misc: restructure contents

contents/algorithms/dynamic-programming.md

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+---
+id: dynamic-programming
+title: 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]`.