reorg Silver sorting and searching modules, move some modules to Gold

content/3_Silver/Binary_Search.mdx

@@ -6,15 +6,12 @@ redirects:
 title: 'Binary Search'
 author: Darren Yao, Abutalib Namazov, Andrew Wang, Qi Wang, Dustin Miao
 prerequisites:
-  - greedy-sorting
+  - binary-search-sorted-array
 description:
-  'Binary searching on arbitrary monotonic functions and built-in functions for
-  binary search.'
+  'Binary searching on arbitrary monotonic functions.'
 frequency: 3
 ---
 
-<!-- process numbers from left to right, keep track of the last element of each block and use binary search of lower_bound to find which block the current numbers belongs -->
-
 ## Introduction
 
 <Resources>
@@ -57,13 +54,14 @@ frequency: 3
 
 <YouTube id="GU7DpgHINWQ" />
 
-When we binary search on an answer, we start with a search space of size $N$
+When we binary search, we start with a search space of size $N$
 which we know the answer lies in. Then each iteration of the binary search cuts
 the search space in half, so the algorithm tests $\mathcal{O}(\log N)$ values.
 This is efficient and much better than testing each possible value in the search
 space.
 
-## Binary Searching on Monotonic Functions
+
+## Binary Search on Monotonic Functions
 
 Let's say we have a boolean function `f(x)`. Usually, in such problems, we want
 to find the maximum or minimum value of $x$ such that `f(x)` is true. Similarly
@@ -812,311 +810,6 @@ The first version of `firstTrue` won't work if `hi-lo` initially exceeds
 `INT_MAX` at any point during execution. If this is an issue, use `long long`s
 instead of `int`s.
 
