From 28617d13110a266b969e47ae17da004f62227582 Mon Sep 17 00:00:00 2001
From: Hao Chen <haoel@hotmail.com>
Date: Sun, 30 May 2021 15:56:58 +0800
Subject: [PATCH] New Problem Solution - "1870. Minimum Speed to Arrive on
 Time"

---
 README.md                                     |  1 +
 .../MinimumSpeedToArriveOnTime.cpp            | 89 +++++++++++++++++++
 2 files changed, 90 insertions(+)
 create mode 100644 algorithms/cpp/minimumSpeedToArriveOnTime/MinimumSpeedToArriveOnTime.cpp

diff --git a/README.md b/README.md
index c748001..fd1b4ff 100644
--- a/README.md
+++ b/README.md
@@ -9,6 +9,7 @@ LeetCode
 
 | # | Title | Solution | Difficulty |
 |---| ----- | -------- | ---------- |
+|1870|[Minimum Speed to Arrive on Time](https://leetcode.com/problems/minimum-speed-to-arrive-on-time/) | [C++](./algorithms/cpp/minimumSpeedToArriveOnTime/MinimumSpeedToArriveOnTime.cpp)|Medium|
 |1869|[Longer Contiguous Segments of Ones than Zeros](https://leetcode.com/problems/longer-contiguous-segments-of-ones-than-zeros/) | [C++](./algorithms/cpp/longerContiguousSegmentsOfOnesThanZeros/LongerContiguousSegmentsOfOnesThanZeros.cpp)|Easy|
 |1862|[Sum of Floored Pairs](https://leetcode.com/problems/sum-of-floored-pairs/) | [C++](./algorithms/cpp/sumOfFlooredPairs/SumOfFlooredPairs.cpp)|Hard|
 |1861|[Rotating the Box](https://leetcode.com/problems/rotating-the-box/) | [C++](./algorithms/cpp/rotatingTheBox/RotatingTheBox.cpp)|Medium|
diff --git a/algorithms/cpp/minimumSpeedToArriveOnTime/MinimumSpeedToArriveOnTime.cpp b/algorithms/cpp/minimumSpeedToArriveOnTime/MinimumSpeedToArriveOnTime.cpp
new file mode 100644
index 0000000..c1448f3
--- /dev/null
+++ b/algorithms/cpp/minimumSpeedToArriveOnTime/MinimumSpeedToArriveOnTime.cpp
@@ -0,0 +1,89 @@
+// Source : https://leetcode.com/problems/minimum-speed-to-arrive-on-time/
+// Author : Hao Chen
+// Date   : 2021-05-30
+
+/***************************************************************************************************** 
+ *
+ * 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 i^th 
+ * 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 1^st train ride takes 1.5 hours, you must wait for an additional 0.5 
+ * hours before you can depart on the 2^nd 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 10^7 and hour will have at most two digits 
+ * after the decimal point.
+ * 
+ * Example 1:
+ * 
+ * Input: dist = [1,3,2], hour = 6
+ * Output: 1
+ * Explanation: 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.
+ * 
+ * Example 2:
+ * 
+ * Input: dist = [1,3,2], hour = 2.7
+ * Output: 3
+ * Explanation: 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.
+ * 
+ * Example 3:
+ * 
+ * Input: dist = [1,3,2], hour = 1.9
+ * Output: -1
+ * Explanation: It is impossible because the earliest the third train can depart is at the 2 hour mark.
+ * 
+ * Constraints:
+ * 
+ * 	n == dist.length
+ * 	1 <= n <= 10^5
+ * 	1 <= dist[i] <= 10^5
+ * 	1 <= hour <= 10^9
+ * 	There will be at most two digits after the decimal point in hour.
+ ******************************************************************************************************/
+
+class Solution {
+public:
+    bool verify(vector<int>& dist, double hour, int speed) {
+        double t = 0;
+        int n = dist.size();
+        for (int i=0; i<n-1; i++){
+            t += (dist[i] + speed -1) / speed;
+        }
+        t += (double)dist[n-1]/speed;
+        return t <= hour;
+    }
+    
+    int minSpeedOnTime(vector<int>& dist, double hour) {
+        int n = dist.size();
+        if (hour <= n-1) return -1;
+        
+        int low = 1, high = 1e7;
+        while (low < high) {
+            int mid = low + (high - low) / 2;
+            if (verify(dist, hour, mid)) {
+                high = mid;
+            } else {
+                low = mid + 1;
+            }
+        }
+        return high;
+    }
+};