Maximise number of cuts in a rod if it can be cut only in given 3 sizes

Given a rod of length** N** meters, and the rod can be cut in only 3 sizes **A**, **B** and **C**. The task is to maximizes the number of cuts in rod. If it is impossible to make cut then print **-1**.**Examples:**

Input:N = 17, A = 10, B = 11, C = 3Output:3Explanation:

The maximum cut can be obtain after making 2 cut of length 3 and one cut of length 11.Input:N = 10, A = 9, B = 7, C = 11Output:-1Explanation:

It is impossible to make any cut so output will be -1.

**Naive Approach: **

- Let us assume x, y, and z numbers of rods of sizes A, B, and C respectively are cut. And this can be written as a linear equation: x*A + y*B + z*C = N
- Now, simply iterate over all possible value of x and y and compute z using (N – x*A + y*B) / c.
- If x*A + y*B + z*C = N, then it is one of the possible answers.
- Finally compute the maximum value of x + y + z.

**Time Complexity:** O(N^{2})**Auxiliary Space:** O(1)**Efficient Approach: **The problem can be solve using Dynamic Programming.

- Create a
**dp[]**array of size**N**and initialise all value to**INT_MIN**. - Set dp[0] = 0, as it will be base case for our approach.
- Iterate from
**1**to**N**and check if it is possible to make a cut of any of possible length i.e A, B and C, and update**dp[i]**to minimum of all.