IBM社会招聘笔试题
- 一个粗细均匀的长直管子，两端开口，里面有4个白球和4个黑球，球的直径、两端开口的直径等于管子的内径，现在白球和黑球的排列是wwwwbbbb，要求不取出任何一个球，使得排列变为bbwwwwbb。
把管子两端接起来形成一个通环，将黑球从接口挤过去两个 - 一只蜗牛从井底爬到井口，每天白天蜗牛要睡觉，晚上才出来活动，一个晚上蜗牛可以向上爬3尺，但是白天睡觉的时候会往下滑2尺，井深10尺，问蜗牛几天可以爬出来？ 8
- 在一个平面上画1999条直线最多能将这一平面划分成多少个部分？
1999001 - 在太平洋的一个小岛上生活着土人，他们不愿意被外人打扰，一天，一个探险家到了岛上，被土人抓住，土人的祭司告诉他，你临死前还可以有一个机会留下一句话，如果这句话是真的，你将被烧死，是假的，你将被五马分尸，可怜的探险家如何才能活下来？
我将被五马分尸 - 怎样种四棵树使得任意两棵树的距离相等。
种山上，等边三角锥 - 27个小运动员在参加完比赛后，口渴难耐，去小店买饮料，饮料店搞促销，凭三个空瓶可以再换一瓶，他们最少买多少瓶饮料才能保证一人一瓶？
19 - 有一座山，山上有座庙，只有一条路可以从山上的庙到山脚，每周一早上8点，有一个聪明的小和尚去山下化缘，周二早上8点从山脚回山上的庙里，小和尚的上下山的速度是任意的，在每个往返中，他总是能在周一和周二的同一钟点到达山路上的同一点。例如，有一次他发现星期一的8点30和星期二的8点30他都到了山路靠山脚的3/4的地方，问这是为什么？
那时肯定的，因为上下山只有一条路 - 有两根不均匀分布的香，每根香烧完的时间是一个小时，你能用什么方法来确定一段15分钟的时间？
把第一根一头点着，同时把第二根两头都点着，在第二根燃尽的同时点燃第一根的另一头，这时开始计时，至第一根燃尽就是十五分钟
IBM面试题目
Describe your greatest achievement in the past 4-5 years?
What are your short & long term career objectives? What do you think is the most ideal job for you?
Why do you want to join IBM? What do you think you can contribute to IBM?
Google 中国笔试题目
1．1关于IP协议那个正确
A IP是TCP上层协议B IP协议是应用层协议C由于两个属于同一层协议，他们之间可以直接通信DIP协议不提供可靠的通信
1.2 关于内存正确的是
A内存的存取速度不能低于cpu速度，否则会造成数据丢失
B程序只有在数据和代码等被调入内存后才能运行
C采用虚拟内存技术后程序可以在硬盘上直接运行
D某计算机的内存容量为16MB，那么他的地址总线为24位
1.3单链表中结点的结构为（data，link），若想删除结点p（不是头节点或者尾结点）的直接后继，则应执行下列哪个操作
A p=p->link ; p->link=p->link->linkB p->link->link=p->link;C p=p->link->link Dp->link=p->link->link
1.4已知x>=y and y>=z 为真，那么x>z or y=z 值为
A真B假C无法确定Dx y z同为正数时为真
1.5某请求被随即分配到四台机器进行处理，分配到每台机器的概率A15% B20% C 30% D 35%, 处理请求的失败概率分别为5% ，4%， 3% 2%，现在请求失败，问由C造成的概率最接近A26% B28% C 30% D 32%
1.6假设我们用d=(a1,a2,….a5)表示无向无环图G的5个顶点的度数，下面给出的哪组值是可能的
A{3,4,4,3,1}B{4,2,2,1,1}C{3,3,3,2,2}D{3,4,3,2,1}
