Errata to CLRS-book
Severity levels
1.
2.
3.
4.
A minor typographical error that should not affect your understanding.
A minor technical or expository error.
A more significant technical or expository error.
A serious error in the exposition of an algorithm, or an error that requires significant change
to the text.
Page 104, line 2 of PERMUTE-WITHOUT-IDENTITY. Change ``1 to n'' to ``1 to n-1''.
Reported by John Buck. Posted 20 February 2002.
Severity level: 4
Corrected in the third printing.
Page 251, Problem 11-4. The problem has been rewritten. You can get the new text in
PDF.
Reported by Charles Leiserson. Posted 5 November 2001.
Severity level: 4
Corrected in the third printing.
Page 278, procedure LEFT-ROTATE. Replace line 3 by the two lines
if left[y] ≠ nil[T]
then p[left[y]] ← x
[Note: In some browsers, the left arrow symbol that we use for ``gets'' appears as ←.]
Reported by Timothy Haritun. Posted 22 October 2001.
Severity level: 4
Corrected in the third printing.
Pages 375-378. As written, the procedure RECURSIVE-ACTIVITY-SELECTOR is flawed,
in that it works only when j = n+1. It so happens that in the initial call and all recursive
calls, j does equal n+1, but for general values of j, the statement on page 375, lines 4-5
from the bottom, ``It returns a maximum-size subset of mutually compatible activities in
Sij'' does not hold. The best remedy is to rewrite the procedure so that the fourth
parameter is always n, and have it return a maximum-size subset of mutually compatible
activities in Si,n+1. Pages 375-378 have been rewritten to accommodate this change. You
can get the updated pages in PDF. Note: these updated pages were changed on 12
February 2002.
Reported by Paulo Feofiloff and Augusto Fernandes Vellozo. Posted 16 November
2001.
Severity level: 4
Corrected in the third printing.
Page 482, line 4 of FIB-HEAP-UNION. Change the condition ``min[H2] < min[H1]'' to
``key[min[H2]] < key[min[H1]]''.
Reported by Doug Dunham. Posted 10 April 2002.
Severity level: 4
Corrected in the third printing.
Pages 696-697, Problem 26-7. In line 3 of the HOPCROFT-KARP procedure, change
``maximum set'' to ``maximal set''. In line 7 on page 697, change ``maximum set'' to
``maximal set''. Change part (e) to read ``Prove that if a shortest augmenting path with
respect to M has l edges, the size of the maximum matching is at most |M| + |V|/(l+1).''
In line 1 of part (g), change ``maximum set'' to ``maximal set''.
Reported by Greg Plaxton. Posted 29 April 2002.
Severity level: 4
To be corrected in the fourth printing.
Pages 819-820, Problem 29-4 (Farkas's lemma). Change ``and b be an m-vector'' to
``and c be an n-vector''. Change ``bx > 0'' to ``cTx > 0''. Change ``yA = b'' to ``ATy = c''.
Reported by Greg Plaxton. Posted 29 April 2002.
Severity level: 4
To be corrected in the fourth printing.
Pages 823-827. There are several passages related to degree-bounds that need to be
changed. The problem is that one cannot precisely refer to the degree-bound of a
polynomial, since for a degree-n polynomial, any integer greater than n is a
degree-bound. Make the following changes:



Page 823, lines 1-6 from the bottom. Change these lines to ``Note that degree(C) = degree(A)
+ degree(B), implying that if A is a polynomial of degree-bound na and B is a polynomial of
degree-bound nb, then C is a a polynomial of degree-bound na + nb - 1. Since a polynomial
of degree-bound k is also a polynomial of degree-bound k+1, we will normally say that the
product polynomial C is a polynomial of degree-bound na + nb.''
Page 825, lines 7-9 from the bottom. Change the last sentence before Theorem 30.1 to ``The
following theorem shows that interpolation is well defined when the desired interpolating
polynomial must have a degree-bound equal to the given number of point-value pairs.''
Page 827, lines 11-16. Change the three sentences beginning on line 11 to ``We must face
the problem, however, that degree(C) = degree(A) + degree(B); if A and B are of
degree-bound n, then C is of degree-bound 2n. A standard point-value representation for A
and B consists of n point-value pairs for each polynomial. Multiplying these together gives
us n point-value pairs, but we need 2n pairs to interpolate a unique polynomial C of
degree-bound 2n.''
Reported by San Skulrattanakulchai. Posted 28 November 2001.
