import random from collections import deque from typing import Optional, List from ...environment import VerifiableEnvironment class CirculatingGrid_Environment(VerifiableEnvironment) : # Source : https://www.luogu.com.cn/problem/P3965 prompt_template = \ r"""Consider a {R} × {C} grid, where each cell has coordinates (i, j) (0 ≤ i < {R}, 0 ≤ j < {C}). Each cell contains one of the characters `L`, `R`, `U`, or `D`, meaning: - `L`: moves to (i, (j - 1) MOD {C}) - `R`: moves to (i, (j + 1) MOD {C}) - `U`: moves to ((i - 1) MOD {R}, j) - `D`: moves to ((i + 1) MOD {R}, j) Here, (-1 MOD N) = N - 1. You are given such a grid: {grid} Modify any number of cells so that the resulting grid satisfies the following condition: Starting from any cell, it must be possible to eventually return to the same cell (simply standing there at the beginning does not count). Can you use as small the number of changes (i.e., number of cells modified) as possible? Output the modified grid in the same format — exactly {R} lines, each containing {C} characters (`L`, `R`, `U`, or `D`) with **no separators**.""" def __init__(self, wrong_format : float = -1.0, invalid_solution : float = -0.5, rewarding_strategy : str = "(gold/answer)^beta", rewarding_weight : float = +1.0, rewarding_beta : float = 5.0, **kwargs) : """ Initialize the CirculatingGrid_Environment instance. """ super().__init__(**kwargs) self.rewards = { "wrong_format": wrong_format, "invalid_solution": invalid_solution, "rewarding_strategy": rewarding_strategy, "rewarding_weight": rewarding_weight, "rewarding_beta": rewarding_beta, } def _generate(self) -> None : assert "MAX_R_C" in self.parameter, "MAX_R_C is required in parameter" MAX_R_C = self.parameter["MAX_R_C"] assert MAX_R_C >= 3, "MAX_R_C must be at least 3" R, C = self.parameter["R"], self.parameter["C"] = random.randint(2, MAX_R_C), random.randint(2, MAX_R_C) LRUD_distribution = [random.randint(1, R * C) for _ in range(4)] grid = self.parameter["grid"] = [[random.choices(['L', 'R', 'U', 'D'], weights = LRUD_distribution)[0] for _ in range(C)] for _ in range(R)] # Directions: L, R, U, D DX = [0, 0, -1, 1] # row delta DY = [-1, 1, 0, 0] # col delta DIR_ID = {'L': 0, 'R': 1, 'U': 2, 'D': 3} class Edge: __slots__ = ('to', 'rev', 'cap', 'cost') def __init__(self, to, rev, cap, cost): self.to = to self.rev = rev self.cap = cap self.cost = cost def add_edge(graph, u, v, cap, cost): graph[u].append(Edge(v, len(graph[v]), cap, cost)) graph[v].append(Edge(u, len(graph[u]) - 1, 0, -cost)) def min_cost_max_flow(graph, N, s, t, INF): flow = 0 cost = 0 dist = [0] * N inq = [False] * N prev_node = [-1] * N prev_edge = [-1] * N while True: # SPFA to find shortest augmenting path by cost for i in range(N): dist[i] = INF inq[i] = False prev_node[i] = -1 prev_edge[i] = -1 dist[s] = 0 q = deque([s]) inq[s] = True while q: u = q.popleft() inq[u] = False for ei, e in enumerate(graph[u]): if e.cap > 0: v = e.to nd = dist[u] + e.cost if nd < dist[v]: dist[v] = nd prev_node[v] = u prev_edge[v] = ei if not inq[v]: inq[v] = True q.append(v) if prev_node[t] == -1: break # no more augmenting paths # Find bottleneck addf = INF v = t while v != s: u = prev_node[v] ei = prev_edge[v] e = graph[u][ei] if e.cap < addf: addf = e.cap v = u # Augment v = t while v != s: u = prev_node[v] ei = prev_edge[v] e = graph[u][ei] e.cap -= addf graph[v][e.rev].cap += addf cost += addf * e.cost v = u flow += addf return flow, cost def compute(): # MP holds the direction id (0..3) for each cell MP = [[0] * C for _ in range(R)] for i in range(R): for j in range(C): MP[i][j] = DIR_ID[grid[i][j]] n_left = R * C offset = n_left s = 2 * n_left t = s + 1 N = t + 1 # INF derived from input size; safely larger than any possible path cost INF = R * C * 4 + 5 graph = [[] for _ in range(N)] # Build edges from each cell (left partition) to its 4 neighbors (right partition) for i in range(R): for j in range(C): u = i * C + j for k in range(4): ni = (i + DX[k]) % R nj = (j + DY[k]) % C v = offset + (ni * C + nj) cost = 0 if k == MP[i][j] else 1 add_edge(graph, u, v, 1, cost) # Source to all left nodes; all right nodes to sink for u in range(n_left): add_edge(graph, s, u, 1, 0) for v in range(offset, offset + n_left): add_edge(graph, v, t, 1, 0) _, total_cost = min_cost_max_flow(graph, N, s, t, INF) return total_cost self.parameter["gold_answer"] = compute() assert self.parameter["gold_answer"] >= 0, "Gold answer must be non-negative" def _prompt_generate(self) -> str : return self.prompt_template.format( R = self.parameter["R"], C = self.parameter["C"], grid = "\n".join("".join(row) for row in self.parameter["grid"]), ) def _process(self, answer : Optional[str]) -> Optional[List[str]] : if answer is not None : answer = answer.strip() grid = [] for line in answer.splitlines() : line = line.strip() if line : grid.append(line) return grid else : return None def scorer(self, output : str) -> float : processed_result = self.processor(output) if processed_result is not None : grid = processed_result if len(grid) != self.parameter["R"] : return self.rewards["wrong_format"] if not all(len(row) == self.parameter["C"] for row in grid) : return self.rewards["wrong_format"] if not all(all(c in "LRUD" for c in row) for row in grid) : return self.rewards["wrong_format"] in_degree = [[0] * self.parameter["C"] for _ in range(self.parameter["R"])] for i in range(self.parameter["R"]) : for j in range(self.parameter["C"]) : if grid[i][j] == "L" : in_degree[i][(j - 1 + self.parameter["C"]) % self.parameter["C"]] += 1 elif grid[i][j] == "R" : in_degree[i][(j + 1) % self.parameter["C"]] += 1 elif grid[i][j] == "U" : in_degree[(i - 1 + self.parameter["R"]) % self.parameter["R"]][j] += 1 elif grid[i][j] == "D" : in_degree[(i + 1) % self.parameter["R"]][j] += 1 else : assert False, "Invalid character in grid" if not all(in_degree[i][j] == 1 for i in range(self.parameter["R"]) for j in range(self.parameter["C"])) : return self.rewards["invalid_solution"] answer, gold = sum(int(grid[i][j] != self.parameter["grid"][i][j]) for i in range(self.parameter["R"]) for j in range(self.parameter["C"])), self.parameter["gold_answer"] assert gold <= answer, "Gold answer is greater than the computed answer" if self.rewards["rewarding_strategy"] == "(gold/answer)^beta" : if answer == 0 : assert gold == 0, "Gold answer is non-zero but computed answer is zero" return self.rewards["rewarding_weight"] * 1.0 return self.rewards["rewarding_weight"] * ((gold / answer) ** self.rewards["rewarding_beta"]) elif self.rewards["rewarding_strategy"] == "gold=answer" : return self.rewards["rewarding_weight"] * (gold == answer) else : raise NotImplementedError("Unknown rewarding strategy: {}".format(self.rewards["rewarding_strategy"])) else : return self.rewards["wrong_format"]