What is the space complexity of the following dynamic programming implementation of the rod cutting problem?
#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<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;
}A. O(1)
B. O(n)
C. O(n2)
D. O(2n)
Answer: Option B
This Question Belongs to Data Structure >> Dynamic Programming In Data Structures
What is the main principle behind Dynamic Programming (DP)?
A. Recursion with memoization.
B. Greedy approach.
C. Divide and conquer.
D. Overlapping subproblems and optimal substructure.
Which of the following problems can be solved using Dynamic Programming?
A. Binary Search
B. Depth-First Search
C. Longest Common Subsequence
D. Quick Sort
What is the key advantage of using Dynamic Programming over plain recursion?
A. It makes the code simpler.
B. It reduces the time complexity by storing results of subproblems.
C. It uses more memory.
D. It makes the code simpler.
In the context of Dynamic Programming, what does the term "memoization" refer to?
A. Using a stack to manage function calls.
B. A method for dividing problems.
C. Storing intermediate results to avoid redundant calculations.
D. A technique to speed up sorting.
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