Solution for 3225.Maximum Score From Grid Operations#5247
Solution for 3225.Maximum Score From Grid Operations#5247Abhijit-Gautam wants to merge 1 commit into
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Added detailed explanation and implementation for the maximum score problem using dynamic programming and prefix sums.
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3. Other notesWhen adding solutions and code, you need to create a Solution.xxx source code file (if it already exists, please confirm whether the algorithm is better, if yes, overwrite the existing algorithm code), and at the same time, you need to add the corresponding code snippets in README.md and README_EN.md (do not have Chinese comments in the English file) |
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Pull request overview
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Adds a full written explanation and multi-language reference implementations for LeetCode 3225 using a DP + prefix-sum approach.
Changes:
- Documented the DP state, transition, and optimization using prefix/suffix maxima.
- Added complete reference solutions for Python, Java, C++, Go, and TypeScript.
- Standardized solution framing around “Dynamic Programming + Prefix Sum”.
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| func maximumScore(grid [][]int) int64 { | ||
| n := len(grid) | ||
| const NEG = math.MinInt64 / 2 | ||
| prefix := make([][]int64, n) |
| We define $\textit{dp}[h_1][h_2]$ as the maximum score for columns $0\ldots j$, where $k[j] = h_1$ and $k[j-1] = h_2$. | ||
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| **Transition** (choosing $k[j+1] = hp$): | ||
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| $$\textit{dp\_new}[hp][h_1] = \max_{h_2}\left(\textit{dp}[h_1][h_2] + \max\left(0,\ \textit{prefix}[j][\max(h_2, hp)] - \textit{prefix}[j][h_1]\right)\right)$$ |
| ``` | ||
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| #### Go | ||
| #### GO |
| for h in range(n + 1): | ||
| dp[h][0] = 0 | ||
| for j in range(n - 1): | ||
| new = [[NEG] * (n + 1) for _ in range(n + 1)] |
| v1 := int64(NEG) | ||
| if prefMax[hp] != NEG { v1 = prefMax[hp] + rc } |
Added detailed explanation and implementation for the maximum score problem using dynamic programming and prefix sums.