CS6515 Exam 1 Prep with verified answers
Knapsack without repetition - correct answer ✔k(0) = 0
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for w = 1 to W:
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if w_j >w: k(w,j) = k(w, j - 1)
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else: K(w,j) = max{K(w, j -1),K(w - w_j, j -1) + v_i}
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knapsack with repetition - correct answer ✔knapsack repeat(w_i....w_n, w_i... w_n, B)
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k(0) = 0 |!| |!|
for i = 1 to n
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if w_i <= b & k(b) <v_i + K(b-w_i)
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then k(b) = v_i + K(b-w_i)
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Longest Increasing Subsequence - correct answer ✔LIS(a_1.... a_n)
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for i = 1 to n
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L(i) = 1
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for j = 1 to n -1
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if a_j < a_i & L(i) < 1 + L(j)
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L(i) = 1 + L(j)
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max = 1 |!| |!|
for i = 2 to n
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if L(i) > L(max) then max = i
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return(L(max))
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longest common subsequence algo - correct answer ✔LCS(X,Y)
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for i = 0 to n: L(i, 0) = 0
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for j = 0 to n: L(0,j) = 0
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, for i = 1 to n
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for j = 1 to n
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if X_i == Y_j:
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L(i,j) = L(i - 1, j - 1) + 1
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else:
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L(i,j) = max(L(i - 1, j),L(i,j-1)
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return(L(i,j)
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longest common substring - correct answer ✔
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what is Big oh of LCS? - correct answer ✔O(n* * 2 )
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what is big Oh of longest common substring? - correct answer ✔O(mn)
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what is important to remember when calculating longest common subsequence as opposed
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to substring? - correct answer ✔substring is very diagonal and plus 1
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subsequence you have to use a max function |!| |!| |!| |!| |!| |!| |!|
Perform longest common substring and subsequence on:
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"abcdaf"
"3bcdf"
What are the recurrences? write down the algorithm and results - correct answer ✔
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if you are presented with a coins (1,5,6,8) and your knapsack is k = 11, what is the
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minimum number of coins, what would be the computational time, and what is the
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recurrence? - correct answer ✔https://www.youtube.com/watch?v=Y0ZqKpToTic
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how to calculate longest increasing substring. Try it using the following:
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541208563 - correct answer ✔It should only require two separate loops: |!| |!| |!| |!| |!| |!| |!| |!| |!| |!|
one to loop to go through to calculate the values
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Knapsack without repetition - correct answer ✔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}
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knapsack with repetition - correct answer ✔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)
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Longest Increasing Subsequence - correct answer ✔LIS(a_1.... a_n)
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for i = 1 to n
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L(i) = 1
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for j = 1 to n -1
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if a_j < a_i & L(i) < 1 + L(j)
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L(i) = 1 + L(j)
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max = 1 |!| |!|
for i = 2 to n
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if L(i) > L(max) then max = i
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return(L(max))
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longest common subsequence algo - correct answer ✔LCS(X,Y)
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for i = 0 to n: L(i, 0) = 0
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for j = 0 to n: L(0,j) = 0
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, for i = 1 to n
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for j = 1 to n
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if X_i == Y_j:
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L(i,j) = L(i - 1, j - 1) + 1
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else:
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L(i,j) = max(L(i - 1, j),L(i,j-1)
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return(L(i,j)
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longest common substring - correct answer ✔
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what is Big oh of LCS? - correct answer ✔O(n* * 2 )
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what is big Oh of longest common substring? - correct answer ✔O(mn)
|!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!|
what is important to remember when calculating longest common subsequence as opposed
|!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!|
to substring? - correct answer ✔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 - correct answer ✔
|!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!|
if you are presented with a coins (1,5,6,8) and your knapsack is k = 11, what is the
|!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!|
minimum number of coins, what would be the computational time, and what is the
|!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!| |!|
recurrence? - correct answer ✔https://www.youtube.com/watch?v=Y0ZqKpToTic
|!| |!| |!| |!|
how to calculate longest increasing substring. Try it using the following:
|!| |!| |!| |!| |!| |!| |!| |!| |!| |!|
541208563 - correct answer ✔It should only require two separate loops: |!| |!| |!| |!| |!| |!| |!| |!| |!| |!|
one to loop to go through to calculate the values
|!| |!| |!| |!| |!| |!| |!| |!| |!|
