向量的加法运算



向量加法运算——“首尾相接，首尾连”这是在线性代数中唯一出现的可以让向量离开原点的情形。

理解：把每个向量都看做是一种特定的运动，即在空间中朝着某个方向迈出一定距离

某一个点先沿着向量1运动，之后再沿着向量2运动，其效果和该点从初始位置沿着向量1与2的和运动没有差异。





向量的数乘运算


向量的数乘运算就相当于对向量进行放缩

运算方式即对每一个分量分别乘上缩放系数



视频：https://www.bilibili.com/video/BV1ys411472E?p=2