From ac0b5ff6d57bc572b62ccdd64feeb1437822fa9a Mon Sep 17 00:00:00 2001
From: Ilya Nikokoshev <ilya.nikokoshev@gmail.com>
Date: Tue, 16 Jan 2024 12:55:36 +0100
Subject: [PATCH] Solve trains

---
 trains.py | 118 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 118 insertions(+)
 create mode 100644 trains.py

diff --git a/trains.py b/trains.py
new file mode 100644
index 0000000..d6d469c
--- /dev/null
+++ b/trains.py
@@ -0,0 +1,118 @@
+import unittest
+
+
+class TestFenwickTree(unittest.TestCase):
+    def setUp(self):
+        self.t = FenwickTree(3)
+
+    def test_add_and_upto(self):
+        self.t.add(2)
+        self.assertEqual(self.t.upto(0), 0)
+        self.assertEqual(self.t.upto(1), 0)
+        self.assertEqual(self.t.upto(2), 1)
+        self.assertEqual(self.t.upto(3), 1)
+
+    def test_min_free(self):
+        self.t.add(2)
+        self.assertEqual(self.t.min_free(), 1)
+        self.t.add(1)
+        self.t.add(3)
+        self.assertEqual(self.t.min_free(), 4)
+
+    def test_remove(self):
+        self.t.add(2)
+        self.t.add(1)
+        self.assertEqual(self.t.min_free(), 3)
+        self.t.add(3)
+        self.t.remove(2)
+        self.assertEqual(self.t.min_free(), 2)
+
+
+class FenwickTree:
+    """Simple Fenwick tree. The keys are numbered from 1 to 2^k."""
+
+    def __init__(self, N):
+        while N != (N & -N):
+            N += N & -N
+        self.N = N
+        self.cell = [0] * (N + 1)
+
+    def add(self, key, value=1):
+        """Add a value to the specified key in the tree."""
+        while key <= self.N:
+            self.cell[key] += value
+            key += key & -key
+
+    def remove(self, key):
+        """Subtract 1 from the value of the specified key in the tree."""
+        self.add(key, -1)
+
+    def upto(self, key):
+        """Sum the values of the keys that are smaller or equal to the given tree."""
+        s = 0
+        c = min(key, self.N)
+        while c:
+            s += self.cell[c]
+            c -= c & -c
+        return s
+
+    def min_free(self):
+        """Find the smallest key for which the value is 0.
+
+        Requirement: all values are 0 or 1.
+
+        :return: The minimum free key (self.N + 1 if all keys are set).
+        """
+        r = 1
+        while self.cell[r] == r:
+            r *= 2
+            if r > self.N:
+                return self.N + 1
+
+        b = r // 2
+        while b > 1:
+            # [r - b + 1; r] has the answer
+            b = b // 2
+            m = r - b
+            if self.cell[m] < b:
+                r = m
+            else:
+                assert self.cell[m] == b
+
+        return r
+
+
+def main():
+    k, n = map(int, input().split())
+
+    def gen():
+        for train in range(n):
+            arrive, leave = [int(s) for s in input().split()]
+            yield arrive, False, train
+            yield leave, True, train
+
+    events = sorted(list(gen()))
+
+    # platforms are numbered from 1 to k
+    platforms = FenwickTree(k)
+    # trains are numbered from 0 to n-1
+    trains = []
+
+    def find_platforms():
+        for _, leave, train in events:
+            if leave:
+                assert train < len(trains)
+                platforms.remove(trains[train])
+            elif (platform := platforms.min_free()) <= k:
+                assert len(trains) == train
+                trains.append(platform)
+                platforms.add(platform)
+            else:
+                return 0, train + 1
+        return trains
+
+    print(*find_platforms())
+
+
+if __name__ == "__main__":
+    main()