Severity level: 4
Corrected in the third printing.
Page 89, line 2. Change ``For the ``only if'' part'' to ``For the ``if'' part''.
Reported by Hui Zheng. Posted 12 November 2001.
Severity level: 3
Corrected in the third printing.
Page 99, Exercise 5.2-5. Change ``Suppose that each element of A is chosen randomly,
independently, and uniformly from the range 1 through n.'' to ``Suppose that the
elements of A form a uniform random permutation of <1, 2, ..., n>.''
Reported by Tom Cormen. Posted 5 April 2002.
Severity level: 3
Corrected in the third printing.
Page 116, lines 1-5. Change ``whereas Bi depends only on whether the value in position
i is greater than all the values 1 through i-1. The ordering of positions 1 through i-1 does
not affect whether i is greater than all of them, and the value of i does not affect the
ordering of positions 1 through i-1.'' to ``whereas Bi depends only on whether the value
in position i is greater than the values in all other positions. The ordering of the values
in positions 1 through i-1 does not affect whether the value in position i is greater than
all of them, and the value in position i does not affect the ordering of the values in
positions 1 through i-1.''
Reported by Tom O'Connell. Posted 12 October 2001.
Severity level: 3
Corrected in the third printing.
Page 157, line 20. Add the sentence ``Our analysis assumes that each pivot is chosen
randomly and independently.'' Page 158, line 8. Change ``Because the set Zij has j-i+1
elements,'' to ``Because the set Zij has j-i+1 elements, and because pivots are chosen
randomly and independently,''.
Reported by Charles Leiserson. Posted 15 September 2001.
Severity level: 3
Corrected in the second printing.
Page 161, Problem 7-2. In part (c), change ``Show that equation (7.5) simplifies to'' to
``Show that equation (7.5) can be rewritten as'', and change the summation to start at
q=2. In part (d), change the summation to start at k=2, and in the hint change ``one for k
= 1, 2, ...'' to ``one for k = 2, 3, ...''. In part (e), change the hint to read ``Show, by
substitution, that E[T(n)] < an lg n for sufficiently large n and for some positive
constant a.''
Reported by Charles Leiserson. Posted 26 September 2001.
Severity level: 3
Corrected in the second printing.
Page 187, line 19. Remove the outermost parentheses of the expression, so that the O(n)
term is not in the summation.
Reported by Randy Goldman. Posted 3 November 2001.
Severity level: 3
Corrected in the third printing.
Page 296, Problem 13-3(d). The statement of part (d) asks for something that is not true.
Change part (d) to read ``Show that AVL-INSERT, run on an n-node AVL tree, takes
O(lg n) time and performs O(1) rotations.''.
Reported by Vassos Hadzilacos. Posted 10 October 2002.
Severity level: 3
To be corrected in the fourth printing.
Page 314, line 10 from the bottom. Remove the sentence ``(Note that no interval in the
right subtree overlaps i--we shall see why later.)''
Reported by Jørgen Villadsen. Posted 6 May 2002.
Severity level: 3
To be corrected in the fourth printing.
Page 373, equation (16.3). The max needs to be over all k such that i < k < j and also ak
is in Sij.
Reported by Bob Roos. Posted 16 November 2001.
Severity level: 3
Corrected in the third printing.
Pages 408-409. Replace ``floor(lg n)'' by ``k-1''. (HTML does not permit us to print the
appropriate floor symbol.) Specifically, on page 408, line 2 from the bottom, change
``for i = 0, 1, ..., floor(lg n)'' to ``for i = 0, 1, ..., k-1''; on page 408, last line, change
``For i > lg n'' to ``For i > k''; and in page 409, line 2 of the text, change the upper bound
of the first summation from ``floor(lg n)'' to ``k-1''.
Reported by Tom Cormen. Posted 23 April 2002.
Severity level: 3
To be corrected in the fourth printing.
Page 604, bottom two lines. Change the inequalities to read
xk-1 - xk-2 < w(vk-2, vk-1) ,
xk - xk-1 < w(vk-1, vk) .
Page 605, line 4. Change ``subtracted out once'' to ``subtracted out once (remember that
v1 = vk implies x1 = xk)''.
Reported by Sam Slee. Posted 15 May 2002.
Severity level: 3
To be corrected in the fourth printing.
Page 669, lines 3 and 4 from the bottom. Remove the sentence ``That is, the total net
flow at each vertex other than the source is nonnegative.'' Change the next sentence
from ``We call the total net flow at a vertex u the excess flow into u, given by ...'' to
``We call this quantity the excess flow into vertex u, given by ...''.
