Kth Missing Positive Number
Given an array arr of positive integers sorted in a strictly increasing order, and an integer k.
Find the kth positive integer that is missing from this array.
Example
Input: arr=[2,3,4,7,11], k=5
Output: 9
Explanation: The missing positive integers are [1,5,6,8,9,10,12,13,...]. The 5th missing positive integer is 9.
Solution
Python solution
def binary_search(arr: List[int], k: int) -> int: if arr[0] > k: return k
1l = 0 2r = len(arr) - 1 3while l < r: 4 mid = (l + r) // 2 5 x = arr[mid] if mid < len(arr) else 10**9 6 if x - mid - 1 >= k: 7 r = mid 8 else: 9 l = mid + 1 10 11return k - (arr[l - 1] - (l - 1) - 1) + arr[l - 1]
Java Solution
public int binarySearch(int[] arr) { if (arr[0] > k) { return k; }
1int l = 0; 2int r = arr.length - 1; 3while (l < r) { 4 int mid = (l + r) / 2; 5 int x = mid < arr.length ? arr[mid] : Integer.MAX_VALUE; 6 if (x - mid - 1 >= k) { 7 r = mid; 8 } else { 9 l = mid + 1; 10 } 11} 12 13return k - (arr[l - 1] - (l - 1) - 1) + arr[l - 1];
}
What is an advantages of top-down dynamic programming vs bottom-up dynamic programming?
Breadth first search can be used to find the shortest path between two nodes in a directed graph.
Solution Implementation
Depth first search can be used to find whether two components in a graph are connected.
What's the output of running the following function using input 56?
1KEYBOARD = {
2 '2': 'abc',
3 '3': 'def',
4 '4': 'ghi',
5 '5': 'jkl',
6 '6': 'mno',
7 '7': 'pqrs',
8 '8': 'tuv',
9 '9': 'wxyz',
10}
11
12def letter_combinations_of_phone_number(digits):
13 def dfs(path, res):
14 if len(path) == len(digits):
15 res.append(''.join(path))
16 return
17
18 next_number = digits[len(path)]
19 for letter in KEYBOARD[next_number]:
20 path.append(letter)
21 dfs(path, res)
22 path.pop()
23
24 res = []
25 dfs([], res)
26 return res
271private static final Map<Character, char[]> KEYBOARD = Map.of(
2 '2', "abc".toCharArray(),
3 '3', "def".toCharArray(),
4 '4', "ghi".toCharArray(),
5 '5', "jkl".toCharArray(),
6 '6', "mno".toCharArray(),
7 '7', "pqrs".toCharArray(),
8 '8', "tuv".toCharArray(),
9 '9', "wxyz".toCharArray()
10);
11
12public static List<String> letterCombinationsOfPhoneNumber(String digits) {
13 List<String> res = new ArrayList<>();
14 dfs(new StringBuilder(), res, digits.toCharArray());
15 return res;
16}
17
18private static void dfs(StringBuilder path, List<String> res, char[] digits) {
19 if (path.length() == digits.length) {
20 res.add(path.toString());
21 return;
22 }
23 char next_digit = digits[path.length()];
24 for (char letter : KEYBOARD.get(next_digit)) {
25 path.append(letter);
26 dfs(path, res, digits);
27 path.deleteCharAt(path.length() - 1);
28 }
29}
301const KEYBOARD = {
2 '2': 'abc',
3 '3': 'def',
4 '4': 'ghi',
5 '5': 'jkl',
6 '6': 'mno',
7 '7': 'pqrs',
8 '8': 'tuv',
9 '9': 'wxyz',
10}
11
12function letter_combinations_of_phone_number(digits) {
13 let res = [];
14 dfs(digits, [], res);
15 return res;
16}
17
18function dfs(digits, path, res) {
19 if (path.length === digits.length) {
20 res.push(path.join(''));
21 return;
22 }
23 let next_number = digits.charAt(path.length);
24 for (let letter of KEYBOARD[next_number]) {
25 path.push(letter);
26 dfs(digits, path, res);
27 path.pop();
28 }
29}
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