-## Library Functions For Binary Search
-
-<LanguageSection>
-
-<CPPSection>
-
-<Resources>
-	<Resource
-		source="CPP"
-		url="http://www.cplusplus.com/reference/algorithm/lower_bound/"
-		title="lower_bound, upper_bound"
-		starred
-	>
-		with examples
-	</Resource>
-</Resources>
-
-</CPPSection>
-
-<JavaSection>
-
-<Resources>
-	<Resource
-		source="JAVA"
-		url="https://docs.oracle.com/javase/7/docs/api/java/util/Arrays.html#binarySearch(int[],%20int)"
-		title="Arrays.binarySearch"
-	/>
-	<Resource
-		source="JAVA"
-		url="https://docs.oracle.com/javase/7/docs/api/java/util/Collections.html#binarySearch(java.util.List,%20T)"
-		title="Collections.binarySearch"
-	/>
-</Resources>
-
-</JavaSection>
-
-<PySection>
-
-<Resources>
-	<Resource
-		source="Python"
-		url="https://docs.python.org/3/library/bisect.html"
-		title="Array bisection algorithm"
-	/>
-	<Resource
-		source="GFG"
-		url="https://www.geeksforgeeks.org/binary-search-bisect-in-python/"
-		title="Binary Search (bisect) in Python"
-	/>
-</Resources>
-
-</PySection>
-
-</LanguageSection>
-
-### Example - Counting Haybales
-
-<FocusProblem problem="count" />
-
-As each of the points are in the range $0 \ldots 1\,000\,000\,000$, storing
-locations of haybales in a boolean array and then taking prefix sums of that
-would take too much time and memory.
-
-Instead, let's place all of the locations of the haybales into a list and sort
-it. Now we can use binary search to count the number of cows in any range
-$[A,B]$ in $\mathcal{O}(\log N)$ time.
-
-### With Built-in Function
-
-<LanguageSection>
-
-<CPPSection>
-
-We can use the the built-in
-[`lower_bound`](https://en.cppreference.com/w/cpp/algorithm/lower_bound) and
-[`upper_bound`](https://en.cppreference.com/w/cpp/algorithm/upper_bound)
-functions.
-
-```cpp
-#include <bits/stdc++.h>
-using namespace std;
-
-void setIO(string name = "") {  // name is nonempty for USACO file I/O
-	ios_base::sync_with_stdio(0);
-	cin.tie(0);  // see Fast Input & Output
-	// alternatively, cin.tie(0)->sync_with_stdio(0);
-	if (!name.empty()) {
-		freopen((name + ".in").c_str(), "r", stdin);  // see Input & Output
-		freopen((name + ".out").c_str(), "w", stdout);
-	}
-}
-
-int main() {
-	setIO("haybales");
-	int bale_num;
-	int query_num;
-	cin >> bale_num >> query_num;
-	vector<int> bales(bale_num);
-	for (int i = 0; i < bale_num; i++) { cin >> bales[i]; }
-
-	sort(begin(bales), end(bales));
-	for (int i = 0; i < query_num; i++) {
-		int q_start;
-		int q_end;
-		cin >> q_start >> q_end;
-		cout << upper_bound(begin(bales), end(bales), q_end) -
-		            lower_bound(begin(bales), end(bales), q_start)
-		     << "\n";
-	}
-}
-```
-
-</CPPSection>
-<JavaSection>
-
-We can use the builtin
-[`Arrays.binarySearch`](<https://docs.oracle.com/javase/7/docs/api/java/util/Arrays.html#binarySearch(int[],%20int)>)
-function.
-
-```java
-import java.io.*;
-import java.util.*;
-
-public class Haybales {
-	public static void main(String[] args) throws IOException {
-		BufferedReader br = new BufferedReader(new FileReader(new File("haybales.in")));
-		PrintWriter out = new PrintWriter("haybales.out");
-		StringTokenizer st = new StringTokenizer(br.readLine());
-
-		int baleNum = Integer.parseInt(st.nextToken());
-		int queryNum = Integer.parseInt(st.nextToken());
-		int[] bales = new int[baleNum];
-		st = new StringTokenizer(br.readLine());
-		for (int i = 0; i < baleNum; i++) {
-			bales[i] = Integer.parseInt(st.nextToken());
-		}
-
-		Arrays.sort(bales);
-		for (int i = 0; i < queryNum; i++) {
-			st = new StringTokenizer(br.readLine());
-			int start = Integer.parseInt(st.nextToken());
-			int end = Integer.parseInt(st.nextToken());
-
-			// Get the left-est bale that's still in the interval
-			int bi = Arrays.binarySearch(bales, start);
-			if (bi < 0) { bi = Math.abs(bi + 1); }
-
-			// And also get the right-est bale that's still in the interval
-			int ti = Arrays.binarySearch(bales, end);
-			if (ti < 0) { ti = Math.abs(ti + 2); }
-			out.println(ti - bi + 1);
-		}
-		out.close();
-	}
-}
-```
-
-</JavaSection>
-<PySection>
-
-We can use the builtin
-[`bisect.bisect`](https://docs.python.org/3/library/bisect.html#bisect.bisect)
-function.
-
-```py
-from bisect import bisect
-
-inp = open("haybales.in", "r")
-out = open("haybales.out", "w")
-
-bale_num, query_num = map(int, inp.readline().split())
-bales = sorted(list(map(int, inp.readline().split())))
-for _ in range(query_num):
-	start, end = map(int, inp.readline().split())
-	print(bisect(bales, end) - bisect(bales, start - 1), file=out)
-```
-
-</PySection>
-</LanguageSection>
-
-### Without Using Built-in Functions
-
-<LanguageSection>
-<CPPSection>
-
-```cpp
-#include <bits/stdc++.h>
-using namespace std;
-
-void setIO(string name = "") {  // name is nonempty for USACO file I/O
-	ios_base::sync_with_stdio(0);
-	cin.tie(0);  // see Fast Input & Output
-	// alternatively, cin.tie(0)->sync_with_stdio(0);
-	if (!name.empty()) {
-		freopen((name + ".in").c_str(), "r", stdin);  // see Input & Output
-		freopen((name + ".out").c_str(), "w", stdout);
-	}
-}
-
-int main() {
-	setIO("haybales");
-	int bale_num;
-	int query_num;
-	cin >> bale_num >> query_num;
-	vector<int> bales(bale_num);
-	for (int &i : bales) { cin >> i; }
-
-	sort(begin(bales), end(bales));
-	// Returns the number of elements that are at most x
-	auto atMost = [&](int x) {
-		int lo = 0;
-		int hi = bales.size();
-		while (lo < hi) {
-			int mid = (lo + hi) / 2;
-			if (bales[mid] <= x) {
-				lo = mid + 1;
-			} else {
-				hi = mid;
-			}
-		}
-		return lo;
-	};
-
-	for (int i = 0; i < query_num; ++i) {
-		int q_start;
-		int q_end;
-		cin >> q_start >> q_end;
-		cout << atMost(q_end) - atMost(q_start - 1) << "\n";
-	}
-}
-```
-
-</CPPSection>
-<JavaSection>
-
-```java
-import java.io.*;
-import java.util.*;
-
-public class Haybales {
-	static int[] bales;
-	public static void main(String[] args) throws IOException {
-		Kattio io = new Kattio("haybales");
-		int baleNum = io.nextInt();
-		int queryNum = io.nextInt();
-		bales = new int[baleNum];
-		for (int i = 0; i < baleNum; i++) { bales[i] = io.nextInt(); }
-		Arrays.sort(bales);
-
-		for (int i = 0; i < queryNum; ++i) {
-			int start = io.nextInt();
-			int end = io.nextInt();
-			io.println(atMost(end) - atMost(start - 1));
-		}
-		io.close();
-	}
-
-	// Returns the number of elements that are at most x
-	public static int atMost(int x) {
-		int lo = 0;
-		int hi = bales.length;
-		while (lo < hi) {
-			int mid = (lo + hi) / 2;
-			if (bales[mid] <= x) {
-				lo = mid + 1;
-			} else {
-				hi = mid;
-			}
-		}
-		return lo;
-	}
-
-	// CodeSnip{Kattio}
-}
-```
-
-</JavaSection>
-<PySection>
-
-```py
-def at_most(x: int) -> int:
-	lo = 0
-	hi = len(bales)
-	while lo < hi:
-		mid = (lo + hi) // 2
-		if bales[mid] <= x:
-			lo = mid + 1
-		else:
-			hi = mid
-	return lo
-
-
-inp = open("haybales.in", "r")
-out = open("haybales.out", "w")
-
-bale_num, query_num = map(int, inp.readline().split())
-bales = sorted(list(map(int, inp.readline().split())))
-for _ in range(query_num):
-	start, end = map(int, inp.readline().split())
-	print(at_most(end) - at_most(start - 1), file=out)
-```
-
-</PySection>
-
-</LanguageSection>
 
