init

1M.py

@@ -0,0 +1,68 @@
+import sys
+
+data = sys.stdin.read().split()
+if not data:
+    exit()
+n = int(data[0])
+m = int(data[1])
+k = int(data[2])
+a = [0] * (n + 1)
+max_val = 0
+for i in range(1, n + 1):
+    a[i] = int(data[2 + i])
+    if a[i] > max_val:
+        max_val = a[i]
+adj = [[] for _ in range(n + 1)]
+idx = 3 + n
+for _ in range(m):
+    u = int(data[idx])
+    v = int(data[idx+1])
+    adj[u].append(v)
+    idx += 2
+l = 1
+r = max_val
+ans = -1
+while l <= r:
+    mid = (l + r) // 2
+    in_degree = [0] * (n + 1)
+    valid_count = 0
+    for u in range(1, n + 1):
+        if a[u] <= mid:
+            valid_count += 1
+            for v in adj[u]:
+                if a[v] <= mid:
+                    in_degree[v] += 1
+    q = []
+    dp = [0] * (n + 1)
+    possible = False
+    for i in range(1, n + 1):
+        if a[i] <= mid:
+            dp[i] = 1
+            if dp[i] >= k:
+                possible = True
+            if in_degree[i] == 0:
+                q.append(i)
+    head = 0
+    visited_count = 0
+    while head < len(q) and not possible:
+        u = q[head]
+        head += 1
+        visited_count += 1
+        for v in adj[u]:
+            if a[v] <= mid:
+                if dp[u] + 1 > dp[v]:
+                    dp[v] = dp[u] + 1
+                    if dp[v] >= k:
+                        possible = True
+                        break
+                in_degree[v] -= 1
+                if in_degree[v] == 0:
+                    q.append(v)
+    if visited_count < valid_count:
+        possible = True
+    if possible:
+        ans = mid
+        r = mid - 1
+    else:
+        l = mid + 1
+print(ans)