Dynamic Programming in Data Structures MCQ question and answer with solution

#include<stdio.h>
#include<string.h>
int get_min(int a, int b)
{
      if(a < b)
        return a;
      return b;
}
int edit_distance(char *s1, char *s2)
{
     int len1,len2,i,j,min;
     len1 = strlen(s1);
     len2 = strlen(s2);
     int arr[len1 + 1][len2 + 1];
     for(i = 0;i <= len1; i++)
       arr[i][0] = i;
     for(i = 0; i <= len2; i++)
       arr[0][i] = i;
     for(i = 1; i <= len1; i++)
     {
         for(j = 1; j <= len2; j++)
         {
               min = get_min(arr[i-1][j],arr[i][j-1]) + 1;
               if(s1[i - 1] == s2[j - 1])
               {
                    if(arr[i-1][j-1] < min)
                       min = arr[i-1][j-1];
               }
               else
               {
                     if(arr[i-1][j-1] + 1 < min)
                         min = arr[i-1][j-1] + 1;
               }
                arr[i][j] = min;
         }
     }
     return arr[len1][len2];
}
int main()
{
     char s1[] = "abcd", s2[] = "defg";
     int ans = edit_distance(s1, s2);
     printf("%d",ans);
     return 0;
}

#include<stdio.h>
#include<limits.h>
int rod_cut(int *prices, int len)
{
      int max_val[len + 1];
      int i,j,tmp_price,tmp_idx; 
      max_val[0] = 0;
      for(i = 1; i <= len; i++)
      {
	   int tmp_max = INT_MIN; // minimum value an integer can hold
	   for(j = 1; j <= i; j++)
	   {
	         tmp_idx = i - j;
                //subtract 1 because index of prices starts from 0
	         tmp_price = prices[j-1] + max_val[tmp_idx];
	         if(tmp_price > tmp_max)
		    tmp_max = tmp_price;
	   }
	   max_val[i] = tmp_max;
     }
     return max_val[len];
}
int main()
{
      int prices[]={2, 5, 6, 9, 9, 17, 17, 18, 20, 22},len_of_rod = 5;
      int ans = rod_cut(prices, len_of_rod);
      printf("%d",ans);
      return 0;
}

#include<stdio.h>
#include<string.h>
int count_bool_parenthesization(char *sym, char *op)
{
     int str_len = strlen(sym);
     int True[str_len][str_len],False[str_len][str_len];
     int row,col,length,l;
     for(row = 0, col = 0; row < str_len; row++,col++)
     {
         if(sym[row] == 'T')
         {
             True[row][col] = 1;
             False[row][col] = 0;
         }
         else
         {
             True[row][col] = 0;
             False[row][col] = 1;
         }
     }
     for(length = 1; length < str_len; length++)
     {
         for(row = 0, col = length; col < str_len; col++, row++)
         {
             True[row][col] = 0;
             False[row][col] = 0;
             for(l = 0; l < length; l++)
             {
                 int pos = row + l;
                 int t_row_pos = True[row][pos] + False[row][pos];
                 int t_pos_col = True[pos+1][col] + False[pos+1][col];
                 if(op[pos] == '|')
                 {
                     False[row][col] += False[row][pos] * False[pos+1][col];
                     True[row][col] += t_row_pos * t_pos_col - False[row][pos] * False[pos+1][col];
                 }
                 if(op[pos] == '&')
                 {
                     True[row][col] += True[row][pos] * True[pos+1][col];
                     False[row][col] += t_row_pos * t_pos_col - True[row][pos] * True[pos+1][col];
                 }
                 if(op[pos] == '^')
                 {
                     True[row][col] += True[row][pos] * False[pos+1][col] 
                                       + False[row][pos] * True[pos + 1][col];
                     False[row][col] += True[row][pos] * True[pos+1][col] 
                                       + False[row][pos] * False[pos+1][col];
                 }
             }
         }
     }
     return True[0][str_len-1];
}
int main()
{
     char sym[] = "TTTT";
     char op[] = "|^^";
     int ans = count_bool_parenthesization(sym,op);
     printf("%d",ans);
     return 0;
}

#include<stdio.h>
int main()
{
     int arr[1000] = {-2, -5, 6, -2, 3, -1, 0,-5, 6}, len = 9;
     int cur_max, tmp_max, strt_idx, sub_arr_idx;
     cur_max = arr[0];
     for(strt_idx = 0; strt_idx < len; strt_idx++)
     {
	   tmp_max = 0;
	   for(sub_arr_idx = strt_idx; sub_arr_idx < len; sub_arr_idx++)
	   {
	        tmp_max += arr[sub_arr_idx];
	        if(tmp_max > cur_max)
	        cur_max = tmp_max;
	   }
     }
     printf("%d",cur_max);
     return 0;
}

#include<stdio.h>
int longest_inc_sub(int *arr, int len)
{
      int i, j, tmp_max;
      int LIS[len];  // array to store the lengths of the longest increasing subsequence 
      LIS[0]=1;
      for(i = 1; i < len; i++)
      { 
           tmp_max = 0;
	   for(j = 0; j < i; j++)
	   {
	        if(arr[j] < arr[i])
	        {
		    if(LIS[j] > tmp_max)
		     ___________;  
	        }
           }
	   LIS[i] = tmp_max + 1;
      }
      int max = LIS[0];
      for(i = 0; i < len; i++)
	if(LIS[i] > max)
	   max = LIS[i];
      return max;
}
int main()
{
      int arr[] = {10,22,9,33,21,50,41,60,80}, len = 9;
      int ans = longest_inc_sub(arr, len);
      printf("%d",ans);
      return 0;
}

1. int fibo(int n)
2.	int fibo_terms[100000]  //arr to store the fibonacci numbers
3.	fibo_terms[0] = 0
4.	fibo_terms[1] = 1
5.		
6.	for i: 2 to n
7.		fibo_terms[i] = fibo_terms[i - 1] + fibo_terms[i - 2]
8.	
9.	return fibo_terms[n]

#include<stdio.h>
int max_num(int a,int b)
{
     if(a> b)
	return a;
     return b;
}
int maximum_subarray_sum(int *arr, int len)
{
     int sum[len], idx;
     sum[0] = arr[0];
     for(idx = 1; idx < len; idx++)
	sum[idx] = max_num(sum[idx - 1] + arr[idx], arr[idx]);
     int mx = sum[0];
     for(idx = 0; idx < len; idx++)
	if(sum[idx] > mx)
	   mx =sum[idx];
     return mx;
}
int main()
{
     int arr[] = {-20, 23, 10, 3, -10, 11, -5},len = 7;
     int ans = maximum_subarray_sum(arr, len);
     printf("%d",ans);
     return 0;
}