added day7 binary search solutions

Author: MANISH-BEESA

Problems/Binary-Search/Day-07/sol/BEESA-MANISH/Solution1.cpp

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+
+/*
+
+Submission link: https://codeforces.com/contest/1538/submission/356096805
+
+TC - O(N \log N)
+SC - O(N)
+
+Approach :
+Sort the numbers first so they are in increasing order. This makes searching easier.
+Take one number and look for another number after it such that their sum lies between l and r.
+Find the range of numbers that can be added to the current number to stay within l and r.
+Count how many numbers fall in that range and add this count to the answer.
+
+*/
+
+#include <iostream>
+#include <vector>
+#include <algorithm>
+
+using namespace std;
+long long countPairsUnder(const vector<int>& a, int limit) {
+    long long count = 0;
+    int left = 0;
+    int right = a.size() - 1;
+    while (left < right) {
+        if (a[left] + a[right] <= limit) {
+            count += (right - left);
+            left++;
+        } else {
+            right--;
+        }
+    }
+    return count;
+}
+
+void solve() {
+    int n, l, r;
+    cin >> n >> l >> r;
+    vector<int> a(n);
+    for (int i = 0; i < n; i++) {
+        cin >> a[i];
+    }
+    sort(a.begin(), a.end());
+    long long result = countPairsUnder(a, r) - countPairsUnder(a, l - 1);
+    cout << result << "\n";
+}
+
+int main() {
+    int t;
+    cin >> t;
+    while (t--) {
+        solve();
+    }
+    return 0;
+}

Problems/Binary-Search/Day-07/sol/BEESA-MANISH/Solution2.cpp

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+/*
+Submission link: https://codeforces.com/contest/1777/submission/356097157
+- Tc: O(n log n + n√max(a))
+- Sc: O(m)
+
+Approach : 
+Sort the students by smartness so they are in increasing order.
+Use two pointers to form a window of students, adding one student at a time from the right.
+Each student can cover some topics, and we keep track of which topics are covered inside the window.
+When all topics are covered, try removing students from the left to make the smartness difference as small as possible.
+*/
+
+#include <iostream>
+#include <vector>
+#include <algorithm>
+
+using namespace std;
+const int MAXA = 100005;
+vector<int> divisors[MAXA];
+void precompute() {
+    for (int i = 1; i < MAXA; i++) {
+        for (int j = i; j < MAXA; j += i) {
+            divisors[j].push_back(i);
+        }
+    }
+}
+
+void solve() {
+    int n, m;
+    cin >> n >> m;
+    vector<int> a(n);
+    for (int i = 0; i < n; i++) cin >> a[i];
+    
+    sort(a.begin(), a.end());
+    
+    vector<int> count(m + 1, 0);
+    int covered_topics = 0;
+    int min_diff = 1e9;
+    int left = 0;
+
+    for (int right = 0; right < n; right++) {
+        for (int d : divisors[a[right]]) {
+            if (d > m) break; 
+            if (count[d] == 0) covered_topics++;
+            count[d]++;
+        }
+        while (covered_topics == m) {
+            min_diff = min(min_diff, a[right] - a[left]);
+
+            for (int d : divisors[a[left]]) {
+                if (d > m) break;
+                count[d]--;
+                if (count[d] == 0) covered_topics--;
+            }
+            left++;
+        }
+    }
+
+    if (min_diff == 1e9) cout << -1 << "\n";
+    else cout << min_diff << "\n";
+}
+
+int main() {
+    precompute();
+
+    int t;
+    cin >> t;
+    while (t--) {
+        solve();
+    }
+    return 0;
+}