+ problem 1870

fruit-in · fruit-in · commit f1374d2d980c · 2023-11-29T23:07:14.000+08:00
diff --git a/Problemset/1870-Minimum Speed to Arrive on Time/README.md b/Problemset/1870-Minimum Speed to Arrive on Time/README.md
@@ -0,0 +1,73 @@
+# 1870. Minimum Speed to Arrive on Time
+You are given a floating-point number `hour`, representing the amount of time you have to reach the office. To commute to the office, you must take `n` trains in sequential order. You are also given an integer array `dist` of length `n`, where `dist[i]` describes the distance (in kilometers) of the <code>i<sup>th</sup></code> train ride.
+
+Each train can only depart at an integer hour, so you may need to wait in between each train ride.
+
+* For example, if the <code>1<sup>st</sup></code> train ride takes `1.5` hours, you must wait for an additional `0.5` hours before you can depart on the <code>2<sup>nd</sup></code> train ride at the 2 hour mark.
+
+Return *the **minimum positive integer** speed **(in kilometers per hour)** that all the trains must travel at for you to reach the office on time, or* `-1` *if it is impossible to be on time*.
+
+Tests are generated such that the answer will not exceed <code>10<sup>7</sup></code> and `hour` will have at most two digits after the decimal point.
+
+#### Example 1:
+<pre>
+<strong>Input:</strong> dist = [1,3,2], hour = 6
+<strong>Output:</strong> 1
+<strong>Explanation:</strong> At speed 1:
+- The first train ride takes 1/1 = 1 hour.
+- Since we are already at an integer hour, we depart immediately at the 1 hour mark. The second train takes 3/1 = 3 hours.
+- Since we are already at an integer hour, we depart immediately at the 4 hour mark. The third train takes 2/1 = 2 hours.
+- You will arrive at exactly the 6 hour mark.
+</pre>
+
+#### Example 2:
+<pre>
+<strong>Input:</strong> dist = [1,3,2], hour = 2.7
+<strong>Output:</strong> 3
+<strong>Explanation:</strong> At speed 3:
+- The first train ride takes 1/3 = 0.33333 hours.
+- Since we are not at an integer hour, we wait until the 1 hour mark to depart. The second train ride takes 3/3 = 1 hour.
+- Since we are already at an integer hour, we depart immediately at the 2 hour mark. The third train takes 2/3 = 0.66667 hours.
+- You will arrive at the 2.66667 hour mark.
+</pre>
+
+#### Example 3:
+<pre>
+<strong>Input:</strong> dist = [1,3,2], hour = 1.9
+<strong>Output:</strong> -1
+<strong>Explanation:</strong> It is impossible because the earliest the third train can depart is at the 2 hour mark.
+</pre>
+
+#### Constraints:
+* `n == dist.length`
+* <code>1 <= n <= 10<sup>5</sup></code>
+* <code>1 <= dist[i] <= 10<sup>5</sup></code>
+* <code>1 <= hour <= 10<sup>9</sup></code>
+* There will be at most two digits after the decimal point in `hour`.
+
+## Solutions (Python)
+
+### 1. Solution
+```Python
+from math import ceil
+
+
+class Solution:
+    def minSpeedOnTime(self, dist: List[int], hour: float) -> int:
+        if len(dist) - 0.999 > hour:
+            return -1
+
+        lo = 1
+        hi = 10000000
+
+        while lo < hi:
+            v = (lo + hi) // 2
+            t = sum(ceil(d / v) for d in dist[:-1]) + dist[-1] / v
+
+            if t > hour:
+                lo = v + 1
+            else:
+                hi = v
+
+        return hi
+```
diff --git a/Problemset/1870-Minimum Speed to Arrive on Time/README_CN.md b/Problemset/1870-Minimum Speed to Arrive on Time/README_CN.md