1.7设栈S和队列Q的初始状态为空，元素e1，e2，e3，e4，e5，e6一次压入栈S,一个元素出栈后即进入队列Q，若出队列的顺序为e2,e4,e3,e6,e5,e1则栈S的容量要求最小值为
A2B3C4D5
1.8 在堆排序算法中我们用一个数组A来模拟二叉树T，如果该A[0]存放的是T的根节点，那么AK的父亲节点是
A (K-1)/2 B K/2 C(K+1)/2 D 都不对 ( via: unus.cn )
1.9 现有如下任务需要安排在若干机器上并行完成，每个任务都有开始时间和结束时间（开始和结束时间都包括在任务执行时间内）的要求
任务名称 开始时间 结束时间
a 1 7
b 8 9
c 2 5
d 7 11
e 3 6
f 7 9
g 10 13
则最少需要使用的机器数目为
A1B2C3D4
1.10 在设计一个操作系统时，哪项不是必须考虑的
A 设备管理模块B文件系统模块C用户管理模块D进程管理模块
2.1正整数序列Q中的每个元素都至少能被正整数a和b中的一个整除，现给定a和b，需要计算出Q中的前几项，例如，当a=3，b=5，N=6时，序列为3，5，6，9，10，12
（1）设计一个函数void generate（int a,int b,int N ,int * Q）计算Q的前几项
（2）设计测试数据来验证函数程序在各种输入下的正确性
2.2 有一个由大小写组成的字符串，现在需要对他进行修改，将其中的所有小写字母排在答谢字母的前面（大写或小写字母之间不要求保持原来次序），如有可能尽量选择时间和空间效率高的算法 c语言函数原型void proc（char *str） 也可以采用你自己熟悉的语言
2.3 已知一颗无向无环连通图T的所有顶点和边的信息，现需要将其转换为一棵树，要求树的深度最小，请设计一个算法找到所有满足要求的树的根结点，并分析时空复杂度（描述算法即可，无需代码）
1．1关于IP协议那个正确
A IP是TCP上层协议B IP协议是应用层协议C由于两个属于同一层协议，他们之间可以直接通信DIP协议不提供可靠的通信
1.2 关于内存正确的是
A内存的存取速度不能低于cpu速度，否则会造成数据丢失
B程序只有在数据和代码等被调入内存后才能运行
C采用虚拟内存技术后程序可以在硬盘上直接运行
D某计算机的内存容量为16MB，那么他的地址总线为24位
1.3单链表中结点的结构为（data，link），若想删除结点p（不是头节点或者尾结点）的直接后继，则应执行下列哪个操作
A p=p->link ; p->link=p->link->linkB p->link->link=p->link;C p=p->link->link Dp->link=p->link->link
1.4已知x>=y and y>=z 为真，那么x>z or y=z 值为
A真B假C无法确定Dx y z同为正数时为真
1.5某请求被随即分配到四台机器进行处理，分配到每台机器的概率A15% B20% C 30% D 35%, 处理请求的失败概率分别为5% ，4%， 3% 2%，现在请求失败，问由C造成的概率最接近A26% B28% C 30% D 32%
1.6假设我们用d=(a1,a2,….a5)表示无向无环图G的5个顶点的度数，下面给出的哪组值是可能的
A{3,4,4,3,1}B{4,2,2,1,1}C{3,3,3,2,2}D{3,4,3,2,1}
1.7设栈S和队列Q的初始状态为空，元素e1，e2，e3，e4，e5，e6一次压入栈S,一个元素出栈后即进入队列Q，若出队列的顺序为e2,e4,e3,e6,e5,e1则栈S的容量要求最小值为
A2B3C4D5
1.8 在堆排序算法中我们用一个数组A来模拟二叉树T，如果该A[0]存放的是T的根节点，那么AK的父亲节点是
A (K-1)/2 B K/2 C(K+1)/2 D 都不对 ( via: unus.cn )
1.9 现有如下任务需要安排在若干机器上并行完成，每个任务都有开始时间和结束时间（开始和结束时间都包括在任务执行时间内）的要求
