Dynamic Programming Questions Medium
Dynamic Programming can be used to solve the Rod Cutting problem by breaking it down into smaller subproblems and solving them in a bottom-up manner.
The Rod Cutting problem involves finding the maximum value obtainable by cutting a rod of length n into smaller pieces, each with a certain value.
To solve this problem using Dynamic Programming, we can create an array dp[] of size n+1, where dp[i] represents the maximum value obtainable by cutting a rod of length i.
We start by initializing dp[0] to 0, as there is no value for a rod of length 0.
Then, for each length i from 1 to n, we iterate through all possible cuts j from 1 to i and calculate the maximum value obtainable by either keeping the rod of length i-j as it is or cutting it further.
The formula to calculate dp[i] is:
dp[i] = max(dp[i], price[j] + dp[i-j])
Here, price[j] represents the value of the rod of length j.
By iteratively calculating dp[i] for all lengths i, we can find the maximum value obtainable for the given rod length n.
Finally, the value stored in dp[n] will be the maximum value obtainable by cutting the rod.