@@ -0,0 +1,73 @@
+# 1870. 准时到达的列车最小时速
+给你一个浮点数 `hour` ，表示你到达办公室可用的总通勤时间。要到达办公室，你必须按给定次序乘坐 `n` 趟列车。另给你一个长度为 `n` 的整数数组 `dist` ，其中 `dist[i]` 表示第 `i` 趟列车的行驶距离（单位是千米）。
+
+每趟列车均只能在整点发车，所以你可能需要在两趟列车之间等待一段时间。
+
+* 例如，第 `1` 趟列车需要 `1.5` 小时，那你必须再等待 `0.5` 小时，搭乘在第 `2` 小时发车的第 2 趟列车。
+
+返回能满足你准时到达办公室所要求全部列车的 **最小正整数** 时速（单位：千米每小时），如果无法准时到达，则返回 `-1` 。
+
+生成的测试用例保证答案不超过 <code>10<sup>7</sup></code> ，且 `hour` 的 **小数点后最多存在两位数字** 。
+
+#### 示例 1:
+<pre>
+<strong>输入:</strong> dist = [1,3,2], hour = 6
+<strong>输出:</strong> 1
+<strong>解释:</strong> 速度为 1 时：
+- 第 1 趟列车运行需要 1/1 = 1 小时。
+- 由于是在整数时间到达，可以立即换乘在第 1 小时发车的列车。第 2 趟列车运行需要 3/1 = 3 小时。
+- 由于是在整数时间到达，可以立即换乘在第 4 小时发车的列车。第 3 趟列车运行需要 2/1 = 2 小时。
+- 你将会恰好在第 6 小时到达。
+</pre>
+
+#### 示例 2:
+<pre>
+<strong>输入:</strong> dist = [1,3,2], hour = 2.7
+<strong>输出:</strong> 3
+<strong>解释:</strong> 速度为 3 时：
+- 第 1 趟列车运行需要 1/3 = 0.33333 小时。
+- 由于不是在整数时间到达，故需要等待至第 1 小时才能搭乘列车。第 2 趟列车运行需要 3/3 = 1 小时。
+- 由于是在整数时间到达，可以立即换乘在第 2 小时发车的列车。第 3 趟列车运行需要 2/3 = 0.66667 小时。
+- 你将会在第 2.66667 小时到达。
+</pre>
+
+#### 示例 3:
+<pre>
+<strong>输入:</strong> dist = [1,3,2], hour = 1.9
+<strong>输出:</strong> -1
+<strong>解释:</strong> 不可能准时到达，因为第 3 趟列车最早是在第 2 小时发车。
+</pre>
+
+#### 提示:
+* `n == dist.length`
+* <code>1 <= n <= 10<sup>5</sup></code>
+* <code>1 <= dist[i] <= 10<sup>5</sup></code>
+* <code>1 <= hour <= 10<sup>9</sup></code>
+* `hours` 中，小数点后最多存在两位数字
+
+## 题解 (Python)
+
+### 1. 题解
+```Python
+from math import ceil
+
+
+class Solution:
+    def minSpeedOnTime(self, dist: List[int], hour: float) -> int:
+        if len(dist) - 0.999 > hour:
+            return -1
+
+        lo = 1
+        hi = 10000000
+
+        while lo < hi:
+            v = (lo + hi) // 2
+            t = sum(ceil(d / v) for d in dist[:-1]) + dist[-1] / v
+
+            if t > hour:
+                lo = v + 1
+            else:
+                hi = v
+
+        return hi
+```
diff --git a/Problemset/1870-Minimum Speed to Arrive on Time/Solution.py b/Problemset/1870-Minimum Speed to Arrive on Time/Solution.py
@@ -0,0 +1,21 @@
+from math import ceil
+
+
+class Solution:
+    def minSpeedOnTime(self, dist: List[int], hour: float) -> int:
+        if len(dist) - 0.999 > hour:
+            return -1
+
+        lo = 1
+        hi = 10000000
+
+        while lo < hi:
+            v = (lo + hi) // 2
+            t = sum(ceil(d / v) for d in dist[:-1]) + dist[-1] / v
+
+            if t > hour:
+                lo = v + 1
+            else:
+                hi = v
+
+        return hi
diff --git a/README.md b/README.md
@@ -966,6 +966,7 @@
 [1863][1863l]|[Sum of All Subset XOR Totals][1863]                                                  |![py]
 [1866][1866l]|[Number of Ways to Rearrange Sticks With K Sticks Visible][1866]                      |![rs]
 [1869][1869l]|[Longer Contiguous Segments of Ones than Zeros][1869]                                 |![rs]
+[1870][1870l]|[Minimum Speed to Arrive on Time][1870]                                               |![py]
 [1876][1876l]|[Substrings of Size Three with Distinct Characters][1876]                             |![rs]
 [1877][1877l]|[Minimize Maximum Pair Sum in Array][1877]                                            |![rs]
 [1880][1880l]|[Check if Word Equals Summation of Two Words][1880]                                   |![rs]
@@ -2260,6 +2261,7 @@
 [1863]:Problemset/1863-Sum%20of%20All%20Subset%20XOR%20Totals/README.md#1863-sum-of-all-subset-xor-totals
