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Welcome to the Dynamic Programming MCQs Page

Dive deep into the fascinating world of Dynamic Programming with our comprehensive set of Multiple-Choice Questions (MCQs). This page is dedicated to exploring the fundamental concepts and intricacies of Dynamic Programming, a crucial aspect of Data Structures and Algorithms. In this section, you will encounter a diverse range of MCQs that cover various aspects of Dynamic Programming, from the basic principles to advanced topics. Each question is thoughtfully crafted to challenge your knowledge and deepen your understanding of this critical subcategory within Data Structures and Algorithms.

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Check out the MCQs below to embark on an enriching journey through Dynamic Programming. Test your knowledge, expand your horizons, and solidify your grasp on this vital area of Data Structures and Algorithms.

Note: Each MCQ comes with multiple answer choices. Select the most appropriate option and test your understanding of Dynamic Programming. You can click on an option to test your knowledge before viewing the solution for a MCQ. Happy learning!

Dynamic Programming MCQs | Page 19 of 22

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Q181.
Given an array, check if the array can be divided into two subsets such that the sum of elements of the two subsets is equal. This is the balanced partition problem. Which of the following methods can be used to solve the balanced partition problem?
Discuss
Answer: (d).All of the mentioned
Q182.
In which of the following cases, it is not possible to have two subsets with equal sum?
Discuss
Answer: (c).When the sum of elements is odd
Q183.
What is the time complexity of the brute force algorithm used to solve the balanced partition problem?
Discuss
Answer: (d).O(2^n)
Q184.
Consider a variation of the balanced partition problem in which we find two subsets such that |S1 โ€“ S2| is minimum. Consider the array {1, 2, 3, 4, 5}. Which of the following pairs of subsets is an optimal solution for the above problem?
Discuss
Answer: (d).{5, 3} & {4, 2, 1}
Q185.
Consider the following code.
Which of the following lines should be inserted to complete the below code?
#include<stdio.h>
int balanced_partition(int *arr, int len)
{
     int sm = 0, i, j;
     for(i = 0;i < len; i++)
      sm += arr[i];
     if(sm % 2 != 0)
        return 0;
     int ans[sm/2 + 1][len + 1];
     for(i = 0; i <= len; i++)
      ans[0][i] = 1;
     for(i = 1; i <= sm/2; i++)
      ans[i][0] = 0;
     for(i = 1; i <= sm/2; i++)
     {
         for(j = 1;j <= len; j++)
         {
             ans[i][j] = ans[i][j-1];
             if(i >= arr[j - 1])
                ans[i][j] = _______________;
         }
     }
     return ans[sm/2][len];
}
int main()
{
     int arr[] = {3, 4, 5, 6, 7, 1}, len = 6;
     int ans = balanced_partition(arr,len);
     if(ans == 0)
       printf("false");
     else
       printf("true");
     return 0;
}

Discuss
Answer: (c).ans[i][j] || ans[i โ€“ arr[j โ€“ 1]][j โ€“ 1].
Q186.
What is the output of the following code?
#include<stdio.h>
int balanced_partition(int *arr, int len)
{
      int sm = 0, i, j;
      for(i = 0;i < len; i++)
      sm += arr[i];
      if(sm % 2 != 0)
        return 0;
      int ans[sm/2 + 1][len + 1];
      for(i = 0; i <= len; i++)
      ans[0][i] = 1;
      for(i = 1; i <= sm/2; i++)
      ans[i][0] = 0;
      for(i = 1; i <= sm/2; i++)
      {
          for(j = 1;j <= len; j++)
          {
              ans[i][j] = ans[i][j-1];
              if(i >= arr[j - 1])
                ans[i][j] = ans[i][j] || ans[i - arr[j - 1]][j - 1];
          }
      }
      return ans[sm/2][len];
}
int main()
{
      int arr[] = {3, 4, 5, 6, 7, 1}, len = 6;
      int ans = balanced_partition(arr,len);
      if(ans == 0)
         printf("false");
      else
         printf("true");
      return 0;
}
Discuss
Answer: (a).True
Q187.
What is the value stored in ans[3][3] when the following code is executed?
#include<stdio.h>
int balanced_partition(int *arr, int len)
{
     int sm = 0, i, j;
     for(i = 0;i < len; i++)
      sm += arr[i];
     if(sm % 2 != 0)
        return 0;
     int ans[sm/2 + 1][len + 1];
     for(i = 0; i <= len; i++)
      ans[0][i] = 1;
     for(i = 1; i <= sm/2; i++)
      ans[i][0] = 0;
     for(i = 1; i <= sm/2; i++)
     {
         for(j = 1;j <= len; j++)
         {
             ans[i][j] = ans[i][j-1];
             if(i >= arr[j - 1])
                ans[i][j] = ans[i][j] || ans[i - arr[j - 1]][j - 1];
         }
     }
     return ans[sm/2][len];
}
int main()
{
     int arr[] = {3, 4, 5, 6, 7, 1}, len = 6;
     int ans = balanced_partition(arr,len);
     if(ans == 0)
        printf("false");
     else
        printf("true");
     return 0;
}
Discuss
Answer: (b).1
Q188.
What is the sum of each of the balanced partitions for the array {5, 6, 7, 10, 3, 1}?
Discuss
Answer: (a).16
Q189.
What is the output of the following code?
#include<stdio.h>
int balanced_partition(int *arr, int len)
{
     int sm = 0, i, j;
     for(i = 0;i < len; i++)
      sm += arr[i];
     if(sm % 2 != 0)
        return 0;
     int ans[sm/2 + 1][len + 1];
     for(i = 0; i <= len; i++)
      ans[0][i] = 1;
     for(i = 1; i <= sm/2; i++)
      ans[i][0] = 0;
     for(i = 1; i <= sm/2; i++)
     {
         for(j = 1;j <= len; j++)
         {
             ans[i][j] = ans[i][j-1];
             if(i >= arr[j - 1])
                 ans[i][j] = ans[i][j] || ans[i - arr[j - 1]][j - 1];
         }
     }
     return ans[sm/2][len];
}
int main()
{
     int arr[] = {5, 6, 7, 10, 3, 1}, len = 6;
     int ans = balanced_partition(arr,len);
     if(ans == 0)
       printf("false");
     else
       printf("true");
     return 0;
}
Discuss
Answer: (a).True
Q190.
What is the output of the following code?
#include<stdio.h>
int balanced_partition(int *arr, int len)
{
     int sm = 0, i, j;
     for(i = 0;i < len; i++)
      sm += arr[i];
     if(sm % 2 != 0)
        return 0;
     int ans[sm/2 + 1][len + 1];
     for(i = 0; i <= len; i++)
      ans[0][i] = 1;
     for(i = 1; i <= sm/2; i++)
      ans[i][0] = 0;
     for(i = 1; i <= sm/2; i++)
     {
         for(j = 1;j <= len; j++)
         {
             ans[i][j] = ans[i][j-1];
             if(i >= arr[j - 1])
                 ans[i][j] = ans[i][j] || ans[i - arr[j - 1]][j - 1];
         }
     }
     return ans[sm/2][len];
}
int main()
{
     int arr[] = {1, 2, 3, 4, 5, 6, 7, 8, 9}, len = 9;
     int ans = balanced_partition(arr,len);
     if(ans == 0)
       printf("false");
     else
       printf("true");
     return 0;
}
Discuss
Answer: (b).False

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