maximize-amount-after-two-days-of-conversions

java

python

python3

mysql

mssql

oraclesql

csharp

javascript

typescript

bash

swift

kotlin

dart

golang

ruby

scala

rust

racket

erlang

elixir

pythondata

postgresql

cangjie

Algorithms

You are given a string <code>initialCurrency</code>, and you start with <code>1.0</code> of <code>initialCurrency</code>.

You are also given four arrays with currency pairs (strings) and rates (real numbers):

<ul>
	<li><code>pairs1[i] = [startCurrencyi, targetCurrencyi]</code> denotes that you can convert from <code>startCurrencyi</code> to <code>targetCurrencyi</code> at a rate of <code>rates1[i]</code> on day 1.</li>
	<li><code>pairs2[i] = [startCurrencyi, targetCurrencyi]</code> denotes that you can convert from <code>startCurrencyi</code> to <code>targetCurrencyi</code> at a rate of <code>rates2[i]</code> on day 2.</li>
	<li>Also, each <code>targetCurrency</code> can be converted back to its corresponding <code>startCurrency</code> at a rate of <code>1 / rate</code>.</li>
</ul>

You can perform any number of conversions, including zero, using <code>rates1</code> on day 1, followed by any number of additional conversions, including zero, using <code>rates2</code> on day 2.

Return the maximum amount of <code>initialCurrency</code> you can have after performing any number of conversions on both days in order.

Note: Conversion rates are valid, and there will be no contradictions in the rates for either day. The rates for the days are independent of each other.

&nbsp;
Example 1:

<div class="example-block">
Input: initialCurrency = &quot;EUR&quot;, pairs1 = [[&quot;EUR&quot;,&quot;USD&quot;],[&quot;USD&quot;,&quot;JPY&quot;]], rates1 = [2.0,3.0], pairs2 = [[&quot;JPY&quot;,&quot;USD&quot;],[&quot;USD&quot;,&quot;CHF&quot;],[&quot;CHF&quot;,&quot;EUR&quot;]], rates2 = [4.0,5.0,6.0]

Output: 720.00000

Explanation:

To get the maximum amount of EUR, starting with 1.0 EUR:

<ul>
	<li>On Day 1:
	<ul>
		<li>Convert EUR to USD to get 2.0 USD.</li>
		<li>Convert USD to JPY to get 6.0 JPY.</li>
	</ul>
	</li>
	<li>On Day 2:
	<ul>
		<li>Convert JPY to USD to get 24.0 USD.</li>
		<li>Convert USD to CHF to get 120.0 CHF.</li>
		<li>Finally, convert CHF to EUR to get 720.0 EUR.</li>
	</ul>
	</li>
</ul>
</div>

Example 2:

<div class="example-block">
Input: initialCurrency = &quot;NGN&quot;, pairs1 = [[&quot;NGN&quot;,&quot;EUR&quot;]], rates1 = [9.0], pairs2 = [[&quot;NGN&quot;,&quot;EUR&quot;]], rates2 = [6.0]

Output: 1.50000

Explanation:

Converting NGN to EUR on day 1 and EUR to NGN using the inverse rate on day 2 gives the maximum amount.
</div>

Example 3:

<div class="example-block">
Input: initialCurrency = &quot;USD&quot;, pairs1 = [[&quot;USD&quot;,&quot;EUR&quot;]], rates1 = [1.0], pairs2 = [[&quot;EUR&quot;,&quot;JPY&quot;]], rates2 = [10.0]

Output: 1.00000

Explanation:

In this example, there is no need to make any conversions on either day.
</div>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= initialCurrency.length &lt;= 3</code></li>
	<li><code>initialCurrency</code> consists only of uppercase English letters.</li>
	<li><code>1 &lt;= n == pairs1.length &lt;= 10</code></li>
	<li><code>1 &lt;= m == pairs2.length &lt;= 10</code></li>
	<li><code>pairs1[i] == [startCurrencyi, targetCurrencyi]</code></li>
	<li><code>pairs2[i] == [startCurrencyi, targetCurrencyi]</code></li>
	<li><code>1 &lt;= startCurrencyi.length, targetCurrencyi.length &lt;= 3</code></li>
	<li><code>startCurrencyi</code> and <code>targetCurrencyi</code> consist only of uppercase English letters.</li>
	<li><code>rates1.length == n</code></li>
	<li><code>rates2.length == m</code></li>
	<li><code>1.0 &lt;= rates1[i], rates2[i] &lt;= 10.0</code></li>
	<li>The input is generated such that there are no contradictions or cycles in the conversion graphs for either day.</li>
	<li>The input is generated such that the output is at most <code>5 * 1010</code>.</li>
</ul>

maxAmount

Maximize Amount After Two Days of Conversions

Evaluate Division

evaluate-division

除法求值

Depth-First Search

Breadth-First Search

Graph

Array

String

给你一个字符串 <code>initialCurrency</code>，表示初始货币类型，并且你一开始拥有 <code>1.0</code> 单位的 <code>initialCurrency</code>。