Reported by San Skulrattanakulchai. Posted 19 September 2001.
Severity level: 3
Corrected in the second printing.
Page 786, line (29.44). Change ``minimize d[t]'' to ``maximize d[t]''.
Reported by Tom O'Connell. Posted 15 September 2001.
Severity level: 3
Corrected in the second printing.
Page 818, lines 6-7 from the bottom. Change ``be an optimal solution to a primal linear
program'' to ``be a feasible solution to the primal linear program'' and change ``be the
optimal solution to the dual linear program'' to ``be a feasible solution to the dual linear
program''.
Reported by Tom O'Connell. Posted 8 November 2001.
Severity level: 3
Corrected in the third printing.
Page 819, Problem 29-3. In the last sentence of part (c), change ``Show that'' to
``Assuming that both the primal integer program and the dual integer program are
feasible and bounded, show that''.
Reported by Greg Plaxton. Posted 29 April 2002.
Severity level: 3
To be corrected in the fourth printing.
Page 832, statement of Lemma 30.6. Change ``nonnegative'' to ``nonzero''.
Reported by Michiel Smid. Posted 14 February 2002.
Severity level: 3
Corrected in the third printing.
Page 855. Exercise 31.1-6 should read ``Prove that if a and b are any positive integers
such that a | b ...'' That is, both a and b are required to be positive. (Note: we misspelled
``positive'' as ``postive'' in the second printing.)
Reported by San Skulrattanakulchai. Posted 8 September 2001.
Severity level: 3
Corrected in the second printing.
Page 966, lines 5-7 from the bottom. Change ``Finding the longest simple path between
two vertices is NP-complete, however. In fact, it is NP-complete even if all edge
weights are 1.'' to ``Finding a longest simple path between two vertices is difficult,
however. Merely determining whether a graph contains a simple path with at least a
given number of edges is NP-complete.'' (Also reported by Joel Seiferas.)
Reported by San Skulrattanakulchai. Posted 12 November 2001.
Severity level: 3
Corrected in the third printing.
Page 968, line 5. Change ``then every NP-complete problem'' to ``then every problem in
NP''.
Reported by San Skulrattanakulchai. Posted 12 November 2001.
Severity level: 3
Corrected in the third printing.
Page 1032, line 10. Change ``there is a gap of at least |V|'' to ``there is a gap of at least
ρ|V|''.
Reported by Tom O'Connell. Posted 9 November 2001.
Severity level: 3
Corrected in the third printing.
Page 1032, lines 21 and 24. Change ``we can produce a minimization problem Y'' to
``we can produce in polynomial time a minimization problem Y'', and change ``there is
no ρ-approximation algorithm for problem Y'' to ``there is no polynomial-time
ρ-approximation algorithm for problem Y''.
Reported by San Skulrattanakulchai. Posted 19 November 2001.
Severity level: 3
Corrected in the third printing.
Page 1033, Exercise 35.2-3. Change the first sentence to ``Consider the following
closest-point heuristic for building an approximate traveling-salesman tour whose cost
function satisfies the triangle inequality.''
Reported by San Skulrattanakulchai. Posted 19 November 2001.
Severity level: 3
Corrected in the third printing.
Page 1117, Exercise C.4-8. In the inequality to be proven, change less-than-or-equal to
greater-than-or-equal.
Reported by Guolong Lin. Posted 27 September 2002.
Severity level: 3
To be corrected in the fourth printing.
Page 20, line 13. Change ``x and y point to (``are'') the same object'' to ``x and y point to
the same object''.
Reported by Jinoh Kim. Posted 25 March 2002.
Severity level: 2
Corrected in the third printing.
Page 26, lines 17-18. Change ``so tj = j/2. If we work out the resulting average-case
running time, it turns out to be a quadratic function of the input size'' to ``so tj is about
j/2. The resulting average-case running time turns out to be a quadratic function of the
input size''.
Reported by Carlos Brizuela. Posted 26 October 2002.
Severity level: 2
To be corrected in the fourth printing.
Page 44, line 26. Change ``the function f(n) is on or below g(n)'' to ``the function f(n) is
on or below cg(n)''.
Reported by San Skulrattanakulchai. Posted 26 September 2001.
Severity level: 2
Corrected in the second printing.
Page 44, line 31. Change ``any quadratic function is in O(n2)'' to ``any such quadratic
function is in O(n2)''.
