joi 17-soccer

Author: thecodingwizard

JOI/JOI 17-soccer.cpp

@@ -0,0 +1,121 @@
+/*
+ * It's never optimal for someone to touch the ball twice.
+ *
+ * We can solve with dijkstra's, where our state is
+ *
+ * dist(i, j, k): min cost to get the ball to (i,j) where:
+ * - if 0 <= k <= 3, k represents the direction the ball is currently traveling
+ *   (the ball is is being kicked)
+ * - if k = 4, the ball is no longer traveling and is under the posession of a player
+ *
+ * We can use multi source BFS to find the min dist between every grid cell and the closest
+ * player. Then, to transition to k = 4, we can just move the closest player to the
+ * location of the ball.
+ */
+
+#include <bits/stdc++.h>
+
+using namespace std;
+
+using ll = long long;
+#define ii pair<int, int>
+#define f first
+#define s second
+#define pb push_back
+#define mp make_pair
+#define all(x) x.begin(), x.end()
+#define sz(x) (int)x.size()
+#define F0R(i, n) for (int i = 0; i < n; i++)
+#define FOR(i, a, b) for (int i = a; i < b; i++)
+#define inf 1000000010
+
+int h, w; 
+// min dist to get a player to (i, j)
+ll getPlayer[501][501];
+// min cost to get ball to (i, j)
+// {0-3}: direction the ball is currently traveling (kicked)
+// 4: The ball has landed and a person is currently holding it
+ll dist[501][501][5];
+ll a, b, c;
+
+bool g(ii x) {
+    return x.f >= 0 && x.f <= h && x.s >= 0 && x.s <= w;
+}
+
+int main() {
+    cin.tie(0)->sync_with_stdio(0);
+
+    cin >> h >> w;
+    F0R(i, h+1) F0R(j, w+1) getPlayer[i][j] = 1e18;
+    F0R(i, h+1) F0R(j, w+1) F0R(k, 5) dist[i][j][k] = 1e18;
+    cin >> a >> b >> c;
+    int n; cin >> n;
+    queue<ii> q;
+    ii first;
+    F0R(i, n-1) {
+        int x, y; cin >> x >> y; q.push(mp(x, y));
+        if (i == 0) first = mp(x,y);
+        getPlayer[x][y] = 0;
+    }
+    int dx[4]{-1,0,1,0};
+    int dy[4]{0,-1,0,1};
+    while (!q.empty()) {
+        ii u = q.front(); q.pop();
+        F0R(i, 4) {
+            ii v = mp(u.f+dx[i], u.s+dy[i]);
+            if (g(v) && getPlayer[v.f][v.s] == 1e18) {
+                getPlayer[v.f][v.s] = getPlayer[u.f][u.s]+1;
+                q.push(v);
+            }
+        }
+    }
+    ii dest; cin >> dest.f >> dest.s;
+
+    priority_queue<pair<ll, pair<ii, int>>, vector<pair<ll, pair<ii, int>>>, greater<pair<ll, pair<ii, int>>>> pq;
+    pq.push(mp(0, mp(first, 4)));
+    dist[first.f][first.s][4] = 0;
+    while (!pq.empty()) {
+        pair<ll, pair<ii, int>> top = pq.top(); pq.pop();
+        ll d = top.f;
+        ii u = top.s.f;
+        int dir = top.s.s;
+        if (dist[u.f][u.s][dir] != d) continue;
+        
+        if (dir == 4) {
+            // choose a direction and kick it
+            F0R(i, 4) {
+                ii v = u;
+                if (g(v) && dist[v.f][v.s][i] > d+b) {
+                    dist[v.f][v.s][i] = d+b;
+                    pq.push(mp(d+b, mp(v, i)));
+                }
+            }
+            // or, choose a direction and move
+            F0R(i, 4) {
+                ii v = mp(u.f+dx[i], u.s+dy[i]);
+                if (g(v) && dist[v.f][v.s][4] > d+c) {
+                    dist[v.f][v.s][4] = d+c;
+                    pq.push(mp(d+c, mp(v, 4)));
+                }
+            }
+        } else {
+            // keep kicking it
+            ii v = mp(u.f+dx[dir], u.s+dy[dir]);
+            if (g(v) && dist[v.f][v.s][dir] > d+a) {
+                dist[v.f][v.s][dir] = d+a;
+                pq.push(mp(d+a, mp(v, dir)));
+            }
+            // stop, get somebody to pick it up
+            if (dist[u.f][u.s][4] > d+getPlayer[u.f][u.s]*c) {
+                dist[u.f][u.s][4] = d+getPlayer[u.f][u.s]*c;
+                pq.push(mp(d+getPlayer[u.f][u.s]*c, mp(u, 4)));
+            }
+        }
+    }
+
+    ll ans = dist[dest.f][dest.s][4];
+    F0R(i, 4) ans = min(ans, dist[dest.f][dest.s][i]);
+    cout << ans << endl;
+
+    return 0;
+}

input.txt

@@ -1,2 +1,10 @@
+300 500
+1000000000 1000000000 1000000000
 2
-1 2
+0 0
+300 500
+3 0
+3 0
+4 0
+0 4
+