Dynamic Programming in Data Structures MCQ question and answer with solution

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11.
What is the time complexity of the following dynamic programming implementation of the longest common subsequence problem where length of one string is "m" and the length of the other string is "n"?
#include<stdio.h>
#include<string.h>
int max_num(int a, int b)
{
      if(a > b)
        return a;
      return b;
}
int lcs(char *str1, char *str2)
{
      int i,j,len1,len2;
      len1 = strlen(str1);
      len2 = strlen(str2);
      int arr[len1 + 1][len2 + 1];
      for(i = 0; i <= len1; i++)
          arr[i][0] = 0;
      for(i = 0; i <= len2; i++)
          arr[0][i] = 0;
      for(i = 1; i <= len1; i++)
      {
            for(j = 1; j <= len2; 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[len1][len2];
}
int main()
{
      char str1[] = " abcedfg", str2[] = "bcdfh";
      int ans = lcs(str1,str2);
      printf("%d",ans);
      return 0;
}

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14.
Consider the following code:
#include<stdio.h>
int get_min(int a, int b)
{
     if(a<b)
        return a;
     return b;
}
int minimum_time_required(int reach[][3],int spent[][4], int *entry, int *exit, int n)
{
     int t1[n], t2[n],i;
     t1[0] = entry[0] + spent[0][0];
     t2[0] = entry[1] + spent[1][0];
     for(i = 1; i < n; i++)
     {
         t1[i] = get_min(t1[i-1]+spent[0][i], t2[i-1]+reach[1][i-1]+spent[0][i]);
         __________;
     }
     return get_min(t1[n-1]+exit[0], t2[n-1]+exit[1]);
}
Which of the following lines should be inserted to complete the above code?

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17.
Which of the following errors will occur when the below code is executed?
#include<stdio.h>
int cat_number(int n)
{
     int i,j,arr[n],k;
     arr[0] = 1;
     for(i = 1; i < n; i++)
     {
         arr[i] = 0;
         for(j = 0,k = i - 1; j < i; j++,k--)
           arr[i] += arr[j] * arr[k];
     }
     return arr[n-1];
}
int main()
{
     int ans, n = 100;
     ans = cat_number(n);
     printf("%d\n",ans);
     return 0;
}

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18.
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;
}

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19.
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?

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