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Author: BrandonTang89

Other_Tasks/CF2051_G_Snakes.cpp

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+/**CF2051G Snakes
+ * Construct a graph G(V, E) such that V = {1, 2, ..., n} and E = {(u, v, w) | the minimum distance snake v must be put to the immediate right of snake u (i.e. s_u - s_v) must be at least w}.
+ * Now we are just looking for a variation of the shortest hamiltonian path (where we also need to count the number of positions the last snake moves, i.e. the final head position of the last snake).
+ * This is done with bitmask DP in O(n^2 2^n)
+ */
+#pragma GCC optimize("Ofast")
+#pragma GCC optimize("unroll-loops")
+#include <bits/stdc++.h>
+using namespace std;
+
+typedef long long ll;
+
+constexpr ll inf = 1e18;
+int n, q;
+vector<int> heads;
+vector<int> tails;
+vector<vector<int>> adjmat;
+vector<vector<ll>> memo;
+ll dp(int u, int avail) {
+    if (avail == 0) return heads[u];
+    if (memo[u][avail] != -1) return memo[u][avail];
+
+    memo[u][avail] = inf;
+    int bm = avail;
+    while (bm) {
+        int v = __builtin_ctz(bm);
+        bm ^= (1 << v);
+        memo[u][avail] = min(memo[u][avail], dp(v, avail ^ (1 << v)) + adjmat[u][v]);
+    }
+
+    return memo[u][avail];
+}
+
+int main() {
+    cin >> n >> q;
+    heads.assign(n, 0);
+    tails.assign(n, 0);
+    adjmat.assign(n, vector<int>(n, 1));
+
+    for (int i = 0; i < q; i++) {
+        int u;
+        char op;
+        cin >> u >> op;
+        u--;
+        if (op == '+') {
+            heads[u]++;
+            for (int v = 0; v < n; v++) {
+                if (u != v) {
+                    adjmat[u][v] = max(adjmat[u][v], heads[u] - tails[v] + 1);
+                }
+            }
+        } else {
+            tails[u]++;
+        }
+    }
+
+    memo.assign(n, vector<ll>(1 << n, -1));
+    ll ans = inf;
+    for (int i = 0; i < n; i++) {
+        ans = min(ans, dp(i, ((1 << n) - 1) ^ (1 << i)));
+    }
+    cout << ans + 1 << endl;
+
+    return 0;
+}