 ## Problems
 

content/3_Silver/Binary_Search.problems.json

@@ -116,33 +116,7 @@
       }
     }
   ],
-  "count": [
-    {
-      "uniqueId": "usaco-666",
-      "name": "Counting Haybales",
-      "url": "http://www.usaco.org/index.php?page=viewproblem2&cpid=666",
-      "source": "Silver",
-      "difficulty": "Easy",
-      "isStarred": false,
-      "tags": ["Binary Search"],
-      "solutionMetadata": {
-        "kind": "internal"
-      }
-    }
-  ],
   "general": [
-    {
-      "uniqueId": "cf-702C",
-      "name": "Cellular Network",
-      "url": "https://codeforces.com/contest/702/problem/C",
-      "source": "CF",
-      "difficulty": "Easy",
-      "isStarred": false,
-      "tags": ["Binary Search"],
-      "solutionMetadata": {
-        "kind": "internal"
-      }
-    },
     {
       "uniqueId": "cses-1620",
       "name": "Factory Machines",
@@ -179,6 +153,18 @@
         "kind": "internal"
       }
     },
+    {
+      "uniqueId": "cf-862E",
+      "name": "Mahmoud & Ehab & Function",
+      "url": "https://codeforces.com/contest/862/problem/E",
+      "source": "CF",
+      "difficulty": "Normal",
+      "isStarred": false,
+      "tags": ["Binary Search"],
+      "solutionMetadata": {
+        "kind": "internal"
+      }
+    },
     {
       "uniqueId": "cc-TRPTSTIC",
       "name": "TripTastic",