Given an array of integers cost and an integer target. Return the maximum integer you can paint under the following rules:

• The cost of painting a digit (i+1) is given by cost[i] (0 indexed).
• The total cost used must be equal to target.
• Integer does not have digits 0.

Since the answer may be too large, return it as string.

If there is no way to paint any integer given the condition, return “0”.

Example 1:

Input: cost = [4,3,2,5,6,7,2,5,5], target = 9
Output: "7772"
Explanation:  The cost to paint the digit '7' is 2, and the digit '2' is 3. Then cost("7772") = 2*3+ 3*1 = 9. You could also paint "997", but "7772" is the largest number.
Digit    cost
1  ->   4
2  ->   3
3  ->   2
4  ->   5
5  ->   6
6  ->   7
7  ->   2
8  ->   5
9  ->   5


Example 2:

Input: cost = [7,6,5,5,5,6,8,7,8], target = 12
Output: "85"
Explanation: The cost to paint the digit '8' is 7, and the digit '5' is 5. Then cost("85") = 7 + 5 = 12.


Example 3:

Input: cost = [2,4,6,2,4,6,4,4,4], target = 5
Output: "0"
Explanation: It's not possible to paint any integer with total cost equal to target.


Example 4:

Input: cost = [6,10,15,40,40,40,40,40,40], target = 47
Output: "32211"


Constraints:

• cost.length == 9
• 1 <= cost[i] <= 5000
• 1 <= target <= 5000

## Solution: DP

dp(target) := largest number to print with cost == target.
dp(target) = max(dp(target – d) + cost[d])

Time complexity: O(target^2)
Space complexity: O(target^2)

## C++ / Bottom Up

To avoid string copying, we can store digit added (in order to back track the parent) and length of the optimal string.

Time complexity: O(target)
Space complexity: O(target)

## C++ / O(target)

Given a binary tree root, a node X in the tree is named good if in the path from root to X there are no nodes with a value greater than X.

Return the number of good nodes in the binary tree.

Example 1:

Input: root = [3,1,4,3,null,1,5]
Output: 4
Explanation: Nodes in blue are good.
Root Node (3) is always a good node.
Node 4 -> (3,4) is the maximum value in the path starting from the root.
Node 5 -> (3,4,5) is the maximum value in the path
Node 3 -> (3,1,3) is the maximum value in the path.

Example 2:

Input: root = [3,3,null,4,2]
Output: 3
Explanation: Node 2 -> (3, 3, 2) is not good, because "3" is higher than it.

Example 3:

Input: root = [1]
Output: 1
Explanation: Root is considered as good.

Constraints:

• The number of nodes in the binary tree is in the range [1, 10^5].
• Each node’s value is between [-10^4, 10^4].

## Solution: Recursion

Time complexity: O(n)
Space complexity: O(n)

## C++

Given an integer n, return a list of all simplified fractions between 0 and 1 (exclusive) such that the denominator is less-than-or-equal-to n. The fractions can be in any order.

Example 1:

Input: n = 2
Output: ["1/2"]
Explanation: "1/2" is the only unique fraction with a denominator less-than-or-equal-to 2.

Example 2:

Input: n = 3
Output: ["1/2","1/3","2/3"]


Example 3:

Input: n = 4
Output: ["1/2","1/3","1/4","2/3","3/4"]
Explanation: "2/4" is not a simplified fraction because it can be simplified to "1/2".

Example 4:

Input: n = 1
Output: []


Constraints:

• 1 <= n <= 100

## Solution: GCD

if gcd(a, b) == 1 then a/b is a simplified frication.

std::gcd is available since c++17.

Time complexity: O(n^2logn)
Space complexity: O(1)

## C++

Given a string s, the power of the string is the maximum length of a non-empty substring that contains only one unique character.

Return the power of the string.

Example 1:

Input: s = "leetcode"
Output: 2
Explanation: The substring "ee" is of length 2 with the character 'e' only.


Example 2:

Input: s = "abbcccddddeeeeedcba"
Output: 5
Explanation: The substring "eeeee" is of length 5 with the character 'e' only.


Example 3:

Input: s = "triplepillooooow"
Output: 5


Example 4:

Input: s = "hooraaaaaaaaaaay"
Output: 11


Example 5:

Input: s = "tourist"
Output: 1


Constraints:

• 1 <= s.length <= 500
• s contains only lowercase English letters.

## Solution: Run length encoding?

Time complexity: O(n)
Space complexity: O(1)

## C++

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