Reported by San Skulrattanakulchai. Posted 26 September 2001.
Severity level: 2
Corrected in the second printing.
Page 51, inequality (3.7). There is an extra left parenthesis in the expression on the
right-hand side. The right-hand side should read ''(a - (b - 1)) / b''.
Reported by Georgios Fainekos. Posted 22 July 2002.
Severity level: 2
To be corrected in the fourth printing.
Page 90, line 2. The restriction on bi should read ``all bi are greater than 1''.
Reported by Peter Hoyer. Posted 10 September 2001.
Severity level: 2
Corrected in the second printing.
Page 90, line 7. The summation should run from 1 to k (not from 1 to p).
Reported by Peter Hoyer. Posted 7 September 2001.
Severity level: 2
Corrected in the second printing.
Page 98, line 12. Change ``The expected interview cost'' to ``The expected hiring cost''.
Reported by Kiyoung Yang. Posted 20 September 2001.
Severity level: 2
Corrected in the second printing.
Page 103, line 9. Change ``(See Appendix B.)'' to ``(See Appendix C.)''
Reported by Tom O'Connell. Posted 15 October 2001.
Severity level: 2
Corrected in the third printing.
Page 103, line 10 from the bottom. Change ``We assume that just before the (i - 1)st
iteration'' to ``We assume that just before the ith iteration''.
Reported by Tom Cormen. Posted 26 June 2002.
Severity level: 2
To be corrected in the fourth printing.
Page 114. The last sentence before Subsection 5.4.4 should read ``From these rough
estimates alone, we can conclude that the expected length of the longest streak is
Theta(lg n).'' (Add the word ``expected.'')
Reported by Tom O'Connell. Posted 10 September 2001.
Severity level: 2
Corrected in the second printing.
Page 133, last line. Change ``so we can express the total cost of BUILD-MAX-HEAP as''
to ``so we can express the total cost of BUILD-MAX-HEAP as being bounded from above
by''.
Reported by Artem Matsak. Posted 26 August 2002.
Severity level: 2
To be corrected in the fourth printing.
Page 147, Figure 7.1 caption. In part (f), change ``The values 3 and 8 are swapped'' to
``The values 3 and 7 are swapped''.
Reported by Nafees Ud Din Ahmad. Posted 8 January 2002.
Severity level: 2
Corrected in the third printing.
Page 152, last line. Change ``of the average case'' to ``of the average case of a
randomized version of quicksort''.
Reported by Joel Seiferas. Posted 2 December 2001.
Severity level: 2
Corrected in the third printing.
Page 174, first line of Section 8.4. Change ''Bucket sort runs in linear time'' to ''Bucket
sort runs in linear expected time''.
Reported by Brendan McKay. Posted 23 July 2002.
Severity level: 2
To be corrected in the fourth printing.
Page 189, line 4. Change ``we have T(n) = O(n)'' to ``we have E[T(n)] = O(n)''.
Reported by Tom Cormen. Posted 21 May 2002.
Severity level: 2
To be corrected in the fourth printing.
Page 190, last line of main text. Change ``greater than1 the median-of-medians x.'' to
``greater than or equal to the median-of-medians x.1''. Change the footnote to read
``Because of our assumption that the numbers are distinct, all medians except x are
either greater than or less than x.''
Reported by Tom Cormen. Posted 1 June 2002.
Severity level: 2
To be corrected in the fourth printing.
Page 191. Lines 13-14, change ''that any input of 140 or fewer elements'' to ''that any
input of fewer than 140 elements''. Lines 16-17 (the bound on T(n)), change the first
case to ''O(1) if n < 140'' and change the second case to hold ''if n > 140''. Line 20,
change ''and all n < 140'' to ''and all n < 140''.
Reported by Tom Cormen. Posted 6 June 2002.
Severity level: 2
To be corrected in the fourth printing.
Page 235, line 4 from the bottom. Change ``(by inequality (3.7))'' to ``(by inequality
(3.6))''.
Reported by H. Jun Lee. Posted 10 April 2002.
Severity level: 2
Corrected in the third printing.
Page 244, Exercise 11.4-1. Change ``with the primary hash function'' to ``with the
auxiliary hash function''.
Reported by Scot Anderson. Posted 11 October 2001.
Severity level: 2
Corrected in the third printing.
Page 267, line 7 (second line of the math display bounding E[Yn]). Change the equal
sign to less-than-or-equal.
