# Data Structure Questions and Answers – Longest Palindromic Subsequence

This set of Data Structure Multiple Choice Questions & Answers (MCQs) focuses on “Longest Palindromic Subsequence”.

1. Which of the following methods can be used to solve the longest palindromic subsequence problem?
a) Dynamic programming
b) Recursion
c) Brute force
d) Dynamic programming, Recursion, Brute force

Explanation: Dynamic programming, Recursion, Brute force can be used to solve the longest palindromic subsequence problem.

2. Which of the following is not a palindromic subsequence of the string “ababcdabba”?
a) abcba
b) abba
c) abbbba

Explanation: ‘adba’ is not a palindromic sequence.

3. For which of the following, the length of the string is not equal to the length of the longest palindromic subsequence?
a) A string that is a palindrome
b) A string of length one
c) A string that has all the same letters(e.g. aaaaaa)
d) Some strings of length two

Explanation: A string of length 2 for eg: ab is not a palindrome.

4. What is the length of the longest palindromic subsequence for the string “ababcdabba”?
a) 6
b) 7
c) 8
d) 9

Explanation: The longest palindromic subsequence is “abbabba” and its length is 7.

5. What is the time complexity of the brute force algorithm used to find the length of the longest palindromic subsequence?
a) O(1)
b) O(2n)
c) O(n)
d) O(n2)

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.
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6. For every non-empty string, the length of the longest palindromic subsequence is at least one.
a) True
b) False

Explanation: A single character of any string can always be considered as a palindrome and its length is one.

7. Longest palindromic subsequence is an example of ______________
a) Greedy algorithm
b) 2D dynamic programming
c) 1D dynamic programming
d) Divide and conquer

Explanation: Longest palindromic subsequence is an example of 2D dynamic programming.

8. Consider the following code:

```#include<stdio.h>
#include<string.h>
int max_num(int a, int b)
{
if(a > b)
return a;
return b;
}
int lps(char *str1)
{
int i,j,len;
len = strlen(str1);
char str2[len + 1];
strcpy(str2, str1);
______________;
int arr[len + 1][len + 1];
for(i = 0; i <= len; i++)
arr[i][0] = 0;
for(i = 0; i <= len; i++)
arr[0][i] = 0;
for(i = 1; i <= len; i++)
{
for(j = 1; j <= len; j++)
{
if(str1[i-1] == str2[j - 1])
arr[i][j] = 1 + arr[i - 1][j - 1];
else
arr[i][j] = max_num(arr[i - 1][j], arr[i][j - 1]);
}
}
return arr[len][len];
}
int main()
{
char str1[] = "ababcdabba";
int ans = lps(str1);
printf("%d",ans);
return 0;
}```

Which of the following lines completes the above code?
a) strrev(str2)
b) str2 = str1
c) len2 = strlen(str2)
d) strlen(str2)

Explanation: To find the longest palindromic subsequence, we need to reverse the copy of the string, which is done by strrev.

9. What is the time complexity of the following dynamic programming implementation to find the longest palindromic subsequence where the length of the string is n?

```#include<stdio.h>
#include<string.h>
int max_num(int a, int b)
{
if(a > b)
return a;
return b;
}
int lps(char *str1)
{
int i,j,len;
len = strlen(str1);
char str2[len + 1];
strcpy(str2, str1);
strrev(str2);
int arr[len + 1][len + 1];
for(i = 0; i <= len; i++)
arr[i][0] = 0;
for(i = 0; i <= len; i++)
arr[0][i] = 0;
for(i = 1; i <= len; i++)
{
for(j = 1; j <= len; j++)
{
if(str1[i-1] == str2[j - 1])
arr[i][j] = 1 + arr[i - 1][j - 1];
else
arr[i][j] = max_num(arr[i - 1][j], arr[i][j - 1]);
}
}
return arr[len][len];
}
int main()
{
char str1[] = "ababcdabba";
int ans = lps(str1);
printf("%d",ans);
return 0;
}```

a) O(n)
b) O(1)
c) O(n2)
d) O(2)

Explanation: The time complexity of the above dynamic programming implementation to find the longest palindromic subsequence is O(n2).