任务名称 开始时间 结束时间
a 1 7
b 8 9
c 2 5
d 7 11
e 3 6
f 7 9
g 10 13
则最少需要使用的机器数目为
A1B2C3D4
1.10 在设计一个操作系统时，哪项不是必须考虑的
A 设备管理模块B文件系统模块C用户管理模块D进程管理模块
2.1正整数序列Q中的每个元素都至少能被正整数a和b中的一个整除，现给定a和b，需要计算出Q中的前几项，例如，当a=3，b=5，N=6时，序列为3，5，6，9，10，12
（1）设计一个函数void generate（int a,int b,int N ,int * Q）计算Q的前几项
（2）设计测试数据来验证函数程序在各种输入下的正确性
2.2 有一个由大小写组成的字符串，现在需要对他进行修改，将其中的所有小写字母排在答谢字母的前面（大写或小写字母之间不要求保持原来次序），如有可能尽量选择时间和空间效率高的算法 c语言函数原型void proc（char *str） 也可以采用你自己熟悉的语言
2.3 已知一颗无向无环连通图T的所有顶点和边的信息，现需要将其转换为一棵树，要求树的深度最小，请设计一个算法找到所有满足要求的树的根结点，并分析时空复杂度（描述算法即可，无需代码）
intel的笔试题
智力题
1．每天中午从法国塞纳河畔的勒阿佛有一艘轮船驶往美国纽约，在同一时刻纽约也有一艘轮船驶往勒阿佛。已知横渡一次的时间是7天7夜，轮船匀速航行，在同一航线，轮船近距离可见。
请问今天中午从勒阿佛开出的船会遇到几艘从纽约来的船？
2．巴拿赫病故于1945年8月31日。他的出生年份恰好是他在世时某年年龄的平方，问：他是哪年出生的？
答案：
设他在世时某年年龄为x，则x的平方<1945，且x为自然数。其出生年份x的平方-x=x（x-1），他在世年龄1945-x（x-1）。1945的平方根=44.1，则x应为44或略小于此的数。而x=44时，x（x-1）=44×43=1892，算得其在世年龄为1945-1892=53；又x=43时，x（x-1）=43×42=1806，得其在世年龄为1945-1806=139；若x再取小，其在世年龄越大，显然不妥。故x=44，即他出生于1892年，终年53岁。
笔试题目
1．设计一个重采样系统，说明如何anti-alias。
2．y1（n）=x（2n），y2（n）=x（n/2），问：
如果y1为周期函数，那么x是否为周期函数？
如果x为周期函数，那么y1是否为周期函数？
如果y2为周期函数，那么x是否为周期函数？
如果x为周期函数，那么y2是否为周期函数？
3．如果模拟信号的带宽为5kHz，要用8k的采样率，怎么办。
4．某个程序在一个嵌入式系统（200M的CPU，50M的SDRAM）中已经最优化了，换到另一个系统（300M的CPU，50M的SDRAM）中运行，还需要优化吗？
5．x^4+ax^3+x^2+cx+d最少需要做几次乘法。
6．三个float:a,b,c
问值：
（a+b）+c==（b+a）+c
（a+b）+c==（a+c）+b
7．把一个链表反向填空。
8．下面哪种排序法对12354最快？
A. quick sort
B. buble sort
C. merge sort
9．哪种结构平均来讲获取一个值最快？
A. binary tree
B. hash table
C. stack
10．
#include
“stdafx.h”
#include <iostream.h>
struct bit
{ int a:3;
int b:2;
int c:3;
};
int main(int argc, char* argv[])
{
bit s;
char c = (char)&s;
*c = 0x99;
cout <<
s.a <<endl <<s.b<<endl<<s.c<<endl;
return 0;
}
Output:?
