MediumNo. 1937
Maximum Number of Points with Cost — LeetCode 1937 Python Solution
- Pattern
- Matrix and Grid
- Topics
- Array, Dynamic Programming, Matrix
- Reading time
- 3 min
- Source
- leetcode.com
The problem
You are given an m x n integer matrix points (0-indexed). Starting with 0 points, you want to maximize the number of points you can get from the matrix.
Example
- Input
- points = [[1,2,3],[1,5,1],[3,1,1]]
- Output
- 9
- Explanation
- The blue cells denote the optimal cells to pick, which have coordinates (0, 2), (1, 1), and (2, 0).
Python solution
class Solution:
def maxPoints(self, points: List[List[int]]) -> int:
n = len(points[0])
f = points[0][:]
for p in points[1:]:
g = [0] * n
lmx = -inf
for j in range(n):
lmx = max(lmx, f[j] + j)
g[j] = max(g[j], p[j] + lmx - j)
rmx = -inf
for j in range(n - 1, -1, -1):
rmx = max(rmx, f[j] - j)
g[j] = max(g[j], p[j] + rmx + j)
f = g
return max(f)Complexity
- Time
- O(n·m) (typical)
- Space · auxiliary
- O(n·m)or optimized
Pattern: Matrix and Grid
Treat a 2-D grid as a graph whose neighbours are the four adjacent cells. LeetCode 1937. Maximum Number of Points with Cost is filed here because LeetCode tags it Matrix, which is the vocabulary this hub collects.
The matrix and grid guide has the Python template for the pattern and the 216 LeetCode problems that use it.
Related problems
| No. | Problem | Difficulty |
|---|---|---|
| 0063 | Unique Paths II | Medium |
| 0064 | Minimum Path Sum | Medium |
| 0085 | Maximal Rectangle | Hard |
| 0174 | Dungeon Game | Hard |
| 0221 | Maximal Square | Medium |
| 0329 | Longest Increasing Path in a Matrix | Hard |
Frequently asked questions
- How hard is LeetCode 1937. Maximum Number of Points with Cost?
LeetCode 1937. Maximum Number of Points with Cost is rated Medium on LeetCode.
- What topics does LeetCode 1937. Maximum Number of Points with Cost cover?
LeetCode 1937. Maximum Number of Points with Cost is tagged Array, Dynamic Programming and Matrix on LeetCode.