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Author: BrandonTang89

Chapter_3_Problem_Solving_Paradigms/Divide_and_Conquer/kattis_carefulascent.cpp

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+#pragma GCC optimize("Ofast")
+#pragma GCC optimize("unroll-loops")
+#include <bits/stdc++.h>
+using namespace std;
+
+typedef long long ll;
+typedef vector<int> vi;
+#define fast_cin()                    \
+    ios_base::sync_with_stdio(false); \
+    cin.tie(NULL);                    \
+    cout.tie(NULL);
+
+double X, Y;
+int n;
+vector<tuple<int, int, double>> shields;  // bottom, top, factor
+
+double f(double horizontalSpeed) {
+    // returns the x coordinate of the point when the y coordinate is Y
+    double x = 0;
+    double y = 0;
+
+    for (auto [shield_bottom, shield_top, factor] : shields) {
+        // go to the shield
+        double dist_to_shield = shield_bottom - y;
+        double time_to_shield = dist_to_shield;
+        x += time_to_shield * horizontalSpeed;
+
+        // go through the shield
+        double dist_through_shield = shield_top - shield_bottom;
+        double time_through_shield = dist_through_shield;
+        x += time_through_shield * factor * horizontalSpeed;
+
+        y = shield_top;
+    }
+
+    // go to the end
+    double dist_to_end = Y - y;
+    double time_to_end = dist_to_end;
+    x += time_to_end * horizontalSpeed;
+
+    return x;
+}
+
+int main() {
+    fast_cin();
+    bool negate = false;
+    cin >> X >> Y;
+    if (X < 0) {
+        negate = true;
+        X = -X;
+    }
+    cin >> n;
+    shields.resize(n);
+    for (int i = 0; i < n; i++) {
+        int x, y;
+        double f;
+        cin >> x >> y >> f;
+        shields[i] = make_tuple(x, y, f);
+    }
+
+    double l = 0;
+    double r = 1e9;
+    for (int i = 0; i < 500; i++) {
+        double m = (l + r) / 2;
+        if (f(m) < X) {  // too slow
+            l = m;
+        } else {
+            r = m;
+        }
+    }
+
+    cout << setprecision(10);
+    if (negate) {
+        cout << -l << endl;
+    } else {
+        cout << l << endl;
+    }
+
+    return 0;
+}