11．
挑bug，在linux下运行：
#include <stdio.h>
char
reverse(char str)
{
int len=0, i=0;
char pstr=str, ptemp,pd;
while(++pstr)
len++;
pstr–;
//ptemp=(char)malloc(len+1);
ptemp=(char)malloc(len+1);
pd=ptemp;
while(len–){
*ptemp=*pstr;
ptemp++;
pstr–;
i++;
}
*ptemp=*pstr;
ptemp++;
*ptemp=‘\0’;
return pd;
}
main()
{
char string[40]= “Hello World!”;
char *pstr=string;
printf(“％s”, pstr);
printf(“％s”, reverse(pstr));
}
实验室笔试题
1．写出下列信号的奈亏斯特频率
（1）f（t）=1+cos（2000pait）+sin（4000pait）
（2）f（t）=sin（4000pait）/pait
（3）f（t）=（sin（4000pait）的平方）/pait
2．有两个线程
void producer()
{
while(1)
{
GeneratePacket();
PutPacketIntoBuffer();
Signal(customer);
}
}
void customer()
{
while(1)
{
WaitForSignal();
if(PacketInBuffer>10)
{
ReadAllPackets();
ProcessPackets();
}
}
}
（1）有没有其他方法可以提高程序的性能
（2）可不可以不使用信号之类的机制来实现上述的功能
3．优化下面的程序
（0）sum=0
（1）I=1
（2）T1=4I
（3）T2=address(A)-4
（4）T3=T2[T1]
（5）T4=address(B)-4
（6）T5=4I
（7）T6=T4[T5]
（8）T7=T3*T5
（9）sum=sum+T6
（10）I=I+1
（11）IF I<20 GOTO (2)
101道微软IT笔试题
Algorithms and Programming
- Given a rectangular (cuboidal for the puritans) cake with a rectangular piece removed (any size or orientation), how would you cut the remainder of the cake into two equal halves with one straight cut of a knife ?
- You’re given an array containing both positive and negative integers and required to find the sub-array with the largest sum (O(N) a la KBL). Write a routine in C for the above.
- Given an array of size N in which every number is between 1 and N, determine if there are any duplicates in it. You are allowed to destroy the array if you like. [ I ended up giving about 4 or 5 different solutions for this, each supposedly better than the others ].
- Write a routine to draw a circle (x ** 2 + y ** 2 = r ** 2) without making use of any floating point computations at all. [ This one had me stuck for quite some time and I first gave a solution that did have floating point computations ].
- Given only putchar (no sprintf, itoa, etc.) write a routine putlong that prints out an unsigned long in decimal. [ I gave the obvious solution of taking % 10 and / 10, which gives us the decimal value in reverse order. This requires an array since we need to print it out in the correct order. The interviewer wasn’t too pleased and asked me to give a solution which didn’t need the array ].
- Give a one-line C expression to test whether a number is a power of 2. [No loops allowed - it’s a simple test.]
- Given an array of characters which form a sentence of words, give an efficient algorithm to reverse the order of the words (not characters) in it.
- How many points are there on the globe where by walking one mile south, one mile east and one mile north you reach the place where you started.
- Give a very good method to count the number of ones in a “n” (e.g. 32) bit number.
ANS. Given below are simple solutions, find a solution that does it in log (n) steps.
Iterative
function iterativecount (unsigned int n)
begin
int count=0;
while (n)
begin
count += n & 0×1 ;
n >>= 1;
end
return count;
end
Sparse Count
function sparsecount (unsigned int n)
begin
int count=0;
while (n)
begin
count++;
n &= (n-1);
end
return count ;
end - What are the different ways to implement a condition where the value of x can be either a 0 or a 1. Apparently the if then else solution has a jump when written out in assembly. if (x == 0) y=a else y=b There is a logical, arithmetic and a data structure solution to the above problem.
- Reverse a linked list.
- Insert in a sorted list
- In a X’s and 0’s game (i.e. TIC TAC TOE) if you write a program for this give a fast way to generate the moves by the computer. I mean this should be the fastest way possible.
