From adb912f94214aba109f897d7fb4f09aab239955d Mon Sep 17 00:00:00 2001
From: tiennm99 <tiennm99@outlook.com>
Date: Sat, 29 Nov 2025 00:58:51 +0700
Subject: [PATCH] feat(cpp): add prevoi19_robots (wip)

---
 cpp/prevoi19_robots.cpp | 111 ++++++++++++++++++++++++++++++++++++++++
 1 file changed, 111 insertions(+)
 create mode 100644 cpp/prevoi19_robots.cpp

diff --git a/cpp/prevoi19_robots.cpp b/cpp/prevoi19_robots.cpp
new file mode 100644
index 0000000..c26ad4d
--- /dev/null
+++ b/cpp/prevoi19_robots.cpp
@@ -0,0 +1,111 @@
+#include <iostream>
+#include <vector>
+#include <climits>
+using namespace std;
+
+typedef long long ll;
+
+struct Point {
+    ll x, y;
+
+    Point(ll x = 0, ll y = 0) : x(x), y(y) {
+    }
+};
+
+ll manhattan(const Point &a, const Point &b) {
+    return abs(a.x - b.x) + abs(a.y - b.y);
+}
+
+bool isPossible(ll D, const vector<Point> &chargers, const Point &start, ll N) {
+    ll u0 = start.x + start.y;
+    ll v0 = start.x - start.y;
+    ll min_u = u0 - N;
+    ll max_u = u0 + N;
+    ll min_v = v0 - N;
+    ll max_v = v0 + N;
+
+    vector<Point> test_points;
+
+    vector<ll> u_candidates = {min_u, max_u};
+    vector<ll> v_candidates = {min_v, max_v};
+
+    for (const Point &c: chargers) {
+        ll cu = c.x + c.y;
+        ll cv = c.x - c.y;
+
+        u_candidates.push_back(cu - D);
+        u_candidates.push_back(cu + D);
+        v_candidates.push_back(cv - D);
+        v_candidates.push_back(cv + D);
+    }
+
+    u_candidates.push_back(u0);
+    v_candidates.push_back(v0);
+
+    for (ll u: u_candidates) {
+        for (ll v: v_candidates) {
+            if ((u + v) % 2 == 0) {
+                ll x = (u + v) / 2;
+                ll y = (u - v) / 2;
+                test_points.push_back(Point(x, y));
+            } else {
+                ll x1 = (u + v) / 2;
+                ll y1 = (u - v) / 2;
+                test_points.push_back(Point(x1, y1));
+
+                ll x2 = (u + v + 1) / 2;
+                ll y2 = (u - v - 1) / 2;
+                test_points.push_back(Point(x2, y2));
+            }
+        }
+    }
+
+    for (const Point &p: test_points) {
+        if (manhattan(p, start) > N) continue;
+
+        bool valid = true;
+        for (const Point &c: chargers) {
+            if (manhattan(p, c) < D) {
+                valid = false;
+                break;
+            }
+        }
+        if (valid) return true;
+    }
+
+    return false;
+}
+
+int main() {
+    ios_base::sync_with_stdio(false);
+    cin.tie(NULL);
+
+    int U;
+    ll N;
+    cin >> U >> N;
+
+    vector<Point> chargers(U);
+    for (int i = 0; i < U; i++) {
+        cin >> chargers[i].x >> chargers[i].y;
+    }
+
+    Point start;
+    cin >> start.x >> start.y;
+
+    ll left = 0;
+    ll right = 4e9;
+
+    while (left <= right) {
+        ll mid = left + (right - left) / 2;
+
+        if (isPossible(mid, chargers, start, N)) {
+            left = mid + 1;
+        } else {
+            right = mid - 1;
+        }
+    }
+
+    cout << right << endl;
+
+    return 0;
+}