Reported by Tom Cormen. Posted 11 April 2002.
Severity level: 2
Corrected in the third printing.
Page 384, Exercise 16.2-6. Remove the sentence ``Assume that you have a solution to
Problem 9-2.''
Reported by Joel Seiferas. Posted 5 December 2001.
Severity level: 2
Corrected in the third printing.
Page 416, Exercise 17.3-7. In the specification for DELETE-LARGER-HALF(S), change
``ceiling(S/2)'' to ``ceiling(|S|/2)''. (HTML does not permit us to print the appropriate
ceiling symbol.)
Reported by Eric Rupert. Posted 3 October 2002.
Severity level: 2
To be corrected in the fourth printing.
Page 442, line 21. Change ``The number of disk pages accessed by B-TREE-SEARCH is
therefore Theta(h) = Theta(logt n)'' to ``The number of disk pages accessed by
B-TREE-SEARCH is therefore O(h) = O(logt n)''.
Reported by Jouni Järvinen. Posted 10 April 2002.
Severity level: 2
Corrected in the third printing.
Pages 484-485, Figure 20.3. In parts (f), (g), and (h), node w should be the node with
key 7. In part (k), node w should be the node with key 52.
Reported by Jens Kristian Jensen. Posted 20 November 2002.
Severity level: 2
To be corrected in the fourth printing.
Page 517, lines 6, 14, 15, and 19. There should be parentheses around the superscripts
of A, since these superscripts indicate functional iteration.
Reported by Peter Hoyer. Posted 10 September 2001.
Severity level: 2
Corrected in the second printing.
Page 533, line 2 of main text. Change ``Lines 1-4 paint every vertex white'' to ``With
the exception of the source vertex s, lines 1-4 paint every vertex white''. An additional
stylistic change: in the next sentence, change ``Line 5 paints the source vertex s gray'' to
``Line 5 paints s gray''.
Reported by George Havas. Posted 3 September 2002.
Severity level: 2
To be corrected in the fourth printing.
Page 534, line 14. Change ``in lines 11-18'' to ``in line 18''.
Reported by Wilasiree Buranatham. Posted 8 April 2002.
Severity level: 2
Corrected in the third printing.
Page 566, Exercise 23.1-4. The exercise should require the graph to be connected.
Reported by Tom Cormen. Posted 22 August 2001.
Severity level: 2
Corrected in the second printing.
Page 566, Exercise 23.1-5. Change ``Let e be a maximum-weight edge on some cycle of
G = (V, E).'' to Change ``Let e be a maximum-weight edge on some cycle of connected
graph G = (V, E).''
Reported by San Skulrattanakulchai. Posted 11 September 2002.
Severity level: 2
To be corrected in the fourth printing.
Page 578, Problem 23-4. In part (a), change line 5 of MAYBE-MST-A to read ``then T
← T - {e}''. In part (b), change line 4 of MAYBE-MST-B to read ``then T ← T ∪ {e}''.
[Note: In some browsers, the left arrow symbol that we use for ``gets'' appears as &larr;,
and the symbol for set union appears as &cup;.]
Reported by Fredrik Manne. Posted 3 May 2002.
Severity level: 2
To be corrected in the fourth printing.
Page 578, line 5 of MAYBE-MST-C. Change ``the maximum-weight edge'' to ``a
maximum-weight edge''.
Reported by Peter Hoyer. Posted 9 November 2001.
Severity level: 2
Corrected in the third printing.
Page 589, line 3 from the bottom. Change ``relaxes all E edges'' to ``relaxes all |E|
edges''.
Reported by San Skulrattanakulchai. Posted 23 September 2001.
Severity level: 2
Corrected in the second printing.
Page 641, Problem 25-1(b). Add the phrase ``no matter what algorithm is used'' to the
end of the problem statement.
Reported by Adam Chlipala. Posted 25 March 2002.
Severity level: 2
Corrected in the third printing.
Page 652, line 2 of the Figure 26.3 caption. Change ``cf(p) = c(v2, v3) = 4'' to ``cf(p) =
cf(v2, v3) = 4''.
Reported by San Skulrattanakulchai. Posted 15 September 2001.
Severity level: 2
Corrected in the second printing.
Page 658, footnote 2. Delete the sentence ''In practice, however, irrational numbers
cannot be stored on finite-precision computers.''.
Reported by Brendan McKay. Posted 26 July 2002.
Severity level: 2
To be corrected in the fourth printing.
