Counting Stars — Inter-Uni Programming Contest

Description:

https://interunia.unswcpmsoc.com/task/Counting%20Stars/

Thinking:

• Given a set of star positions, we need to calculate the minimum number of stars required to explain these positions.
• Meteors (i.e., moving stars) move from left to right, and from high to low (x coordinates increase, y coordinates decrease), without moving horizontally or vertically.
• Each meteor may appear in multiple positions (because it moves), and the final cumulative image will show all the positions it has passed through.
• The positions of fixed stars remain unchanged.

Therefore, we need to maintain a list of the last y-coordinate of the current chain.

1. Sort the points: Sort them by increasing x coordinates.
2. Initialization: Create an empty list last_y to store the last y-coordinate of each chain.
3. Traverse the set of points:
   • For each point (x, y):
     • Use bisect_right to find the first position in last_y that is greater than the current y.
     • If the index is less than the length of last_y, it means there is an existing chain that can accommodate the current point, so we update the last y-coordinate of that chain to the current y.
     • If the index is equal to the length of last_y, it means no suitable chain is found, so we need to create a new chain and add the current y to last_y.

Code:

import bisect

n = int(input())
stars = []

for _ in range(n):
    x, y = map(int, input().split())
    stars.append((x, y))

# 按 x 坐标递增排序
stars.sort(key=lambda x: (x[0],))

last_y = []

for x, y in stars:
    idx = bisect.bisect_right(last_y, y)
    if idx < len(last_y):
        last_y[idx] = y  # 更新链的最后一个 y 坐标
    else:
        last_y.append(y)  # 创建新的链

print(len(last_y))

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