update cf-702C

solutions/silver/cf-702C.mdx

@@ -12,7 +12,6 @@ author: Nathan Wang, Benjamin Qi, Maggie Liu, Brad Ma, George Pong
 **Time Complexity:** $\mathcal{O}(N \log N)$
 
 <LanguageSection>
-
 <CPPSection>
 
 ```cpp
@@ -21,7 +20,7 @@ using namespace std;
 
 // returns the first index in the array that is >= value, or arr.size() if no
 // such index exists
-int firstAtLeast(const vector<int> &arr, int value) {
+int first_at_least(const vector<int> &arr, int value) {
 	int lo = 0, hi = arr.size();
 	while (lo < hi) {
 		int mid = (lo + hi) / 2;
@@ -48,30 +47,31 @@ int main() {
 		towers.push_back(tower);
 	}
 
-	int minR = 0;
+	int min_r = 0;
 	for (int i = 0; i < n; i++) {
-		int towerRight = firstAtLeast(towers, cities[i]);
-		int towerLeft = towerRight - 1;
-
-		int minRForThisCity = 2e9;
-		if (towerRight < m) {
-			assert(towers[towerRight] >= cities[i]);
-			minRForThisCity = min(minRForThisCity, towers[towerRight] - cities[i]);
+		int tower_right = first_at_least(towers, cities[i]);
+		int tower_left = tower_right - 1;
+
+		int min_r_for_this_city = 2e9;
+		if (tower_right < m) {
+			assert(towers[tower_right] >= cities[i]);
+			min_r_for_this_city =
+			    min(min_r_for_this_city, towers[tower_right] - cities[i]);
 		}
-		if (towerLeft >= 0) {
-			assert(towers[towerLeft] <= cities[i]);
-			minRForThisCity = min(minRForThisCity, cities[i] - towers[towerLeft]);
+		if (tower_left >= 0) {
+			assert(towers[tower_left] <= cities[i]);
+			min_r_for_this_city =
+			    min(min_r_for_this_city, cities[i] - towers[tower_left]);
 		}
 
-		minR = max(minR, minRForThisCity);
+		min_r = max(min_r, min_r_for_this_city);
 	}
 
-	cout << minR << endl;
+	cout << min_r << endl;
 }
 ```
 
 </CPPSection>
-
 <JavaSection>
 
 ```java
@@ -137,7 +137,50 @@ public class CellularNetwork {
 ```
 
 </JavaSection>
+<PySection>
+
+```py
+"""
+returns the first index in the array that is >= value, or len(arr)
+if no such index exists
+"""
+
+
+def first_at_least(value: int) -> int:
+	lo = 0
+	hi = len(towers)
+	while lo < hi:
+		mid = (lo + hi) // 2
+		if towers[mid] > value:
+			hi = mid
+		else:
+			lo = mid + 1
+
+	return lo
+
+
+n, m = map(int, input().split())
+cities = list(map(int, input().split()))
+towers = list(map(int, input().split()))
 
+min_r = 0
+for i in range(n):
+	tower_right = first_at_least(cities[i])
+	tower_left = tower_right - 1
+
+	min_r_for_this_city = float("inf")
+	if tower_right < m:
+		min_r_for_this_city = min(min_r_for_this_city, towers[tower_right] - cities[i])
+
+	if tower_left >= 0:
+		min_r_for_this_city = min(min_r_for_this_city, cities[i] - towers[tower_left])
+
+	min_r = max(min_r, min_r_for_this_city)
+
+print(min_r)
+```
+
+</PySection>
 </LanguageSection>
 
 ## Solution 2 - Two Pointers
@@ -149,7 +192,6 @@ We store two pointers, one for the current city and one for the current tower. W
 **Time Complexity:** $\mathcal{O}(N)$
 
 <LanguageSection>
-
 <CPPSection>
 
 ```cpp
@@ -202,7 +244,6 @@ int main() {
 ```
 
 </CPPSection>
-
 <PySection>
 
 ```py
@@ -242,7 +283,6 @@ print(max_dist)
 ```
 
 </PySection>
-
 <JavaSection>
 
 ```java
@@ -298,8 +338,8 @@ public class CellularNetwork2 {
 	// CodeSnip{Kattio}
 }
 ```
-</JavaSection>
 
+</JavaSection>
 </LanguageSection>
 
 ## Solution 3 - Using a Set
@@ -319,10 +359,9 @@ left of the city. Define $\texttt{dist}$ to be the minimum of the distance to
 the tower on the right and the distance to the tower on the left. Then, set $r$
 to be the maximum of itself and $\texttt{dist}$.
 
-**Time Complexity:** $\mathcal{O}(N\log N)$
+**Time Complexity:** $\mathcal{O}(N \log M)$
 
 <LanguageSection>
-
 <CPPSection>
 
 ```cpp
@@ -346,16 +385,16 @@ int main() {
 	for (int i = 0; i < n; i++) {
 		int dist = 2e9 + 1;
 		// find closest tower to the right of the city
-		auto closesttower = towers.lower_bound(cities[i]);
-		if (closesttower != towers.end()) {
+		auto closest_tower = towers.lower_bound(cities[i]);
+		if (closest_tower != towers.end()) {
 			// if a tower is found, update the distance
-			dist = *closesttower - cities[i];
+			dist = *closest_tower - cities[i];
 		}
 		// find closest tower to the left of the city
-		if (closesttower != towers.begin()) {
-			closesttower--;
+		if (closest_tower != towers.begin()) {
+			closest_tower--;
 			// update dist with the minimum of the distances
-			dist = min(dist, cities[i] - *closesttower);
+			dist = min(dist, cities[i] - *closest_tower);
 		}
 		r = max(r, dist);
 	}
@@ -365,7 +404,6 @@ int main() {
 ```
 
 </CPPSection>
-
 <JavaSection>
 
 ```java
@@ -410,5 +448,4 @@ public class CellularNetwork {
 ```
 
 </JavaSection>
-
 </LanguageSection>