What are some common dynamic programming interview questions in C++?

What are some common dynamic programming interview questions in C++?

Some common questions include:

1. Fibonacci sequence using dynamic programming.
2. Longest Common Subsequence.
3. Coin Change Problem.
4. 0/1 Knapsack Problem.
5. Minimum Edit Distance.

Can you explain the 0/1 Knapsack Problem?

Sure! The 0/1 Knapsack Problem involves a knapsack with a weight limit and a set of items, each with a weight and value. The goal is to maximize the total value in the knapsack without exceeding the weight limit.

How would you implement it in C++?

You can use a 2D array to store the maximum value for each item and weight combination. Here's a simple implementation:

int knapsack(int W, int wt[], int val[], int n) {
    int K[n+1][W+1];
    for (int i = 0; i <= n; i++) {
        for (int w = 0; w <= W; w++) {
            if (i == 0 || w == 0)
                K[i][w] = 0;
            else if (wt[i-1] <= w)
                K[i][w] = max(val[i-1] + K[i-1][w-wt[i-1]], K[i-1][w]);
            else
                K[i][w] = K[i-1][w];
        }
    }
    return K[n][W];
}

This function calculates the maximum value that can be carried in the knapsack.

What are some optimizations for this problem?

You can optimize the space complexity from O(nW) to O(W) by using a 1D array and iterating backwards when updating the array. This way, you only keep track of the current and previous row.