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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 9 of 22

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Discuss
Answer: (b).You are studying for an exam and you have to study N questions. The questions take {t1, t2, t3,โ€ฆ., tn} time(in hours) and carry {m1, m2, m3,โ€ฆ., mn} marks. You can study for a maximum of T hours. You can either study a question or leave it. Choose the questions in such a way that your score is maximized
Q82.
What is the time complexity of the brute force algorithm used to solve the Knapsack problem?
Discuss
Answer: (c).O(2^n)
Q83.
The 0-1 Knapsack problem can be solved using Greedy algorithm.
Discuss
Answer: (b).False
Q84.
Consider the following dynamic programming implementation of the Knapsack problem.
Which of the following lines completes the below code?
#include<stdio.h>
int find_max(int a, int b)
{
      if(a > b)
         return a;
      return b;
}
int knapsack(int W, int *wt, int *val,int n)
{
     int ans[n + 1][W + 1];
     int itm,w;
     for(itm = 0; itm <= n; itm++)
         ans[itm][0] = 0;
     for(w = 0;w <= W; w++)
        ans[0][w] = 0;
     for(itm = 1; itm <= n; itm++)
     {
          for(w = 1; w <= W; w++)
          {
               if(wt[itm - 1] <= w)
                  ans[itm][w] = ______________;
               else
                  ans[itm][w] = ans[itm - 1][w];
          }
     }
     return ans[n][W];
}
int main()
{
     int w[] = {10,20,30}, v[] = {60, 100, 120}, W = 50;
     int ans = knapsack(W, w, v, 3);
     printf("%d",ans);
     return 0;
}

Discuss
Answer: (a).find_max(ans[itm โ€“ 1][w โ€“ wt[itm โ€“ 1]] + val[itm โ€“ 1], ans[itm โ€“ 1][w])
Q85.
What is the output of the following code?
#include<stdio.h>
int find_max(int a, int b)
{
      if(a > b)
        return a;
      return b;
}
int knapsack(int W, int *wt, int *val,int n)
{
     int ans[n + 1][W + 1];
     int itm,w;
     for(itm = 0; itm <= n; itm++)
         ans[itm][0] = 0;
     for(w = 0;w <= W; w++)
         ans[0][w] = 0;
     for(itm = 1; itm <= n; itm++)
     {
          for(w = 1; w <= W; w++)
          {
               if(wt[itm - 1] <= w)
                  ans[itm][w] = find_max(ans[itm - 1][w - wt[itm - 1]] + val[itm - 1], ans[itm - 1][w]);
               else
                   ans[itm][w] = ans[itm - 1][w];
          }
     }
     return ans[n][W];
}
int main()
{
     int w[] = {10,20,30}, v[] = {60, 100, 120}, W = 50;
     int ans = knapsack(W, w, v, 3);
     printf("%d",ans);
     return 0;
}
Discuss
Answer: (d).220
Q86.
Which of the following methods can be used to solve the matrix chain multiplication problem?
Discuss
Answer: (d).All of the mentioned
Discuss
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].
Q88.
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?
Discuss
Answer: (d).10*20*30
Q89.
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?
Discuss
Answer: (a).18000
Q90.
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?
Discuss
Answer: (c).7750

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