10. What is the space complexity of the following dynamic programming implementation to find the longest palindromic subsequence where the length of the string is n?

```#include<stdio.h>
#include<string.h>
int max_num(int a, int b)
{
if(a > b)
return a;
return b;
}
int lps(char *str1)
{
int i,j,len;
len = strlen(str1);
char str2[len + 1];
strcpy(str2, str1);
strrev(str2);
int arr[len + 1][len + 1];
for(i = 0; i <= len; i++)
arr[i][0] = 0;
for(i = 0; i <= len; i++)
arr[0][i] = 0;
for(i = 1; i <= len; i++)
{
for(j = 1; j <= len; j++)
{
if(str1[i-1] == str2[j - 1])
arr[i][j] = 1 + arr[i - 1][j - 1];
else
arr[i][j] = max_num(arr[i - 1][j], arr[i][j - 1]);
}
}
return arr[len][len];
}
int main()
{
char str1[] = "ababcdabba";
int ans = lps(str1);
printf("%d",ans);
return 0;
}```

a) O(n)
b) O(1)
c) O(n2)
d) O(2)

Explanation: The space complexity of the above dynamic programming implementation to find the longest palindromic subsequence is O(n2).

11. What is the value stored in arr[3][3] when the following code is executed?

```#include<stdio.h>
#include<string.h>
int max_num(int a, int b)
{
if(a > b)
return a;
return b;
}
int lps(char *str1)
{
int i,j,len;
len = strlen(str1);
char str2[len + 1];
strcpy(str2, str1);
strrev(str2);
int arr[len + 1][len + 1];
for(i = 0; i <= len; i++)
arr[i][0] = 0;
for(i = 0; i <= len; i++)
arr[0][i] = 0;
for(i = 1; i <= len; i++)
{
for(j = 1; j <= len; j++)
{
if(str1[i-1] == str2[j - 1])
arr[i][j] = 1 + arr[i - 1][j - 1];
else
arr[i][j] = max_num(arr[i - 1][j], arr[i][j - 1]);
}
}
return arr[len][len];
}
int main()
{
char str1[] = "ababcdabba";
int ans = lps(str1);
printf("%d",ans);
return 0;
}```

a) 2
b) 3
c) 4
d) 5

Explanation: The value stored in arr[3][3] when the above code is executed is 2.

12. What is the output of the following code?

```#include<stdio.h>
#include<string.h>
int max_num(int a, int b)
{
if(a > b)
return a;
return b;
}
int lps(char *str1)
{
int i,j,len;
len = strlen(str1);
char str2[len + 1];
strcpy(str2, str1);
strrev(str2);
int arr[len + 1][len + 1];
for(i = 0; i <= len; i++)
arr[i][0] = 0;
for(i = 0; i <= len; i++)
arr[0][i] = 0;
for(i = 1; i <= len; i++)
{
for(j = 1; j <= len; j++)
{
if(str1[i-1] == str2[j - 1])
arr[i][j] = 1 + arr[i - 1][j - 1];
else
arr[i][j] = max_num(arr[i - 1][j], arr[i][j - 1]);
}
}
return arr[len][len];
}
int main()
{
char str1[] = "abcd";
int ans = lps(str1);
printf("%d",ans);
return 0;
}```

a) 0
b) 1
c) 2
d) 3

Explanation: The program prints the length of the longest palindromic subsequence, which is 1.

13. What is the output of the following code?

```#include<stdio.h>
#include<string.h>
int max_num(int a, int b)
{
if(a > b)
return a;
return b;
}
int lps(char *str1)
{
int i,j,len;
len = strlen(str1);
char str2[len + 1];
strcpy(str2, str1);
strrev(str2);
int arr[len + 1][len + 1];
for(i = 0; i <= len; i++)
arr[i][0] = 0;
for(i = 0; i <= len; i++)
arr[0][i] = 0;
for(i = 1; i <= len; i++)
{
for(j = 1; j <= len; j++)
{
if(str1[i-1] == str2[j - 1])
arr[i][j] = 1 + arr[i - 1][j - 1];
else
arr[i][j] = max_num(arr[i - 1][j], arr[i][j - 1]);
}
}
return arr[len][len];
}
int main()
{
char str1[] = "abdgkagdjbccbba";
int ans = lps(str1);
printf("%d",ans);
return 0;
}```

a) 5
b) 7
c) 9
d) 11

Explanation: The program prints the length of the longest palindromic subsequence, which is 9.

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