Merge pull request #440 from Aaryan-Degama/d7q2

D7q2

Author: zonedoutdg

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

@@ -0,0 +1,99 @@
+//link : https://codeforces.com/contest/1777/submission/356090789
+
+#include <bits/stdc++.h>
+using namespace std;
+
+#define fastio ios::sync_with_stdio(false); cin.tie(NULL);
+
+using ll = long long;
+using vi = vector<int>;
+
+void solve() {
+    int n, m;
+    cin >> n >> m;
+
+    vi a(n);
+    for (int i = 0; i < n; i++) cin >> a[i];
+
+    sort(a.begin(), a.end());
+
+    vi cnt(m + 1, 0);
+    int covered = 0;
+
+    auto add = [&](int x) {
+        for (int d = 1; d * d <= x; d++) {
+            if (x % d == 0) {
+                if (d <= m) {
+                    if (cnt[d] == 0) covered++;
+                    cnt[d]++;
+                }
+                int other = x / d;
+                if (other != d && other <= m) {
+                    if (cnt[other] == 0) covered++;
+                    cnt[other]++;
+                }
+            }
+        }
+    };
+
+    auto remove = [&](int x) {
+        for (int d = 1; d * d <= x; d++) {
+            if (x % d == 0) {
+                if (d <= m) {
+                    cnt[d]--;
+                    if (cnt[d] == 0) covered--;
+                }
+                int other = x / d;
+                if (other != d && other <= m) {
+                    cnt[other]--;
+                    if (cnt[other] == 0) covered--;
+                }
+            }
+        }
+    };
+
+    ll ans = LLONG_MAX;
+    int l = 0;
+
+    for (int r = 0; r < n; r++) {
+        add(a[r]);
+
+        while (covered == m) {
+            ans = min(ans, (ll)a[r] - a[l]);
+            remove(a[l]);
+            l++;
+        }
+    }
+
+    if (ans == LLONG_MAX) cout << -1 << '\n';
+    else cout << ans << '\n';
+}
+
+int main() {
+    fastio
+
+    int t;
+    cin >> t;
+    while (t--) {
+        solve();
+    }
+    return 0;
+}
+
+
+/*
+
+Approach:
+- Sort the students by smartness.
+- Use a sliding window (two pointers) on the sorted array.
+- A student with smartness x covers all topics T ≤ m such that T divides x.
+- Maintain a count array for topics and a variable tracking how many topics
+  are currently covered.
+- Expand the right pointer to add students, and once all topics are covered,
+  shrink from the left to minimize the smartness difference.
+
+Complexity:
+- Time: O(n log n + n√max(a))
+- Space: O(m)
+
+*/