CS 6515 Exam
CS 6515 EXAM 1 QUESTIONS AND
ANSWERS
Knapsack without repetition - k(0) = 0
for w = 1 to W:
if w_j >w: k(w,j) = k(w, j - 1)
else: K(w,j) = max{K(w, j -1),K(w - w_j, j -1) + v_i}
knapsack with repetition - knapsack repeat(w_i....w_n, w_i... w_n, B)
k(0) = 0
for i = 1 to n
if w_i <= b & k(b) <v_i + K(b-w_i)
then k(b) = v_i + K(b-w_i)
Longest Increasing Subsequence - LIS(a_1.... a_n)
for i = 1 to n
L(i) = 1
for j = 1 to n -1
if a_j < a_i & L(i) < 1 + L(j)
L(i) = 1 + L(j)
max = 1
for i = 2 to n
if L(i) > L(max) then max = i
return(L(max))
CS 6515 Exam
, CS 6515 Exam
longest common subsequence algo - LCS(X,Y)
for i = 0 to n: L(i, 0) = 0
for j = 0 to n: L(0,j) = 0
for i = 1 to n
for j = 1 to n
if X_i == Y_j:
L(i,j) = L(i - 1, j - 1) + 1
else:
L(i,j) = max(L(i - 1, j),L(i,j-1)
return(L(i,j)
longest common substring -
what is Big oh of LCS? - O(n**2)
what is big Oh of longest common substring? - O(mn)
what is important to remember when calculating longest common subsequence as
opposed to substring? - substring is very diagonal and plus 1
subsequence you have to use a max function
Perform longest common substring and subsequence on:
"abcdaf"
"3bcdf"
What are the recurrences? write down the algorithm and results -
CS 6515 Exam
CS 6515 EXAM 1 QUESTIONS AND
ANSWERS
Knapsack without repetition - k(0) = 0
for w = 1 to W:
if w_j >w: k(w,j) = k(w, j - 1)
else: K(w,j) = max{K(w, j -1),K(w - w_j, j -1) + v_i}
knapsack with repetition - knapsack repeat(w_i....w_n, w_i... w_n, B)
k(0) = 0
for i = 1 to n
if w_i <= b & k(b) <v_i + K(b-w_i)
then k(b) = v_i + K(b-w_i)
Longest Increasing Subsequence - LIS(a_1.... a_n)
for i = 1 to n
L(i) = 1
for j = 1 to n -1
if a_j < a_i & L(i) < 1 + L(j)
L(i) = 1 + L(j)
max = 1
for i = 2 to n
if L(i) > L(max) then max = i
return(L(max))
CS 6515 Exam
, CS 6515 Exam
longest common subsequence algo - LCS(X,Y)
for i = 0 to n: L(i, 0) = 0
for j = 0 to n: L(0,j) = 0
for i = 1 to n
for j = 1 to n
if X_i == Y_j:
L(i,j) = L(i - 1, j - 1) + 1
else:
L(i,j) = max(L(i - 1, j),L(i,j-1)
return(L(i,j)
longest common substring -
what is Big oh of LCS? - O(n**2)
what is big Oh of longest common substring? - O(mn)
what is important to remember when calculating longest common subsequence as
opposed to substring? - substring is very diagonal and plus 1
subsequence you have to use a max function
Perform longest common substring and subsequence on:
"abcdaf"
"3bcdf"
What are the recurrences? write down the algorithm and results -
CS 6515 Exam
