# Coding Interviews: Dynamic Programming

Given a string s, partition s such that every substring of the partition is a palindrome.

Return *the ***minimum*** cuts needed for a palindrome partitioning of* s.

Given an integer array nums, return *the length of the longest ***strictly increasing subsequence**.

Given n non-negative integers representing an elevation map where the width of each bar is 1, compute how much water it can trap after raining.

You are given n balloons, indexed from 0 to n - 1. Each balloon is painted with a number on it represented by an array nums. You are asked to burst all the balloons.

If you burst the ith balloon, you will get nums[i - 1] * nums[i] * nums[i + 1] coins. If i - 1 or i + 1 goes out of bounds of the array, then treat it as if there is a balloon with a 1 painted on it.

Return *the maximum coins you can collect by bursting the balloons wisely*.

The demons had captured the princess and imprisoned her in **the bottom-right corner** of a dungeon. The dungeon consists of m x n rooms laid out in a 2D grid. Our valiant knight was initially positioned in **the top-left room** and must fight his way through dungeon to rescue the princess.

The knight has an initial health point represented by a positive integer. If at any point his health point drops to 0 or below, he dies immediately.

Some of the rooms are guarded by demons (represented by negative integers), so the knight loses health upon entering these rooms; other rooms are either empty (represented as 0) or contain magic orbs that increase the knight's health (represented by positive integers).

To reach the princess as quickly as possible, the knight decides to move only **rightward** or **downward** in each step.

Return *the knight's minimum initial health so that he can rescue the princess*.

**Note** that any room can contain threats or power-ups, even the first room the knight enters and the bottom-right room where the princess is imprisoned.

A **path** in a binary tree is a sequence of nodes where each pair of adjacent nodes in the sequence has an edge connecting them. A node can only appear in the sequence **at most once**. Note that the path does not need to pass through the root.

The **path sum** of a path is the sum of the node's values in the path.

Given the root of a binary tree, return *the maximum ***path sum*** of any ***non-empty*** path*.

You are given an integer array cost where cost[i] is the cost of ith step on a staircase. Once you pay the cost, you can either climb one or two steps.

You can either start from the step with index 0, or the step with index 1.

Return *the minimum cost to reach the top of the floor*.

Given an input string s and a pattern p, implement regular expression matching with support for '.' and '*' where:

'.' Matches any single character.

'*' Matches zero or more of the preceding element.

The matching should cover the **entire** input string (not partial).

Given a rows x cols binary matrix filled with 0's and 1's, find the largest rectangle containing only 1's and return *its area*.

You are given an integer array coins representing coins of different denominations and an integer amount representing a total amount of money.

Return *the fewest number of coins that you need to make up that amount*. If that amount of money cannot be made up by any combination of the coins, return -1.

You may assume that you have an infinite number of each kind of coin.

There is a robot on an m x n grid. The robot is initially located at the **top-left corner** (i.e., grid[0][0]). The robot tries to move to the **bottom-right corner** (i.e., grid[m - 1][n - 1]). The robot can only move either down or right at any point in time.

Given the two integers m and n, return *the number of possible unique paths that the robot can take to reach the bottom-right corner*.

The thief has found himself a new place for his thievery again. There is only one entrance to this area, called root.

Besides the root, each house has one and only one parent house. After a tour, the smart thief realized that all houses in this place form a binary tree. It will automatically contact the police if **two directly-linked houses were broken into on the same night**.

Given the root of the binary tree, return *the maximum amount of money the thief can rob ***without alerting the police**.

Given a string s, return *the longest* *palindromicsubstring*in s.

Given an input string (s) and a pattern (p), implement wildcard pattern matching with support for '?' and '*' where:

'?' Matches any single character.

'*' Matches any sequence of characters (including the empty sequence).

The matching should cover the **entire** input string (not partial).

Given an integer n, return *the number of structurally unique ***BST'***s (binary search trees) which has exactly *n* nodes of unique values from* 1 *to* n.

Given two strings s and t, return *the number of distinct* **subsequences*** of *s* which equals *t.

Given strings s1, s2, and s3, find whether s3 is formed by an **interleaving** of s1 and s2.

You are given a 2D array of integers envelopes where envelopes[i] = [wi, hi] represents the width and the height of an envelope.

One envelope can fit into another if and only if both the width and height of one envelope are greater than the other envelope's width and height.

Return *the maximum number of envelopes you can Russian doll (i.e., put one inside the other)*.

**Note:** You cannot rotate an envelope.

You are climbing a staircase. It takes n steps to reach the top.

Each time you can either climb 1 or 2 steps. In how many distinct ways can you climb to the top?

You are given an integer array prices where prices[i] is the price of a given stock on the ith day, and an integer k.

Find the maximum profit you can achieve. You may complete at most k transactions: i.e. you may buy at most k times and sell at most k times.

**Note:** You may not engage in multiple transactions simultaneously (i.e., you must sell the stock before you buy again).