The answer is that you need to store all possible configurations of the board and the move that is associated with that. Then it boils down to just accessing the right element and getting the corresponding move for it. Do some analysis and do some more optimization in storage since otherwise it becomes infeasible to get the required storage in a DOS machine. - I was given two lines of assembly code which found the absolute value of a number stored in two’s complement form. I had to recognize what the code was doing. Pretty simple if you know some assembly and some fundaes on number representation.
- Give a fast way to multiply a number by 7.
- How would go about finding out where to find a book in a library. (You don’t know how exactly the books are organized beforehand).
- Linked list manipulation.
- Tradeoff between time spent in testing a product and getting into the market first.
- What to test for given that there isn’t enough time to test everything you want to.
- First some definitions for this problem: a) An ASCII character is one byte long and the most significant bit in the byte is always ‘0′. b) A Kanji character is two bytes long. The only characteristic of a Kanji character is that in its first byte the most significant bit is ‘1′.
Now you are given an array of a characters (both ASCII and Kanji) and, an index into the array. The index points to the start of some character. Now you need to write a function to do a backspace (i.e. delete the character before the given index). - Delete an element from a doubly linked list.
- Write a function to find the depth of a binary tree.
- Given two strings S1 and S2. Delete from S2 all those characters which occur in S1 also and finally create a clean S2 with the relevant characters deleted.
- Assuming that locks are the only reason due to which deadlocks can occur in a system. What would be a foolproof method of avoiding deadlocks in the system.
- Reverse a linked list.
Ans: Possible answers -
iterative loop
curr->next = prev;
prev = curr;
curr = next;
next = curr->next
endloop
recursive reverse(ptr)
if (ptr->next == NULL)
return ptr;
temp = reverse(ptr->next);
temp->next = ptr;
return ptr;
end - Write a small lexical analyzer - interviewer gave tokens. expressions like “a*b” etc.
- Besides communication cost, what is the other source of inefficiency in RPC? (answer : context switches, excessive buffer copying). How can you optimize the communication? (ans : communicate through shared memory on same machine, bypassing the kernel _ A Univ. of Wash. thesis)
- Write a routine that prints out a 2-D array in spiral order!
- How is the readers-writers problem solved? - using semaphores/ada .. etc.
- Ways of optimizing symbol table storage in compilers.
- A walk-through through the symbol table functions, lookup() implementation etc. - The interviewer was on the Microsoft C team.
- A version of the “There are three persons X Y Z, one of which always lies”.. etc..
- There are 3 ants at 3 corners of a triangle, they randomly start moving towards another corner.. what is the probability that they don’t collide.
- Write an efficient algorithm and C code to shuffle a pack of cards.. this one was a feedback process until we came up with one with no extra storage.
- The if (x == 0) y = 0 etc..
- Some more bitwise optimization at assembly level
- Some general questions on Lex, Yacc etc.
- Given an array t[100] which contains numbers between 1..99. Return the duplicated value. Try both O(n) and O(n-square).
- Given an array of characters. How would you reverse it. ? How would you reverse it without using indexing in the array.
- Given a sequence of characters. How will you convert the lower case characters to upper case characters. ( Try using bit vector - solutions given in the C lib -typec.h)
- Fundamentals of RPC.
- Given a linked list which is sorted. How will u insert in sorted way.
- Given a linked list How will you reverse it.
- Give a good data structure for having n queues ( n not fixed) in a finite memory segment. You can have some data-structure separate for each queue. Try to use at least 90% of the memory space.
- Do a breadth first traversal of a tree.
- Write code for reversing a linked list.
- Write, efficient code for extracting unique elements from a sorted list of array. e.g. (1, 1, 3, 3, 3, 5, 5, 5, 9, 9, 9, 9) -> (1, 3, 5, 9).
- Given an array of integers, find the contiguous sub-array with the largest sum.
ANS. Can be done in O(n) time and O(1) extra space. Scan array from 1 to n. Remember the best sub-array seen so far and the best sub-array ending in i. - Given an array of length N containing integers between 1 and N, determine if it contains any duplicates.
