# Posts tagged as “recursion”

Implement pow(xn), which calculates x raised to the power n (xn).

Example 1:

Input: 2.00000, 10
Output: 1024.00000


Example 2:

Input: 2.10000, 3
Output: 9.26100


Example 3:

Input: 2.00000, -2
Output: 0.25000
Explanation: 2-2 = 1/22 = 1/4 = 0.25


Note:

• -100.0 < x < 100.0
• n is a 32-bit signed integer, within the range [−231, 231 − 1]

## Solution: Recursion

square x and cut n in half.
if n is negative, compute 1.0 / pow(x, |n|)

pow(x, n) := pow(x * x, n / 2) * (x if n % 2 else 1)pow(x, 0) := 1
Example:pow(x, 5) = pow(x^2, 2) * x           = pow(x^4, 1) * x           = pow(x^8, 0) * x^4 * x          = 1 * x^4 * x = x^5

Time complexity: O(logn)
Space complexity: O(logn)

## Problem

The count-and-say sequence is the sequence of integers with the first five terms as following:

1.     1
2.     11
3.     21
4.     1211
5.     111221


1 is read off as "one 1" or 11.
11 is read off as "two 1s" or 21.
21 is read off as "one 2, then one 1" or 1211.

Given an integer n where 1 ≤ n ≤ 30, generate the nth term of the count-and-say sequence.

Note: Each term of the sequence of integers will be represented as a string.

Example 1:

Input: 1
Output: "1"


Example 2:

Input: 4
Output: "1211"

Solution: Recursion + Simulation

## C++

Given an encoded string, return it’s decoded string.

The encoding rule is: k[encoded_string], where the encoded_string inside the square brackets is being repeated exactly k times. Note that k is guaranteed to be a positive integer.

You may assume that the input string is always valid; No extra white spaces, square brackets are well-formed, etc.

Furthermore, you may assume that the original data does not contain any digits and that digits are only for those repeat numbers, k. For example, there won’t be input like 3a or 2[4].

Examples:

s = "3[a]2[bc]", return "aaabcbc".
s = "3[a2[c]]", return "accaccacc".
s = "2[abc]3[cd]ef", return "abcabccdcdcdef".

## Solution 1: Recursion

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

## C++

Convert a non-negative integer to its english words representation. Given input is guaranteed to be less than 231 – 1.

Example 1:

Input: 123
Output: "One Hundred Twenty Three"


Example 2:

Input: 12345
Output: "Twelve Thousand Three Hundred Forty Five"

Example 3:

Input: 1234567
Output: "One Million Two Hundred Thirty Four Thousand Five Hundred Sixty Seven"


Example 4:

Input: 1234567891
Output: "One Billion Two Hundred Thirty Four Million Five Hundred Sixty Seven Thousand Eight Hundred Ninety One"

Solution: Recursion

Time complexity: O(logn)
Space complexity: O(logn)

## C++

Given the root of a binary tree, each node has a value from 0 to 25representing the letters 'a' to 'z': a value of 0 represents 'a', a value of 1 represents 'b', and so on.

Find the lexicographically smallest string that starts at a leaf of this tree and ends at the root.

(As a reminder, any shorter prefix of a string is lexicographically smaller: for example, "ab" is lexicographically smaller than "aba".  A leaf of a node is a node that has no children.)

Example 1:

Input: [0,1,2,3,4,3,4]
Output: "dba"


Example 2:

Input: [25,1,3,1,3,0,2]


Example 3:

Input: [2,2,1,null,1,0,null,0]
Output: "abc"


Note:

1. The number of nodes in the given tree will be between 1 and 1000.
2. Each node in the tree will have a value between 0 and 25.

## Solution: Recursion

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

## Python3

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