Spaces:
Sleeping
Sleeping
File size: 9,556 Bytes
3bf8430 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 |
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"] |