HardNo. 2188
Minimum Time to Finish the Race — LeetCode 2188 Python Solution
- Pattern
- Dynamic Programming
- Topics
- Array, Dynamic Programming
- Reading time
- 4 min
- Source
- leetcode.com
The problem
You are given a 0-indexed 2D integer array tires where tires[i] = [fi, ri] indicates that the ith tire can finish its xth successive lap in fi * ri(x-1) seconds. For example, if fi = 3 and ri = 2, then the tire would finish its 1st lap in 3 seconds, its 2nd lap in 3 * 2 = 6 seconds, its 3rd lap in 3 * 22 = 12 seconds, etc.
Example
- Input
- tires = [[2,3],[3,4]], changeTime = 5, numLaps = 4
- Output
- 21
- Explanation
- Lap 1: Start with tire 0 and finish the lap in 2 seconds.
Python solution
class Solution:
def minimumFinishTime(
self, tires: List[List[int]], changeTime: int, numLaps: int
) -> int:
cost = [inf] * 18
for f, r in tires:
i, s, t = 1, 0, f
while t <= changeTime + f:
s += t
cost[i] = min(cost[i], s)
t *= r
i += 1
f = [inf] * (numLaps + 1)
f[0] = -changeTime
for i in range(1, numLaps + 1):
for j in range(1, min(18, i + 1)):
f[i] = min(f[i], f[i - j] + cost[j])
f[i] += changeTime
return f[numLaps]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 2188. Minimum Time to Finish the Race is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.
The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.
Related problems
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| 0045 | Jump Game II | Medium |
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| 0064 | Minimum Path Sum | Medium |
| 0085 | Maximal Rectangle | Hard |
Frequently asked questions
- How hard is LeetCode 2188. Minimum Time to Finish the Race?
LeetCode 2188. Minimum Time to Finish the Race is rated Hard on LeetCode.
- What topics does LeetCode 2188. Minimum Time to Finish the Race cover?
LeetCode 2188. Minimum Time to Finish the Race is tagged Array and Dynamic Programming on LeetCode.