ANS. [Is there an O(n) time solution that uses only O(1) extra space and does not destroy the original array?] - Sort an array of size n containing integers between 1 and K, given a temporary scratch integer array of size K.
ANS. Compute cumulative counts of integers in the auxiliary array. Now scan the original array, rotating cycles! [Can someone word this more nicely?]
* 51. An array of size k contains integers between 1 and n. You are given an additional scratch array of size n. Compress the original array by removing duplicates in it. What if k << n?
ANS. Can be done in O(k) time i.e. without initializing the auxiliary array! - An array of integers. The sum of the array is known not to overflow an integer. Compute the sum. What if we know that integers are in 2’s complement form?
ANS. If numbers are in 2’s complement, an ordinary looking loop like for(i=total=0;i< n;total+=array[i++]); will do. No need to check for overflows! - An array of characters. Reverse the order of words in it.
ANS. Write a routine to reverse a character array. Now call it for the given array and for each word in it.
* 54. An array of integers of size n. Generate a random permutation of the array, given a function rand_n() that returns an integer between 1 and n, both inclusive, with equal probability. What is the expected time of your algorithm?
ANS. “Expected time” should ring a bell. To compute a random permutation, use the standard algorithm of scanning array from n downto 1, swapping i-th element with a uniformly random element <= i-th. To compute a uniformly random integer between 1 and k (k < n), call rand_n() repeatedly until it returns a value in the desired range. - An array of pointers to (very long) strings. Find pointers to the (lexicographically) smallest and largest strings.
ANS. Scan array in pairs. Remember largest-so-far and smallest-so-far. Compare the larger of the two strings in the current pair with largest-so-far to update it. And the smaller of the current pair with the smallest-so-far to update it. For a total of <= 3n/2 strcmp() calls. That’s also the lower bound. - Write a program to remove duplicates from a sorted array.
ANS. int remove_duplicates(int * p, int size)
{
int current, insert = 1;
for (current=1; current < size; current++)
if (p[current] != p[insert-1])
{
p[insert] = p[current];
current++;
insert++;
} else
current++;
return insert;
} - C++ ( what is virtual function ? what happens if an error occurs in constructor or destructor. Discussion on error handling, templates, unique features of C++. What is different in C++, ( compare with unix).
- Given a list of numbers ( fixed list) Now given any other list, how can you efficiently find out if there is any element in the second list that is an element of the first list (fixed list).
- Given 3 lines of assembly code : find it is doing. IT was to find absolute value.
- If you are on a boat and you throw out a suitcase, Will the level of water increase.
- Print an integer using only putchar. Try doing it without using extra storage.
- Write C code for (a) deleting an element from a linked list (b) traversing a linked list
- What are various problems unique to distributed databases
- Declare a void pointer ANS. void *ptr;
- Make the pointer aligned to a 4 byte boundary in a efficient manner ANS. Assign the pointer to a long number and the number with 11…1100 add 4 to the number
- What is a far pointer (in DOS)
- What is a balanced tree
- Given a linked list with the following property node2 is left child of node1, if node2 < node1 else, it is the right child.
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How do you convert the above linked list to the form without disturbing the property. Write C code for that.
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determine where do A and C go - Describe the file system layout in the UNIX OS
ANS. describe boot block, super block, inodes and data layout - In UNIX, are the files allocated contiguous blocks of data
ANS. no, they might be fragmented
How is the fragmented data kept track of
ANS. Describe the direct blocks and indirect blocks in UNIX file system - Write an efficient C code for ‘tr’ program. ‘tr’ has two command line arguments. They both are strings of same length. tr reads an input file, replaces each character in the first string with the corresponding character in the second string. eg. ‘tr abc xyz’ replaces all ‘a’s by ‘x’s, ‘b’s by ‘y’s and so on. ANS.
a) have an array of length 26.
put ‘x’ in array element corr to ‘a’
put ‘y’ in array element corr to ‘b’
put ‘z’ in array element corr to ‘c’
put ‘d’ in array element corr to ‘d’
put ‘e’ in array element corr to ‘e’
and so on.