Page 665, 5th line from the bottom. Change ``along with V new edges'' to ``along with
|V| new edges''.
Reported by San Skulrattanakulchai. Posted 19 September 2001.
Severity level: 2
Corrected in the second printing.
Page 666, 6th line from the bottom. Change ``an integer-valued flow in G´ '' to ``an
integer-valued flow f in G´ ''.
Reported by San Skulrattanakulchai. Posted 19 September 2001.
Severity level: 2
Corrected in the second printing.
Page 667, lines 12 and 13. Remove ``defined in the statement of the lemma''.
Reported by San Skulrattanakulchai. Posted 19 September 2001.
Severity level: 2
Corrected in the second printing.
Page 668, line 5. Change ``is the value'' to ``equals the value'' in order to strengthen the
notion that Corollary 26.12 is an ``if and only if'' statement.
Reported by San Skulrattanakulchai. Posted 19 September 2001.
Severity level: 2
Corrected in the second printing.
Page 669, line 11 from the bottom. Change ``the entire residual network G = (V, E) to
find'' to ``the entire residual network to find''.
Reported by San Skulrattanakulchai. Posted 19 September 2001.
Severity level: 2
Corrected in the second printing.
Page 711, Figure 27.5 caption. Change ``f(x) = f(ceiling(x/2))'' to ``f(x) = ceiling(x/2)''.
(HTML does not permit us to print the appropriate ceiling symbol.)
Reported by Xiaozhou Steve Li. Posted 25 November 2001.
Severity level: 2
Corrected in the third printing.
Page 772, lines 3-4 from the bottom. Change ``either linear equalities or linear
equalities'' to ``either linear equalities or linear inequalities''.
Reported by Mike Domaratzki. Posted 19 October 2001.
Severity level: 2
Corrected in the third printing.
Page 779, last line. Change ``and thus the two solutions are equivalent'' to ``and thus the
two linear programs are equivalent''.
Reported by San Skulrattanakulchai. Posted 18 September 2001.
Severity level: 2
Corrected in the second printing.
Page 781, equations (29.30) and (29.32). In the summations, change ``xi'' to ``xj''.
Reported by Selim Akl. Posted 19 October 2001.
Severity level: 2
Corrected in the third printing.
Page 786, lines 15 and 16. Change ``a sink s and a source t'' to ``a source s and a sink t''.
Reported by San Skulrattanakulchai. Posted 11 September 2001.
Severity level: 2
Corrected in the second printing.
Page 789, last equation of the linear program. Change ``fi(s, v)'' to ``fi(si, v)''.
Reported by Xiaozhou Steve Li. Posted 31 October 2001.
Severity level: 2
Corrected in the third printing.
Page 800, line 4 from the bottom. Change ``Since we picked i as any index in i'' to
``Since we picked i as any index in I''.
Reported by Mike Domaratzki. Posted 22 October 2001.
Severity level: 2
Corrected in the third printing.
Page 814, line 10 from the bottom. In the equation for z, change it from ``z = 4/5 + 9x1/5
- x4/5'' to ``z = -4/5 + 9x1/5 - x4/5''. That is, the constant should be -4/5, not 4/5.
Reported by Rance Cleaveland. Posted 26 November 2001.
Severity level: 2
Corrected in the third printing.
Page 818, bottom line. The summation should be over j rather than over i.
Reported by Tom O'Connell. Posted 3 November 2001.
Severity level: 2
Corrected in the third printing.
Page 837, line 10. Change ``-(n-1) < j´-j < n-1'' to ``-(n-1) < j´-j < n-1''.
Reported by San Skulrattanakulchai. Posted 9 November 2001.
Severity level: 2
Corrected in the third printing.
Page 851, line 1. Change ``of an integer a'' to ``of a nonzero integer a''.
Reported by San Skulrattanakulchai. Posted 11 September 2001.
Severity level: 2
Corrected in the second printing.
Page 852, line 23. Change ``If a and b are not both 0'' to ``If a and b are both nonzero''.
Reported by San Skulrattanakulchai. Posted 11 September 2001.
Severity level: 2
Corrected in the second printing.
Page 853, line 9. Change ``since a mod s < s'' to ``since 0 < a mod s < s''.
Reported by San Skulrattanakulchai. Posted 11 September 2001.
Severity level: 2
Corrected in the second printing.
Page 886, line 13 from the bottom. Change ``one-way hash function'' to
``collision-resistant hash function''.
Reported by Ron Rivest. Posted 19 September 2001.
