🥺chore

Author: hppRC

main.py

@@ -19,13 +19,13 @@ def LR(n): return [L() for _ in range(n)]
 def IR(n): return [I() for _ in range(n)]
 def LIR(n): return [LI() for _ in range(n)]
 def LIR1(n): return [LI1() for _ in range(n)]
-def SR(n): return [SL() for _ in range(n)]
+def SLR(n): return [SL() for _ in range(n)]
 def LSR(n): return [LS() for _ in range(n)]
 
 def perm(n, r): return math.factorial(n) // math.factorial(r)
 def comb(n, r): return math.factorial(n) // (math.factorial(r) * math.factorial(n-r))
 
-def make_list(n, *args, default=0): return [make_list(*args, default=default) for _ in range(n)] if len(args) > 0 else [default for _ in range(n)]
+def make_list(n, *args, default=0): return [make_list(*args, default=default) for _ in range(n)] if args else [default for _ in range(n)]
 
 dire = [[1, 0], [0, 1], [-1, 0], [0, -1]]
 dire8 = [[1, 0], [1, 1], [0, 1], [-1, 1], [-1, 0], [-1, -1], [0, -1], [1, -1]]

practice2/d/main.py

@@ -1,3 +1,5 @@
+# thanks: https://atcoder.jp/contests/practice2/submissions/16784996
+
 #!usr/bin/env python3
 from collections import defaultdict, deque, Counter, OrderedDict
 from bisect import bisect_left, bisect_right
@@ -19,13 +21,13 @@ def LR(n): return [L() for _ in range(n)]
 def IR(n): return [I() for _ in range(n)]
 def LIR(n): return [LI() for _ in range(n)]
 def LIR1(n): return [LI1() for _ in range(n)]
-def SR(n): return [SL() for _ in range(n)]
+def SLR(n): return [SL() for _ in range(n)]
 def LSR(n): return [LS() for _ in range(n)]
 
 def perm(n, r): return math.factorial(n) // math.factorial(r)
 def comb(n, r): return math.factorial(n) // (math.factorial(r) * math.factorial(n-r))
 
-def make_list(n, *args, default=0): return [make_list(*args, default=default) for _ in range(n)] if len(args) > 0 else [default for _ in range(n)]
+def make_list(n, *args, default=0): return [make_list(*args, default=default) for _ in range(n)] if args else [default for _ in range(n)]
 
 dire = [[1, 0], [0, 1], [-1, 0], [0, -1]]
 dire8 = [[1, 0], [1, 1], [0, 1], [-1, 1], [-1, 0], [-1, -1], [0, -1], [1, -1]]
@@ -36,8 +38,127 @@ def make_list(n, *args, default=0): return [make_list(*args, default=default) fo
 
 sys.setrecursionlimit(1000000)
 
+class MaxFlowGraph:
+    def __init__(self, N):
+        self.N = N
+        self.graph = [[] for _ in range(N)]
+        self.capacities = [dict() for _ in range(N)]
+
+    def add_edge(self, v, w, cap=1):
+        self.graph[v].append(w)
+        self.graph[w].append(v)
+        self.capacities[v][w] = cap
+        self.capacities[w][v] = 0
+
+    def bfs(self, s, t):
+        self.level = [-1] * self.N
+        q = deque([s])
+        self.level[s] = 0
+        while q:
+            v = q.popleft()
+            for w, cap in self.capacities[v].items():
+                if cap and self.level[w] == -1:
+                    self.level[w] = self.level[v] + 1
+                    if w == t: return True
+                    q.append(w)
+        return False
+
+    def dfs(self, s, t, limit):
+        st = [t]
+        while st:
+            v = st[-1]
+            if v == s: break
+            #vから行ける全ての頂点について
+            while self.it[v] < len(self.graph[v]):
+                # w -> v の cap
+                w = self.graph[v][self.it[v]]
+                cap = self.capacities[w][v]
+                if cap and self.level[w] != -1 and self.level[v] > self.level[w]:
+                    st.append(w)
+                    break
+                self.it[v] += 1
+            else:
+                st.pop()
+                self.level[v] = self.N
+        else: return 0
+
+        flow = min(limit, min(self.capacities[st[i + 1]][st[i]] for i in range(len(st) - 2)))
+        for i in range(len(st) - 1):
+            self.capacities[st[i]][st[i+1]] += flow
+            self.capacities[st[i+1]][st[i]] -= flow
+        return flow
+
+    def flow(self, s, t, flow_limit=18446744073709551615):
+        flow = 0
+        while flow < flow_limit and self.bfs(s, t):
+            self.it = [0]*self.N
+            while flow < flow_limit:
+                f = self.dfs(s, t, flow_limit - flow)
+                if not f: break
+                flow += f
+        return flow
+
+    def min_cut(self, s):
+        visited = [False]*self.N
+        q = [s]
+        while q:
+            v = q.pop()
+            visited[v] = True
+            for w, cap in self.capacities[v].items():
+                if cap and not visited[w]:
+                    q.append(w)
+
 def main():
-    N = I()
+    N, M = LI()
+    S = SLR(N)
+    g = MaxFlowGraph(N*M+2)
+
+    s = N*M
+    t = N*M+1
+
+    # 偶数はblack, 奇数はwhiteとして市松模様に塗る、二部グラフの最大マッチング問題
+    # s -> black -> white -> t の辺を張って最大流を求める
+    for y in range(N):
+        for x in range(M):
+            # black
+            if (y+x) % 2 == 0:
+                g.add_edge(s, M*y+x)
+                for dy, dx in [[1, 0], [0, 1]]:
+                    ny, nx = y + dy, x + dx
+                    if 0 <= ny < N and 0 <= nx < M and S[y][x] == "." and S[ny][nx] == ".":
+                        g.add_edge(M*y+x, M*ny+nx)
+            # white
+            else:
+                g.add_edge(M*y+x, t)
+                for dy, dx in [[1, 0], [0, 1]]:
+                    ny, nx = y + dy, x + dx
+                    if 0 <= ny < N and 0 <= nx < M and S[y][x] == "." and S[ny][nx] == ".":
+                        g.add_edge(M*ny+nx, M*y+x)
+
+    print(g.flow(s, t))
+
+    # blackから考える
+    for u in range(N*M+2):
+        uy, ux = divmod(u, M)
+        if (uy + ux) % 2 == 1: continue
+
+        for v, cap in g.capacities[u].items():
+            if cap != 0: continue
+            vy, vx = divmod(v, M)
+            if u != s and u != t and v != s and v != t:
+                if uy - 1 == vy:
+                    S[uy][ux], S[vy][vx] = "^", "v"
+                elif uy + 1 == vy:
+                    S[uy][ux], S[vy][vx] = "v", "^"
+                elif ux + 1 == vx:
+                    S[uy][ux], S[vy][vx] = ">", "<"
+                elif ux - 1 == vx:
+                    S[uy][ux], S[vy][vx] = "<", ">"
+
+    for p in S:
+        print("".join(p))
+
+
 
 if __name__ == '__main__':
     main()