 [1866]:Problemset/1866-Number%20of%20Ways%20to%20Rearrange%20Sticks%20With%20K%20Sticks%20Visible/README.md#1866-number-of-ways-to-rearrange-sticks-with-k-sticks-visible
 [1869]:Problemset/1869-Longer%20Contiguous%20Segments%20of%20Ones%20than%20Zeros/README.md#1869-longer-contiguous-segments-of-ones-than-zeros
+[1870]:Problemset/1870-Minimum%20Speed%20to%20Arrive%20on%20Time/README.md#1870-minimum-speed-to-arrive-on-time
 [1876]:Problemset/1876-Substrings%20of%20Size%20Three%20with%20Distinct%20Characters/README.md#1876-substrings-of-size-three-with-distinct-characters
 [1877]:Problemset/1877-Minimize%20Maximum%20Pair%20Sum%20in%20Array/README.md#1877-minimize-maximum-pair-sum-in-array
 [1880]:Problemset/1880-Check%20if%20Word%20Equals%20Summation%20of%20Two%20Words/README.md#1880-check-if-word-equals-summation-of-two-words
@@ -3557,6 +3559,7 @@
 [1863l]:https://leetcode.com/problems/sum-of-all-subset-xor-totals/
 [1866l]:https://leetcode.com/problems/number-of-ways-to-rearrange-sticks-with-k-sticks-visible/
 [1869l]:https://leetcode.com/problems/longer-contiguous-segments-of-ones-than-zeros/
+[1870l]:https://leetcode.com/problems/minimum-speed-to-arrive-on-time/
 [1876l]:https://leetcode.com/problems/substrings-of-size-three-with-distinct-characters/
 [1877l]:https://leetcode.com/problems/minimize-maximum-pair-sum-in-array/
 [1880l]:https://leetcode.com/problems/check-if-word-equals-summation-of-two-words/
diff --git a/README_CN.md b/README_CN.md
@@ -966,6 +966,7 @@
 [1863][1863l]|[找出所有子集的异或总和再求和][1863]                      |![py]
 [1866][1866l]|[恰有 K 根木棍可以看到的排列数目][1866]                   |![rs]
 [1869][1869l]|[哪种连续子字符串更长][1869]                              |![rs]
+[1870][1870l]|[准时到达的列车最小时速][1870]                            |![py]
 [1876][1876l]|[长度为三且各字符不同的子字符串][1876]                    |![rs]
 [1877][1877l]|[数组中最大数对和的最小值][1877]                          |![rs]
 [1880][1880l]|[检查某单词是否等于两单词之和][1880]                      |![rs]
@@ -2260,6 +2261,7 @@
 [1863]:Problemset/1863-Sum%20of%20All%20Subset%20XOR%20Totals/README_CN.md#1863-找出所有子集的异或总和再求和
 [1866]:Problemset/1866-Number%20of%20Ways%20to%20Rearrange%20Sticks%20With%20K%20Sticks%20Visible/README_CN.md#1866-恰有-k-根木棍可以看到的排列数目
 [1869]:Problemset/1869-Longer%20Contiguous%20Segments%20of%20Ones%20than%20Zeros/README_CN.md#1869-哪种连续子字符串更长
+[1870]:Problemset/1870-Minimum%20Speed%20to%20Arrive%20on%20Time/README_CN.md#1870-准时到达的列车最小时速
 [1876]:Problemset/1876-Substrings%20of%20Size%20Three%20with%20Distinct%20Characters/README_CN.md#1876-长度为三且各字符不同的子字符串
 [1877]:Problemset/1877-Minimize%20Maximum%20Pair%20Sum%20in%20Array/README_CN.md#1877-数组中最大数对和的最小值
 [1880]:Problemset/1880-Check%20if%20Word%20Equals%20Summation%20of%20Two%20Words/README_CN.md#1880-检查某单词是否等于两单词之和
@@ -3557,6 +3559,7 @@
 [1863l]:https://leetcode.cn/problems/sum-of-all-subset-xor-totals/
 [1866l]:https://leetcode.cn/problems/number-of-ways-to-rearrange-sticks-with-k-sticks-visible/
 [1869l]:https://leetcode.cn/problems/longer-contiguous-segments-of-ones-than-zeros/
+[1870l]:https://leetcode.cn/problems/minimum-speed-to-arrive-on-time/
 [1876l]:https://leetcode.cn/problems/substrings-of-size-three-with-distinct-characters/
 [1877l]:https://leetcode.cn/problems/minimize-maximum-pair-sum-in-array/
 [1880l]:https://leetcode.cn/problems/check-if-word-equals-summation-of-two-words/
