157 practice sets · Page 2 of 8
Find the maximum sub-array sum for the following array: {3, 6, 7, 9, 3, 8}
33
36
23
26
Correct Answer: B — 36
Explanation:
All the elements of the array are positive. So, the maximum sub-array sum is equal to the sum of all the elements, which is 36.
Which method is used by line 4 of the above code snippet?
Divide and conquer
Recursion
Both memoization and divide and conquer
Memoization
Correct Answer: D — Memoization
Explanation:
The array "sum" is used to store the previously calculated values, so that they aren't recalculated. So, line 4 uses the memoization technique.
What is the space complexity of the divide and conquer algorithm used to find the maximum sub-array sum?
O(n)
O(1)
O(n!)
O(n^{2})
Correct Answer: B — O(1)
Explanation:
The divide and conquer algorithm uses a constant space. So, the space complexity is O(1).
What is the time complexity of the divide and conquer algorithm used to find the maximum sub-array sum?
O(n)
O(logn)
O(nlogn)
O(n^{2})
Correct Answer: C — O(nlogn)
Explanation:
The time complexity of the divide and conquer algorithm used to find the maximum sub-array sum is O(nlogn).
Which line should be inserted to complete the above code?
(tmp_max = cur_max)
break
continue
(cur_max = tmp_max)
Correct Answer: D — (cur_max = tmp_max)
Explanation:
If the tmp_max element is greater than the cur_max element, we make cur_max equal to tmp_max, i.e. (cur_max = tmp_max).
Find the maximum sub-array sum for the given elements. {-2, -1, -3, -4, -1, -2, -1, -5, -4}
-3
5
3
-1
Correct Answer: D — -1
Explanation:
All the elements are negative. So, the maximum sub-array sum will be equal to the largest element. The largest element is -1 and therefore, the maximum sub-array sum is -1.
Find the maximum sub-array sum for the given elements. {2, -1, 3, -4, 1, -2, -1, 5, -4}
3
5
8
6
Correct Answer: B — 5
Explanation:
The maximum sub-array sum is 5.
Given a one-dimensional array of integers, you have to find a sub-array with maximum sum. This is the maximum sub-array sum problem. Which of these methods can be used to solve the problem?
Dynamic programming
Two for loops (naive method)
Divide and conquer
Dynamic programming, naïve method and Divide and conquer methods
Correct Answer: D — Dynamic programming, naïve method and Divide and conquer methods
Explanation:
Dynamic programming, naïve method and Divide and conquer methods can be used to solve the maximum sub array sum problem.
Which of the following lines should be inserted to complete the above code?
arr[row][k] - arr[k + 1][col] + mat[row - 1] * mat[k] * mat[col];
arr[row][k] + arr[k + 1][col] - mat[row - 1] * mat[k] * mat[col];
arr[row][k] + arr[k + 1][col] + mat[row - 1] * mat[k] * mat[col];
arr[row][k] - arr[k + 1][col] - mat[row - 1] * mat[k] * mat[col];
Correct Answer: C — arr[row][k] + arr[k + 1][col] + mat[row - 1] * mat[k] * mat[col];
Explanation:
The line arr[row][k] + arr[k + 1][col] + mat[row - 1] * mat[k] * mat[col] should be inserted to complete the above code.
Consider the brute force implementation in which we find all the possible ways of multiplying the given set of n matrices. What is the time complexity of this implementation?
O(n!)
O(n^{3})
O(n^{2})
Exponential
Correct Answer: D — Exponential
Explanation:
The time complexity of finding all the possible ways of multiplying a set of n matrices is given by (n-1)^{th} Catalan number which is exponential.
Consider the matrices P, Q, R and S which are 20 x 15, 15 x 30, 30 x 5 and 5 x 40 matrices respectively. What is the minimum number of multiplications required to multiply the four matrices?
6050
7500
7750
12000
Correct Answer: C — 7750
Explanation:
The minimum number of multiplications required is 7750.
Consider the matrices P, Q and R which are 10 x 20, 20 x 30 and 30 x 40 matrices respectively. What is the minimum number of multiplications required to multiply the three matrices?
18000
12000
24000
32000
Correct Answer: A — 18000
Explanation:
The minimum number of multiplications are 18000. This is the case when the matrices are parenthesized as (P*Q)*R.
Consider the two matrices P and Q which are 10 x 20 and 20 x 30 matrices respectively. What is the number of multiplications required to multiply the two matrices?
10*20
20*30
10*30
102030
Correct Answer: D — 102030
Explanation:
The number of multiplications required is 102030.
Which of the following is the recurrence relation for the matrix chain multiplication problem where mat[i-1] * mat[i] gives the dimension of the ith matrix?
dp[i,j] = 1 if (i=j dp[i,j] = min{dp[i,k] + dp[k+1,j]})
dp[i,j] = 0 if (i=j dp[i,j] = min{dp[i,k] + dp[k+1,j]})
dp[i,j] = 1 if (i=j dp[i,j] = min{dp[i,k] + dp[k+1,j]} + mat[i-1]*mat[k]*mat[j]).
dp[i,j] = 0 if (i=j dp[i,j] = min{dp[i,k] + dp[k+1,j]} + mat[i-1]*mat[k]*mat[j]).
Correct Answer: D — dp[i,j] = 0 if (i=j dp[i,j] = min{dp[i,k] + dp[k+1,j]} + mat[i-1]*mat[k]*mat[j]).
Explanation:
The recurrence relation is given by:
dp[i,j] = 0 if i=j
(dp[i,j] = min{dp[i,k] + dp[k+1,j]} + mat[i-1]*mat[k]*mat[j]).
Which of the following methods can be used to solve the matrix chain multiplication problem?
Dynamic programming
Brute force
Recursion
Dynamic Programming, Brute force, Recursion
Correct Answer: D — Dynamic Programming, Brute force, Recursion
Explanation:
Dynamic Programming, Brute force, Recursion methods can be used to solve the matrix chain multiplication problem.
Which of the following lines completes the above code?
strrev(str2)
str2 = str1
len2 = strlen(str2)
strlen(str2)
Correct Answer: A — strrev(str2)
Explanation:
To find the longest palindromic subsequence, we need to reverse the copy of the string, which is done by strrev.
Longest palindromic subsequence is an example of ______________
Greedy algorithm
2D dynamic programming
1D dynamic programming
Divide and conquer
Correct Answer: B — 2D dynamic programming
Explanation:
Longest palindromic subsequence is an example of 2D dynamic programming.
For every non-empty string, the length of the longest palindromic subsequence is at least one.
True
False
Correct Answer: A — True
Explanation:
A single character of any string can always be considered as a palindrome and its length is one.
What is the time complexity of the brute force algorithm used to find the length of the longest palindromic subsequence?
O(1)
O(2^{n})
O(n)
O(n^{2})
Correct Answer: B — O(2^{n})
Explanation:
In the brute force algorithm, all the subsequences are found and the length of the longest palindromic subsequence is calculated. This takes exponential time.
What is the length of the longest palindromic subsequence for the string "ababcdabba"?
6
7
8
9
Correct Answer: B — 7
Explanation:
The longest palindromic subsequence is "abbabba" and its length is 7.