另给你四个数组，分别表示货币对（字符串）和汇率（实数）：

<ul>
	<li><code>pairs1[i] = [startCurrencyi, targetCurrencyi]</code> 表示在&nbsp;第 1 天，可以按照汇率 <code>rates1[i]</code> 将 <code>startCurrencyi</code> 转换为 <code>targetCurrencyi</code>。</li>
	<li><code>pairs2[i] = [startCurrencyi, targetCurrencyi]</code> 表示在&nbsp;第 2 天，可以按照汇率 <code>rates2[i]</code> 将 <code>startCurrencyi</code> 转换为 <code>targetCurrencyi</code>。</li>
	<li>此外，每种 <code>targetCurrency</code> 都可以以汇率 <code>1 / rate</code> 转换回对应的 <code>startCurrency</code>。</li>
</ul>

你可以在&nbsp;第 1 天&nbsp;使用 <code>rates1</code> 进行任意次数的兑换（包括 0 次），然后在&nbsp;第 2 天&nbsp;使用 <code>rates2</code> 再进行任意次数的兑换（包括 0 次）。

返回在两天兑换后，最大可能拥有的 <code>initialCurrency</code> 的数量。

注意：汇率是有效的，并且第 1 天和第 2 天的汇率之间相互独立，不会产生矛盾。

&nbsp;

示例 1：

<div class="example-block">
输入： initialCurrency = "EUR", pairs1 = [["EUR","USD"],["USD","JPY"]], rates1 = [2.0,3.0], pairs2 = [["JPY","USD"],["USD","CHF"],["CHF","EUR"]], rates2 = [4.0,5.0,6.0]

输出： 720.00000

解释：

根据题目要求，需要最大化最终的 EUR 数量，从 1.0 EUR 开始：

<ul>
	<li>第 1 天：

	<ul>
		<li>将 EUR 换成 USD，得到 2.0&nbsp;USD。</li>
		<li>将 USD 换成 JPY，得到 6.0 JPY。</li>
	</ul>
	</li>
	<li>第 2 天：
	<ul>
		<li>将 JPY 换成 USD，得到 24.0 USD。</li>
		<li>将 USD 换成 CHF，得到 120.0 CHF。</li>
		<li>最后将 CHF 换回 EUR，得到 720.0 EUR。</li>
	</ul>
	</li>
</ul>
</div>

示例 2：

<div class="example-block">
输入： initialCurrency = "NGN", pairs1 = [["NGN","EUR"]], rates1 = [9.0], pairs2 = [["NGN","EUR"]], rates2 = [6.0]

输出： 1.50000

解释：

在第 1 天将 NGN 换成 EUR，并在第 2 天用反向汇率将 EUR 换回 NGN，可以最大化最终的 NGN 数量。
</div>

示例 3：

<div class="example-block">
输入： initialCurrency = "USD", pairs1 = [["USD","EUR"]], rates1 = [1.0], pairs2 = [["EUR","JPY"]], rates2 = [10.0]

输出： 1.00000

解释：

在这个例子中，不需要在任何一天进行任何兑换。
</div>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= initialCurrency.length &lt;= 3</code></li>
	<li><code>initialCurrency</code> 仅由大写英文字母组成。</li>
	<li><code>1 &lt;= n == pairs1.length &lt;= 10</code></li>
	<li><code>1 &lt;= m == pairs2.length &lt;= 10</code></li>
	<li><code>pairs1[i] == [startCurrencyi, targetCurrencyi]</code></li>
	<li><code>pairs2[i] == [startCurrencyi, targetCurrencyi]</code></li>
	<li><code>1 &lt;= startCurrencyi.length, targetCurrencyi.length &lt;= 3</code></li>
	<li><code>startCurrencyi</code> 和 <code>targetCurrencyi</code> 仅由大写英文字母组成。</li>
	<li><code>rates1.length == n</code></li>
	<li><code>rates2.length == m</code></li>
	<li><code>1.0 &lt;= rates1[i], rates2[i] &lt;= 10.0</code></li>
	<li>输入保证两个转换图在各自的天数中没有矛盾或循环。</li>
	<li>输入保证输出&nbsp;最大&nbsp;为&nbsp;<code>5 * 1010</code>。</li>
</ul>