the code
while (!eof)
{
c = getc();
putc(array[c - ‘a’]);
} - what is disk interleaving
- why is disk interleaving adopted
- given a new disk, how do you determine which interleaving is the best a) give 1000 read operations with each kind of interleaving determine the best interleaving from the statistics
- draw the graph with performance on one axis and ‘n’ on another, where ‘n’ in the ‘n’ in n-way disk interleaving. (a tricky question, should be answered carefully)
- I was a c++ code and was asked to find out the bug in that. The bug was that he declared an object locally in a function and tried to return the pointer to that object. Since the object is local to the function, it no more exists after returning from the function. The pointer, therefore, is invalid outside.
- A real life problem - A square picture is cut into 16 squares and they are shuffled. Write a program to rearrange the 16 squares to get the original big square.
- int *a;
char *c;
*(a) = 20;
*c = *a;
printf(”%c”,*c);
what is the output? - Write a program to find whether a given m/c is big-endian or little-endian!
- What is a volatile variable?
- What is the scope of a static function in C ?
- What is the difference between “malloc” and “calloc”?
- struct n { int data; struct n* next}node;
node *c,*t;
c->data = 10;
t->next = null;
*c = *t;
what is the effect of the last statement? - If you’re familiar with the ? operator x ? y : z
you want to implement that in a function: int cond(int x, int y, int z); using only ~, !, ^, &, +, |, <<, >> no if statements, or loops or anything else, just those operators, and the function should correctly return y or z based on the value of x. You may use constants, but only 8 bit constants. You can cast all you want. You’re not supposed to use extra variables, but in the end, it won’t really matter, using vars just makes things cleaner. You should be able to reduce your solution to a single line in the end though that requires no extra vars. - You have an abstract computer, so just forget everything you know about computers, this one only does what I’m about to tell you it does. You can use as many variables as you need, there are no negative numbers, all numbers are integers. You do not know the size of the integers, they could be infinitely large, so you can’t count on truncating at any point. There are NO comparisons allowed, no if statements or anything like that. There are only four operations you can do on a variable.
- You can set a variable to 0.
- You can set a variable = another variable.
- You can increment a variable (only by 1), and it’s a post increment.
- You can loop. So, if you were to say loop(v1) and v1 = 10, your loop would execute 10 times, but the value in v1 wouldn’t change so the first line in the loop can change value of v1 without changing the number of times you loop.
You need to do 3 things. - Write a function that decrements by 1.
- Write a function that subtracts one variable from another.
- Write a function that divides one variable by another.
- See if you can implement all 3 using at most 4 variables. Meaning, you’re not making function calls now, you’re making macros. And at most you can have 4 variables. The restriction really only applies to divide, the other 2 are easy to do with 4 vars or less. Division on the other hand is dependent on the other 2 functions, so, if subtract requires 3 variables, then divide only has 1 variable left unchanged after a call to subtract. Basically, just make your function calls to decrement and subtract so you pass your vars in by reference, and you can’t declare any new variables in a function, what you pass in is all it gets.
Linked lists
* 86. Under what circumstances can one delete an element from a singly linked list in constant time?
ANS. If the list is circular and there are no references to the nodes in the list from anywhere else! Just copy the contents of the next node and delete the next node. If the list is not circular, we can delete any but the last node using this idea. In that case, mark the last node as dummy!
* 87. Given a singly linked list, determine whether it contains a loop or not.
ANS. (a) Start reversing the list. If you reach the head, gotcha! there is a loop!
But this changes the list. So, reverse the list again.
(b) Maintain two pointers, initially pointing to the head. Advance one of them one node at a time. And the other one, two nodes at a time. If the latter overtakes the former at any time, there is a loop!
p1 = p2 = head;
do {
p1 = p1->next;
p2 = p2->next->next;
} while (p1 != p2);
- Given a singly linked list, print out its contents in reverse order. Can you do it without using any extra space?
