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                # 1011. 在 D 天內送達包裹的能力 ## 題目地址(1011. 在 D 天內送達包裹的能力) <https://leetcode-cn.com/problems/capacity-to-ship-packages-within-d-days/> ## 題目描述 ``` <pre class="calibre18">``` 傳送帶上的包裹必須在 D 天內從一個港口運送到另一個港口。 傳送帶上的第 i 個包裹的重量為 weights[i]。每一天,我們都會按給出重量的順序往傳送帶上裝載包裹。我們裝載的重量不會超過船的最大運載重量。 返回能在 D 天內將傳送帶上的所有包裹送達的船的最低運載能力。 示例 1: 輸入:weights = [1,2,3,4,5,6,7,8,9,10], D = 5 輸出:15 解釋: 船舶最低載重 15 就能夠在 5 天內送達所有包裹,如下所示: 第 1 天:1, 2, 3, 4, 5 第 2 天:6, 7 第 3 天:8 第 4 天:9 第 5 天:10 請注意,貨物必須按照給定的順序裝運,因此使用載重能力為 14 的船舶并將包裝分成 (2, 3, 4, 5), (1, 6, 7), (8), (9), (10) 是不允許的。 示例 2: 輸入:weights = [3,2,2,4,1,4], D = 3 輸出:6 解釋: 船舶最低載重 6 就能夠在 3 天內送達所有包裹,如下所示: 第 1 天:3, 2 第 2 天:2, 4 第 3 天:1, 4 示例 3: 輸入:weights = [1,2,3,1,1], D = 4 輸出:3 解釋: 第 1 天:1 第 2 天:2 第 3 天:3 第 4 天:1, 1 提示: 1 <= D <= weights.length <= 50000 1 <= weights[i] <= 500 ``` ``` ## 前置知識 - 二分法 ## 公司 - 阿里 ## 思路 這道題和[猴子吃香蕉](https://github.com/azl397985856/leetcode/blob/master/problems/875.koko-eating-bananas.md) 簡直一摸一樣,沒有看過的建議看一下那道題。 像這種題如何你能發現本質的考點,那么 AC 是瞬間的事情。 這道題本質上就是從 1,2,3,4,。。。total(其中 toal 是總的貨物重量)的有限離散數據中查找給定的數。這里我們不是直接查找 target,而是查找恰好能夠在 D 天運完的載貨量。 - 容量是 1 可以運完么? - 容量是 2 可以運完么? - 容量是 3 可以運完么? - 。。。 - 容量是 total 可以運完么?(當然可以,因為 D 大于等于 1) 上面不斷詢問的過程如果回答是 yes 我們直接 return 即可。如果回答是 no,我們繼續往下詢問。 這是一個典型的二分問題,只不過我們的判斷條件略有不同,大概是: ``` <pre class="calibre18">``` <span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">canShip</span><span class="hljs-params">(opacity)</span>:</span> <span class="hljs-title"># 指定船的容量是否可以在D天運完</span> lo = <span class="hljs-params">0</span> hi = total <span class="hljs-keyword">while</span> lo < hi: mid = (lo + hi) // <span class="hljs-params">2</span> <span class="hljs-keyword">if</span> canShip(mid): hi = mid <span class="hljs-keyword">else</span>: lo = mid + <span class="hljs-params">1</span> <span class="hljs-keyword">return</span> lo ``` ``` ## 關鍵點解析 - 能夠識別出是給定的有限序列查找一個數字(二分查找),要求你對二分查找以及變體十分熟悉 ## 代碼 - 語言支持:`JS`,`Python` `python`: ``` <pre class="calibre18">``` <span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">Solution</span>:</span> <span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">shipWithinDays</span><span class="hljs-params">(self, weights: List[int], D: int)</span> -> int:</span> lo = <span class="hljs-params">0</span> hi = <span class="hljs-params">0</span> <span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">canShip</span><span class="hljs-params">(opacity)</span>:</span> days = <span class="hljs-params">1</span> remain = opacity <span class="hljs-keyword">for</span> weight <span class="hljs-keyword">in</span> weights: <span class="hljs-keyword">if</span> weight > opacity: <span class="hljs-keyword">return</span> <span class="hljs-keyword">False</span> remain -= weight <span class="hljs-keyword">if</span> remain < <span class="hljs-params">0</span>: days += <span class="hljs-params">1</span> remain = opacity - weight <span class="hljs-keyword">return</span> days <= D <span class="hljs-keyword">for</span> weight <span class="hljs-keyword">in</span> weights: hi += weight <span class="hljs-keyword">while</span> lo < hi: mid = (lo + hi) // <span class="hljs-params">2</span> <span class="hljs-keyword">if</span> canShip(mid): hi = mid <span class="hljs-keyword">else</span>: lo = mid + <span class="hljs-params">1</span> <span class="hljs-keyword">return</span> lo ``` ``` `js`: ``` <pre class="calibre18">``` <span class="hljs-title">/** * @param {number[]} weights * @param {number} D * @return {number} */</span> <span class="hljs-keyword">var</span> shipWithinDays = <span class="hljs-function"><span class="hljs-keyword">function</span>(<span class="hljs-params">weights, D</span>) </span>{ <span class="hljs-keyword">let</span> high = weights.reduce((acc, cur) => acc + cur) <span class="hljs-keyword">let</span> low = <span class="hljs-params">0</span> <span class="hljs-keyword">while</span>(low < high) { <span class="hljs-keyword">let</span> mid = <span class="hljs-params">Math</span>.floor((high + low) / <span class="hljs-params">2</span>) <span class="hljs-keyword">if</span> (canShip(mid)) { high = mid } <span class="hljs-keyword">else</span> { low = mid + <span class="hljs-params">1</span> } } <span class="hljs-keyword">return</span> low <span class="hljs-function"><span class="hljs-keyword">function</span> <span class="hljs-title">canShip</span>(<span class="hljs-params">opacity</span>) </span>{ <span class="hljs-keyword">let</span> remain = opacity <span class="hljs-keyword">let</span> count = <span class="hljs-params">1</span> <span class="hljs-keyword">for</span> (<span class="hljs-keyword">let</span> weight <span class="hljs-keyword">of</span> weights) { <span class="hljs-keyword">if</span> (weight > opacity) { <span class="hljs-keyword">return</span> <span class="hljs-params">false</span> } remain -= weight <span class="hljs-keyword">if</span> (remain < <span class="hljs-params">0</span>) { count++ remain = opacity - weight } <span class="hljs-keyword">if</span> (count > D) { <span class="hljs-keyword">return</span> <span class="hljs-params">false</span> } } <span class="hljs-keyword">return</span> count <= D } }; ``` ``` **復雜度分析** - 時間復雜度:O(logN)O(logN)O(logN) - 空間復雜度:O(N)O(N)O(N)
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