You are given a non-negative integer k. There exists a staircase with an infinite number of stairs, with the lowest stair numbered 0.
Alice has an integer jump, with an initial value of 0. She starts on stair 1 and wants to reach stair k using any number of operations. If she is on stair i, in one operation she can:
i - 1. This operation cannot be used consecutively or on stair 0.i + 2jump. And then, jump becomes jump + 1.Return the total number of ways Alice can reach stair k.
Note that it is possible that Alice reaches the stair k, and performs some operations to reach the stair k again.
\n
Example 1:
\n\nInput: k = 0
\n\nOutput: 2
\n\nExplanation:
\n\nThe 2 possible ways of reaching stair 0 are:
\n\nExample 2:
\n\nInput: k = 1
\n\nOutput: 4
\n\nExplanation:
\n\nThe 4 possible ways of reaching stair 1 are:
\n\n\n
Constraints:
\n\n0 <= k <= 109x operations of the second type and y operations of the first type, the stair 2x + 1 - y is reached.",
"Since first operations cannot be consecutive, there are exactly x + 1 positions (before and after each power of 2) to perform the second operation.",
"Using combinatorics, we have x + 1Cy number of ways to select the positions of second operations."
],
"solution": null,
"status": null,
"sampleTestCase": "0",
"metaData": "{\n \"name\": \"waysToReachStair\",\n \"params\": [\n {\n \"name\": \"k\",\n \"type\": \"integer\"\n }\n ],\n \"return\": {\n \"type\": \"integer\"\n }\n}",
"judgerAvailable": true,
"judgeType": "large",
"mysqlSchemas": [],
"enableRunCode": true,
"enableTestMode": false,
"enableDebugger": true,
"envInfo": "{\"cpp\": [\"C++\", \"Compiled with clang 17 using the latest C++ 20 standard, and libstdc++ provided by GCC 11.
Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.
Most standard library headers are already included automatically for your convenience.
\"], \"java\": [\"Java\", \"OpenJDK 21. Using compile arguments: --enable-preview --release 21
Most standard library headers are already included automatically for your convenience.
\\r\\nIncludes Pair class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.
Python 2.7.12.
Most libraries are already imported automatically for your convenience, such as array, bisect, collections. If you need more libraries, you can import it yourself.
\\r\\n\\r\\nFor Map/TreeMap data structure, you may use sortedcontainers library.
\\r\\n\\r\\nNote that Python 2.7 will not be maintained past 2020. For the latest Python, please choose Python3 instead.
\"], \"c\": [\"C\", \"Compiled with gcc 11 using the gnu11 standard.
Your code is compiled with level one optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.
Most standard library headers are already included automatically for your convenience.
\\r\\n\\r\\nFor hash table operations, you may use uthash. \\\"uthash.h\\\" is included by default. Below are some examples:
\\r\\n\\r\\n1. Adding an item to a hash.\\r\\n
\\r\\nstruct hash_entry {\\r\\n int id; /* we'll use this field as the key */\\r\\n char name[10];\\r\\n UT_hash_handle hh; /* makes this structure hashable */\\r\\n};\\r\\n\\r\\nstruct hash_entry *users = NULL;\\r\\n\\r\\nvoid add_user(struct hash_entry *s) {\\r\\n HASH_ADD_INT(users, id, s);\\r\\n}\\r\\n\\r\\n\\r\\n\\r\\n2. Looking up an item in a hash:\\r\\n
\\r\\nstruct hash_entry *find_user(int user_id) {\\r\\n struct hash_entry *s;\\r\\n HASH_FIND_INT(users, &user_id, s);\\r\\n return s;\\r\\n}\\r\\n\\r\\n\\r\\n\\r\\n3. Deleting an item in a hash:\\r\\n
\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n HASH_DEL(users, user); \\r\\n}\\r\\n\\r\\n\"], \"csharp\": [\"C#\", \"C# 12 with .NET 8 runtime
\"], \"javascript\": [\"JavaScript\", \"Node.js 20.10.0.
Your code is run with --harmony flag, enabling new ES6 features.
lodash.js library is included by default.
\\r\\n\\r\\nFor Priority Queue / Queue data structures, you may use 5.4.0 version of datastructures-js/priority-queue and 4.2.3 version of datastructures-js/queue.
\"], \"ruby\": [\"Ruby\", \"Ruby 3.2
Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms
\"], \"swift\": [\"Swift\", \"Swift 5.9.
You may use swift-algorithms 1.2.0 and swift-collections 1.1.0.
\"], \"golang\": [\"Go\", \"Go 1.21
Support https://pkg.go.dev/github.com/emirpasic/gods@v1.18.1 and https://pkg.go.dev/github.com/emirpasic/gods/v2@v2.0.0-alpha library.
\"], \"python3\": [\"Python3\", \"Python 3.11.
Most libraries are already imported automatically for your convenience, such as array, bisect, collections. If you need more libraries, you can import it yourself.
\\r\\n\\r\\nFor Map/TreeMap data structure, you may use sortedcontainers library.
\"], \"scala\": [\"Scala\", \"Scala 3.3.1.
Kotlin 1.9.0.
We are using an experimental compiler provided by JetBrains.
\"], \"rust\": [\"Rust\", \"Rust 1.74.1. Your code will be compiled with opt-level 2.
Supports rand v0.6\\u00a0from crates.io
\"], \"php\": [\"PHP\", \"PHP 8.2.
With bcmath module
\"], \"typescript\": [\"Typescript\", \"TypeScript 5.1.6, Node.js 20.10.0.
Compile Options: --alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2022
Your code is run with --harmony flag, enabling new ES2022 features.
lodash.js library is included by default.
\"], \"racket\": [\"Racket\", \"Racket CS v8.11
\\r\\n\\r\\nUsing #lang racket
Required data/gvector data/queue data/order data/heap automatically for your convenience
Dart 3.2. You may use package collection
\\r\\n\\r\\nYour code will be run directly without compiling
\"]}", "libraryUrl": null, "adminUrl": null, "challengeQuestion": null, "__typename": "QuestionNode" } } }