ANS. Start reversing the list. Do this again, printing the contents. - Given a binary tree with nodes, print out the values in pre-order/in-order/post-order without using any extra space.
- Reverse a singly linked list recursively. The function prototype is node * reverse (node *) ;
ANS.
node * reverse (node * n)
{
node * m ;
if (! (n && n -> next))
return n ;
m = reverse (n -> next) ;
n -> next -> next = n ;
n -> next = NULL ;
return m ;
} - Given a singly linked list, find the middle of the list.
HINT. Use the single and double pointer jumping. Maintain two pointers, initially pointing to the head. Advance one of them one node at a time. And the other one, two nodes at a time. When the double reaches the end, the single is in the middle. This is not asymptotically faster but seems to take less steps than going through the list twice.
Bit-manipulation - Reverse the bits of an unsigned integer.
ANS.
#define reverse(x)
(x=x>>16|(0×0000ffff&x)<<16,
x=(0xff00ff00&x)>>8|(0×00ff00ff&x)<<8,
x=(0xf0f0f0f0&x)>>4|(0×0f0f0f0f&x)<<4,
x=(0xcccccccc&x)>>2|(0×33333333&x)<<2,
x=(0xaaaaaaaa&x)>>1|(0×55555555&x)<<1)
* 93. Compute the number of ones in an unsigned integer.
ANS.
#define count_ones(x)
(x=(0xaaaaaaaa&x)>>1+(0×55555555&x),
x=(0xcccccccc&x)>>2+(0×33333333&x),
x=(0xf0f0f0f0&x)>>4+(0×0f0f0f0f&x),
x=(0xff00ff00&x)>>8+(0×00ff00ff&x),
x=x>>16+(0×0000ffff&x)) - Compute the discrete log of an unsigned integer.
ANS.
#define discrete_log(h)
(h=(h>>1)|(h>>2),
h|=(h>>2),
h|=(h>>4),
h|=(h>>8),
h|=(h>>16),
h=(0xaaaaaaaa&h)>>1+(0×55555555&h),
h=(0xcccccccc&h)>>2+(0×33333333&h),
h=(0xf0f0f0f0&h)>>4+(0×0f0f0f0f&h),
h=(0xff00ff00&h)>>8+(0×00ff00ff&h),
h=(h>>16)+(0×0000ffff&h))
If I understand it right, log2(2) =1, log2(3)=1, log2(4)=2….. But this macro does not work out log2(0) which does not exist! How do you think it should be handled?
* 95. How do we test most simply if an unsigned integer is a power of two?
ANS. #define power_of_two(x) \ ((x)&&(~(x&(x-1)))) - Set the highest significant bit of an unsigned integer to zero.
ANS. (from Denis Zabavchik) Set the highest significant bit of an unsigned integer to zero
#define zero_most_significant(h)
(h&=(h>>1)|(h>>2),
h|=(h>>2),
h|=(h>>4),
h|=(h>>8),
h|=(h>>16)) - Let f(k) = y where k is the y-th number in the increasing sequence of non-negative integers with the same number of ones in its binary representation as y, e.g. f(0) = 1, f(1) = 1, f(2) = 2, f(3) = 1, f(4) = 3, f(5) = 2, f(6) = 3 and so on. Given k >= 0, compute f(k).
Others - A character set has 1 and 2 byte characters. One byte characters have 0 as the first bit. You just keep accumulating the characters in a buffer. Suppose at some point the user types a backspace, how can you remove the character efficiently. (Note: You cant store the last character typed because the user can type in arbitrarily many backspaces)
- What is the simples way to check if the sum of two unsigned integers has resulted in an overflow.
- How do you represent an n-ary tree? Write a program to print the nodes of such a tree in breadth first order.
- Write the ‘tr’ program of UNIX. Invoked as
tr -str1 -str2. It reads stdin and prints it out to stdout, replacing every occurance of str1 with str2.
e.g. tr -abc -xyz
to be and not to be <- input
to ye xnd not to ye <- output
