Celestial Skyline Layout

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This challenge becomes much easier once you know exactly what to keep, change, or count. In Celestial Skyline Layout, you are trying to work toward the right number by following one clear idea.

Build recursive skyline layout structure A good way to think about it is to first understand what goes in, then what rule you must follow, and finally what shape the answer should have.

For example, if the input is blueprint = 4, the answer is 1. Example with input: blueprint = 4 Another example is blueprint = {"base": {"base": 5, "steps": [1]}, "steps": [2, 3]}, which gives 8. Example with input: blueprint = {"base": {"base": 5, "steps": [1]}, "s

This is a friendly practice problem, but it still rewards careful reading. The key is understanding the rule clearly and then applying it carefully.

One helpful habit is to say the rule out loud in your own words before you start solving. If you can explain what counts, what changes, and what the final answer should look like, you are already much closer to the right solution.

Example Input & Output

Example 1

Input

blueprint = 4

Output

Explanation

Example with input: blueprint = 4

Example 2

Input

blueprint = {"base": {"base": 5, "steps": [1]}, "steps": [2, 3]}

Output

Explanation

Example with input: blueprint = {"base": {"base": 5, "steps": [1]}, "s

Example 3

Input

blueprint = {"base": 4, "steps": [2]}

Output

2 (either use only the height-4 tower, or add a mirrored tower of height 6)

Explanation

Example with input: blueprint = {"base": 4, "steps": [2]}

Algorithm Flow

Recommendation Algorithm Flow for Celestial Skyline Layout

Best Answers
These are the verified best solutions for this Challenge. You can use them as a reference to improve your solution.

java

import java.util.*;

class Solution {
    private static final int MOD = 1000000007;

    public int count_valid_skylines(Object blueprint) {
        if (blueprint instanceof Number) {
            return 1;
        }
        Map<String, Object> fork = (Map<String, Object>) blueprint;
        long baseCount = count_valid_skylines(fork.get("base"));
        List<?> steps = (List<?>) fork.get("steps");
        int k = (steps != null) ? steps.size() : 0;
        
        long pow2k = 1;
        long b = 2;
        while (k > 0) {
            if (k % 2 == 1) pow2k = (pow2k * b) % MOD;
            b = (b * b) % MOD;
            k /= 2;
        }
        
        return (int) ((baseCount * pow2k) % MOD);
    }
}

javascript

function count_valid_skylines(blueprint) {
    const MOD = 1000000007;
    if (typeof blueprint === "number") {
        return 1;
    }
    const baseCount = count_valid_skylines(blueprint.base);
    const k = (blueprint.steps || []).length;
    // Quick modular power for 2^k
    let pow2k = 1, b = 2;
    let exp = k;
    while (exp > 0) {
        if (exp % 2 === 1) pow2k = Number((BigInt(pow2k) * BigInt(b)) % BigInt(MOD));
        b = Number((BigInt(b) * BigInt(b)) % BigInt(MOD));
        exp = Math.floor(exp / 2);
    }
    return Number((BigInt(baseCount) * BigInt(pow2k)) % BigInt(MOD));
}

php

function count_valid_skylines($blueprint) {
    $MOD = 1000000007;
    if (is_numeric($blueprint)) {
        return 1;
    }
    $baseCount = count_valid_skylines($blueprint["base"]);
    $steps = isset($blueprint["steps"]) ? $blueprint["steps"] : [];
    $k = count($steps);
    
    $pow2k = bcpowmod("2", (string)$k, (string)$MOD);
    return (int) bcmod(bcmul((string)$baseCount, $pow2k), (string)$MOD);
}

python

def count_valid_skylines(blueprint) -> int:
    MOD = 1_000_000_007
    if isinstance(blueprint, (int, float)):
        return 1
    base_count = count_valid_skylines(blueprint.get("base"))
    steps = blueprint.get("steps", [])
    k = len(steps)
    return (base_count * pow(2, k, MOD)) % MOD

rust

use serde_json::Value;
const MOD: i64 = 1_000_000_007;

pub fn count_valid_skylines(blueprint: &Value) -> i32 {
    match blueprint {
        Value::Number(_) => 1,
        Value::Object(obj) => {
            let base_count = count_valid_skylines(obj.get("base").unwrap()) as i64;
            let steps = obj.get("steps").and_then(|v| v.as_array()).map(|a| a.len()).unwrap_or(0);
            let mut pow2k = 1;
            for _ in 0..steps {
                pow2k = (pow2k * 2) % MOD;
            }
            ((base_count * pow2k) % MOD) as i32
        },
        _ => 1
    }
}

typescript

function count_valid_skylines(blueprint: any): number {
    const MOD = 1000000007;
    if (typeof blueprint === "number") {
        return 1;
    }
    const baseCount = count_valid_skylines(blueprint.base);
    const k = (blueprint.steps || []).length;
    let pow2k = 1, b = 2, exp = k;
    while (exp > 0) {
        if (exp % 2 === 1) pow2k = Number((BigInt(pow2k) * BigInt(b)) % BigInt(MOD));
        b = Number((BigInt(b) * BigInt(b)) % BigInt(MOD));
        exp = Math.floor(exp / 2);
    }
    return Number((BigInt(baseCount) * BigInt(pow2k)) % BigInt(MOD));
}

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Celestial Skyline Layout

Example Input & Output

Algorithm Flow

Best AnswersThese are the verified best solutions for this Challenge. You can use them as a reference to improve your solution.

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Best Answers
These are the verified best solutions for this Challenge. You can use them as a reference to improve your solution.