Severity level: 2
Corrected in the second printing.
Page 896, line 6. Change ``using an improved version of Theorem 31.39'' to ``using an
improved version of Theorem 31.38''.
Reported by Kai Huang. Posted 21 September 2001.
Severity level: 2
Corrected in the second printing.
Page 908, Figure 32.3, part (c). The shaded region of z should be the same width as the
shaded regions of x and y.
Reported by San Skulrattanakulchai. Posted 27 September 2001.
Severity level: 2
Corrected in the second printing.
Page 916, line 4. The summation should run from i=0 to n-1, not to n.
Reported by San Skulrattanakulchai. Posted 27 September 2001.
Severity level: 2
Corrected in the second printing.
Page 927, line 21. Change ``π(i+1)[q] = π[π(i)[q]]'' to ``π(i)[q] = π[π(i-1)[q]]''. [Note: In some
browsers, the Greek letter ``pi'' appears as a question mark. If you see question marks in
the above text, interpret them as lowercase ``pi''s.]
Reported by San Skulrattanakulchai. Posted 27 September 2001.
Severity level: 2
Corrected in the second printing.
Page 968, line 2 from the bottom. Change ``and we wish to find the feasible solution'' to
``and we wish to find a feasible solution''.
Reported by San Skulrattanakulchai. Posted 12 November 2001.
Severity level: 2
Corrected in the third printing.
Page 969, line 1. Change ``and we wish to find the path'' to ``and we wish to find a
path''.
Reported by San Skulrattanakulchai. Posted 12 November 2001.
Severity level: 2
Corrected in the third printing.
Page 977, line 6. Change ``uses breadth-first search to compute the shortest path'' to
``uses breadth-first search to compute a shortest path''.
Reported by San Skulrattanakulchai. Posted 12 November 2001.
Severity level: 2
Corrected in the third printing.
Page 977, line 11. Change ``instances in which the shortest path'' to ``instances in which
a shortest path''.
Reported by San Skulrattanakulchai. Posted 12 November 2001.
Severity level: 2
Corrected in the third printing.
Page 978, line 3 of Exercise 34.1-1. Change ``in the longest simple path'' to ``in a
longest simple path''.
Reported by San Skulrattanakulchai. Posted 12 November 2001.
Severity level: 2
Corrected in the third printing.
Page 981, line 5. Change ``in the hamiltonian cycle'' to ``in some hamiltonian cycle''.
Reported by San Skulrattanakulchai. Posted 12 November 2001.
Severity level: 2
Corrected in the third printing.
Page 997, Theorem 34.9, first line of proof. Change ``Then we prove that
CIRCUIT-SAT is NP-hard'' to ``Then we prove that SAT is NP-hard.''
Reported by He Jun. Posted 15 October 2001.
Severity level: 2
Corrected in the third printing.
Page 1011, lines 16-17. Change ``we form a hamiltonian cycle in G by'' to ``we form a
hamiltonian cycle in G´ by''.
Reported by Xin Li. Posted 9 December 2001.
Severity level: 2
Corrected in the third printing.
Page 1013, line 13. Change ``(G´, c, 0)'' to ``<G´, c, 0>''.
Reported by San Skulrattanakulchai. Posted 12 November 2001.
Severity level: 2
Corrected in the third printing.
Page 1041. Equations (35.13) and (35.16) should apply to each edge (u, v) in E (not to
each vertex v in V).
Reported by Tom O'Connell. Posted 7 September 2001.
Severity level: 2
Corrected in the second printing.
Page 1083, line 7 of the main text. Change ``That is, v is a neighbor of u if either'' to
``That is, v is a neighbor of u if u ≠ v and either''.
Reported by San Skulrattanakulchai. Posted 6 October 2001.
Severity level: 2
Corrected in the third printing.
Page 1091, Exercise B.5-7. Change ``Show that every binary tree'' to ``Show that if L >
2, then every binary tree''.
Reported by San Skulrattanakulchai. Posted 6 October 2001.
Severity level: 2
Corrected in the third printing.
Page 1107, line 9. Remove the set braces from the subscript of the summation.
Reported by Charles Leiserson. Posted 22 August 2002.
Severity level: 2
To be corrected in the fourth printing.
Page 14, bottom line. Change ``Medinas'' to ``Meidanis''.
Reported by Marcel K. de Carli Silva. Posted 6 December 2001.
Severity level: 1
Corrected in the third printing.
Page 94, last sentence before the exercises. There is an extraneous ``a'' after the end of
the sentence.
