cycle in maze

Problems/Graph/Day-12/sol/ishanrajsingh/Solution1.py

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+# Submission Link: https://codeforces.com/contest/769/submission/357188627
+# Approach: use BFS and precompute dist from start and greedy build lexicographically smallest valid cycle by choosing moves in order L,R,U,D
+# Runtime: O(n*m + k)
+import sys
+from collections import deque
+input=sys.stdin.readline
+n,m,k=map(int,input().split())
+maze=[list(input().strip()) for _ in range(n)]
+dirs=[('D',1,0),('L',0,-1),('R',0,1),('U',-1,0)]
+sx=sy=0
+for i in range(n):
+    for j in range(m):
+        if maze[i][j]=='X':
+            sx,sy=i,j
+dist=[[10**18]*m for _ in range(n)]
+dist[sx][sy]=0
+dq=deque([(sx,sy)])
+while dq:
+    x,y=dq.popleft()
+    for _,dx,dy in dirs:
+        nx,ny=x+dx,y+dy
+        if 0<=nx<n and 0<=ny<m and maze[nx][ny]!='*' and dist[nx][ny]>dist[x][y]+1:
+            dist[nx][ny]=dist[x][y]+1
+            dq.append((nx,ny))
+if k%2==1:
+    print("IMPOSSIBLE")
+    sys.exit()
+res=[]
+cx,cy=sx,sy
+for _ in range(k):
+    moved=False
+    for ch,dx,dy in [('D',1,0),('L',0,-1),('R',0,1),('U',-1,0)]:
+        nx,ny=cx+dx,cy+dy
+        if 0<=nx<n and 0<=ny<m and maze[nx][ny]!='*':
+            rem=k-len(res)-1
+            if dist[nx][ny]<=rem:
+                res.append(ch)
+                cx,cy=nx,ny
+                moved=True
+                break
+    if not moved:
+        print("IMPOSSIBLE")
+        sys.exit()
+print("".join(res))