### Microsoft Interview Pattern (Page-8)

Interview :Microsoft Interview Pattern (Page - 8)

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);

88. 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.

89. Given a binary tree with nodes, print out the values in pre-order/in-order/post-order without using any extra space.

90. 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 ;

}

91. 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

92. Reverse the bits of an unsigned integer.

ANS.

#define reverse(x)

(x=x>>16|(0x0000ffff&x)<<16,

x=(0xff00ff00&x)>>8|(0x00ff00ff&x)<<8,

x=(0xf0f0f0f0&x)>>4|(0x0f0f0f0f&x)<<4,

x=(0xcccccccc&x)>>2|(0x33333333&x)<<2,

x=(0xaaaaaaaa&x)>>1|(0x55555555&x)<<1)

93. Compute the number of ones in an unsigned integer.

ANS.

#define count_ones(x)

(x=(0xaaaaaaaa&x)>>1+(0x55555555&x),

x=(0xcccccccc&x)>>2+(0x33333333&x),

x=(0xf0f0f0f0&x)>>4+(0x0f0f0f0f&x),

x=(0xff00ff00&x)>>8+(0x00ff00ff&x),

x=x>>16+(0x0000ffff&x))

94. 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+(0x55555555&h),

h=(0xcccccccc&h)>>2+(0x33333333&h),

h=(0xf0f0f0f0&h)>>4+(0x0f0f0f0f&h),

h=(0xff00ff00&h)>>8+(0x00ff00ff&h),

h=(h>>16)+(0x0000ffff&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))))

96. 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))

97. 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

98. 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)

99. What is the simples way to check if the sum of two unsigned integers has resulted in an overflow. 100. How do you represent an n-ary tree? Write a program to print the nodes of such a tree in breadth first order.

101. 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[i] with str2[i].

e.g. tr -abc -xyz

to be and not to be <- input

to ye xnd not to ye <- output

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