Reported by Tom O'Connell. Posted 4 August 2001.
Severity level: 1
Corrected in the second printing.
Page 118, Problem 5-2. Change the start of the first sentence from ``Thus problem'' to
``This problem''.
Reported by Fredrik Manne. Posted 12 September 2001.
Severity level: 1
Corrected in the second printing.
Page 129, line 19. Change ``presents five basic procedures'' to ``presents some basic
procedures''.
Reported by Nancy Uehara. Posted 13 September 2001.
Severity level: 1
Corrected in the second printing.
Page 159, last line. Change ``T. Hoare'' to ``C. A. R. Hoare''.
Reported by Charles Leiserson. Posted 2 October 2001.
Severity level: 1
Corrected in the third printing.
Page 234, line 29. Change ``hav p > m'' to ``have p > m''.
Reported by Tom O'Connell. Posted 4 September 2001.
Severity level: 1
Corrected in the second printing.
Page 372, line 10. Change ``represent to entire problem'' to ``represent the entire
problem''.
Reported by John Buck. Posted 25 March 2002.
Severity level: 1
Corrected in the third printing.
Page 373, line 2. Change ``producing a another solution'' to ``producing another
solution''.
Reported by Erica Schultz. Posted 10 April 2002.
Severity level: 1
Corrected in the third printing.
Page 373, line 10. Change ``we can build an maximum'' to ``we can build a maximum''.
Reported by Jim Nastos. Posted 12 August 2001.
Severity level: 1
Corrected in the second printing.
Page 400, line 4. Change ``so it also still early'' to ``so it also is still early''.
Reported by Jim Nastos. Posted 12 August 2001.
Severity level: 1
Corrected in the second printing.
Page 539, Exercise 22.2-6. In the last sentence, change ``If is it possible'' to ``If it is
possible''.
Reported by Susan Wang. Posted 29 March 2002.
Severity level: 1
Corrected in the third printing.
Page 569, Figure 23.4 parts (l), (m), and (n). Edge (c, i) should be labeled with weight 2.
Reported by Melissa Crounse. Posted 2 June 2002.
Severity level: 1
To be corrected in the fourth printing.
Page 573, line 2. Change ``The for loop of lines 8-11 update'' to ``The for loop of lines
8-11 updates''.
Reported by San Skulrattanakulchai. Posted 11 September 2002.
Severity level: 1
To be corrected in the fourth printing.
Page 672, line 10. Change ``Thus we can we increase'' to ``Thus we can increase''.
Reported by San Skulrattanakulchai. Posted 19 September 2001.
Severity level: 1
Corrected in the second printing.
Page 785, Exercise 29.1-8. Change ``into standard from'' to ``into standard form''.
Reported by Trivikram Dash. Posted 29 November 2002.
Severity level: 1
To be corrected in the fourth printing.
Page 863, line 4 from the bottom. Change ``This size'' to ``The size''.
Reported by Constance Sawyer. Posted 5 November 2001.
Severity level: 1
Corrected in the third printing.
Page 1021, line 1. Change ``polyomial-time'' to ``polynomial-time''.
Reported by San Skulrattanakulchai. Posted 16 November 2001.
Severity level: 1
Corrected in the third printing.
Page 1021, line 11. Change ``Papadimitiou'' to ``Papadimitriou''.
Reported by Geoffrey King. Posted 11 January 2002.
Severity level: 1
Corrected in the third printing.
Page 1053, line 19. Change ``Christofedes'' to ``Christofides''.
Reported by San Skulrattanakulchai. Posted 21 September 2001.
Severity level: 1
Corrected in the second printing.
Page 1076, line 4 from the bottom. Change ``there may several'' to ``there may be
several''.
Reported by Constance Sawyer. Posted 5 November 2001.
Severity level: 1
Corrected in the third printing.
Page 1135, reference [171]. Change ``Birkäuser'' to ``Birkhäuser''.
Reported by Antal Iványi. Posted 29 October 2001.
Severity level: 1
Corrected in the third printing.
Page 1140, reference [266]. The title should be in title case: ``Theory of Linear and
Integer Programming''.
Reported by Antal Iványi. Posted 29 October 2001.
Severity level: 1
Corrected in the third printing.
Page 1150. There should be a blank line between the index entries for ``butterfly
operation'' and ``cache''.
Reported by Tom Cormen. Posted 13 May 2001.
Severity level: 1
Corrected in the second printing.