tech-interview-handbook/algorithms/dynamic-programming.md

Dynamic Programming

• Given a flight itinerary consisting of starting city, destination city, and ticket price (2D list) - find the optimal price flight path to get from start to destination. (A variation of Dynamic Programming Shortest Path)
• Given some coin denominations and a target value M, return the coins combination with the minimum number of coins.
  • Time complexity: O(MN), where N is the number of distinct type of coins.
  • Space complexity: O(M).
• Given a set of numbers in an array which represent a number of consecutive days of Airbnb reservation requested, as a host, pick the sequence which maximizes the number of days of occupancy, at the same time, leaving at least a 1-day gap in-between bookings for cleaning.
  • The problem reduces to finding the maximum sum of non-consecutive array elements.
  • E.g.

    // [5, 1, 1, 5] => 10
    The above array would represent an example booking period as follows -
    // Dec 1 - 5
    // Dec 5 - 6
    // Dec 6 - 7
    // Dec 7 - 12
    
    The answer would be to pick Dec 1-5 (5 days) and then pick Dec 7-12 for a total of 10 days of
    occupancy, at the same time, leaving at least 1-day gap for cleaning between reservations.
    
    Similarly,
    // [3, 6, 4] => 7
    // [4, 10, 3, 1, 5] => 15
    

• Given a list of denominations (e.g., [1, 2, 5] means you have coins worth $1, $2, and $5) and a target number k, find all possible combinations, if any, of coins in the given denominations that add up to k. You can use coins of the same denomination more than once.
• You are climbing a flight of stairs. It takes n steps to reach to the top. Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top? E.g. Input: 3, Output: 3. Explanation: [1, 1, 1], [1, 2], [2, 1].