HardNo. 1900
The Earliest and Latest Rounds Where Players Compete — LeetCode 1900 Python Solution
- Pattern
- Dynamic Programming
- Topics
- Memoization, Dynamic Programming
- Reading time
- 7 min
- Source
- leetcode.com
The problem
There is a tournament where n players are participating. The players are standing in a single row and are numbered from 1 to n based on their initial standing position (player 1 is the first player in the row, player 2 is the second player in the row, etc.).
Example
- Input
- n = 11, firstPlayer = 2, secondPlayer = 4
- Output
- [3,4]
- Explanation
- One possible scenario which leads to the earliest round number:
Python solution
@cache
def dfs(l: int, r: int, n: int):
if l + r == n - 1:
return [1, 1]
res = [inf, -inf]
m = n >> 1
for i in range(1 << m):
win = [False] * n
for j in range(m):
if i >> j & 1:
win[j] = True
else:
win[n - 1 - j] = True
if n & 1:
win[m] = True
win[n - 1 - l] = win[n - 1 - r] = False
win[l] = win[r] = True
a = b = c = 0
for j in range(n):
if j == l:
a = c
if j == r:
b = c
if win[j]:
c += 1
x, y = dfs(a, b, c)
res[0] = min(res[0], x + 1)
res[1] = max(res[1], y + 1)
return res
class Solution:
def earliestAndLatest(
self, n: int, firstPlayer: int, secondPlayer: int
) -> List[int]:
return dfs(firstPlayer - 1, secondPlayer - 1, n)Complexity
- Time
- O(n·m) (typical)
- Space · auxiliary
- O(n·m)or optimized
Pattern: Dynamic Programming
Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1900. The Earliest and Latest Rounds Where Players Compete is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming and Memoization.
The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.
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Frequently asked questions
- How hard is LeetCode 1900. The Earliest and Latest Rounds Where Players Compete?
LeetCode 1900. The Earliest and Latest Rounds Where Players Compete is rated Hard on LeetCode.
- What topics does LeetCode 1900. The Earliest and Latest Rounds Where Players Compete cover?
LeetCode 1900. The Earliest and Latest Rounds Where Players Compete is tagged Memoization and Dynamic Programming on LeetCode.