算法导论题解(我的答案,欢迎指正) introduction to algorithms

 

online reading: 

  http://books.google.com/books?id=NLngYyWFl_YC&pg=PA15&dq=introduction+to+algorithms&psp=1&sig=jX-xfEDWJU3PprUwH8Qfxidli6M#PPA382,M1

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chp1
1.2-1
1.2-2
1.2-3
  n=15

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chp2
2.1-1 to 2.1-4
2.2-* //*: all has been done.

2.2-2

O(n^2),O(n^2)
?2-1

2-2

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chp3
3.1-6
***************

chp4

? 4-6

4-7

ab

c: 

random select row r1 f(r2), we will have A[r1, f(r1)]+A[r2,f(r2)]

d:

nlogm (similar to quicksort)

+++++++++

chp5

5.1-2

rand(a,b) = a + (b-a)*rand(0,1)

O(1)

5.1-3

00: (1-p)^2

01: (1-p)p

10: p(1-p)

11: pp

if out put 00 or 11, just discard it

if output 01, we get 0

if output 10, we get 1

O(1 / (2p(1-p)) )

5.4-1

assume 355days/year.

1)178+1 people(1 is yourself).

2)n*n-n>=355*177

++++++++++++++++++++++++
chp6
6.1-*

6.5-*

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chp7

7.4-2

7.4-4 ? probability analysis

7.6

if [a1,b1] and [a2,b2] overlap, we set these 2 element as equal.

while quicksorting, put those internals equaling to pivot together in 2 place(head and tail).

after a round of partition is finished, put those equal ones to the middle.
7.8

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chp8

8-6

a,c,d

b ?

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chp10

10.1-*

10.2-1 to 10.2-4

10.2-7

10.2-8

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chp12

12.2-2

12.2-3 ？

12.2-6

12.3-3

worst: O(n^2)

best: ? 

 

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chp13

13.1-1 ?

 

13.2-1

//RIGHT-ROTATE(T,y)

x = y.left

y.left = x.right

if(x.right != NIL(T))

  p(x.right) = y

p(x) = p(y)

if( p(y) == NIL(T) )

  root = x

else

  if ( y == p(y).left )

    p(y).left = x

  else

    p(y).right = x

x.right = y

p(y) = x

 

13.2-2

13.2-3

a: the depth of a is added by 1.

b: stay the same.

c: substracted by 1.

13.2-4

one right rotation can add one node to the right-going chain, so at most n - 1 right rotations suffice to transform the tree into a right-going chain.

and, left rotation and right rotation are symmetric.

so, for any 2 n-node binary search tree A and B.

A->right-going chain->B can be done in O(n).

13.2-5 ?

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chp15

15.4-2

compare xi and yi.

then compare c[i-1,j] and c[i,j-1].

15.4-3

as figure 15.6, we only need Y[7] to store each row of the matrix. so that we stores c[i-1,j-1] and c[i-1,j].

and, we only need a integer to store the value c[i,j-1].

 

 

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chp18

In a typical B-tree application, the amount of data handled is so large that all the data do not
fit into main memory at once.

18.1-1

18.1-2

18.1-3

   3: rooted with 2,3,4

18.1-4

   (2t)^h-1

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Given a n*n matrix, whoes elements are all integers.

now, we need to select n elements in this matrix, so that there are neither 2 elements in a single row nor in a single column, and the sum of

these n elements must be minimum.

skill: substract or add the same integer in a row or column would not change the positions of the elements of the result. so we can modify the

matrix until it contains no negative integers.

 

 

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C.1-1

 

C.1-4

O: for odd;

E: for even

there are 4 cases:

a: O O O

b: O O E  => sum is even

c: O E E

d: E E E => sum is even

the chances for a, d to happen are the same.

the chances for b, c to happen are the same.

 

so the answer is C(100,3)/2

 

C.1-5