70 lines
1.4 KiB
Markdown
70 lines
1.4 KiB
Markdown
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# Leetcode Triangle
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#### 2022-07-20 22:59
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> ##### Algorithms:
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> #algorithm #dynamic_programming
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> ##### Difficulty:
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> #coding_problem #difficulty-medium
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> ##### Additional tags:
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> #leetcode
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> ##### Revisions:
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> N/A
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##### Related topics:
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```expander
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tag:#dynamic_programming
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```
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##### Links:
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- [Link to problem](https://leetcode.com/problems/triangle/)
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___
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### Problem
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Given a `triangle` array, return _the minimum path sum from top to bottom_.
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For each step, you may move to an adjacent number of the row below. More formally, if you are on index `i` on the current row, you may move to either index `i` or index `i + 1` on the next row.
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#### Examples
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**Example 1:**
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```
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**Input:** triangle = [[2],[3,4],[6,5,7],[4,1,8,3]]
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**Output:** 11
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**Explanation:** The triangle looks like:
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2
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3 4
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6 5 7
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4 1 8 3
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The minimum path sum from top to bottom is 2 + 3 + 5 + 1 = 11 (underlined above).
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```
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**Example 2:**
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```
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**Input:** triangle = [[-10]]
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**Output:** -10
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```
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#### Constraints
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- `1 <= triangle.length <= 200`
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- `triangle[0].length == 1`
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- `triangle[i].length == triangle[i - 1].length + 1`
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- `-104 <= triangle[i][j] <= 104`
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### Thoughts
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> [!summary]
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> This is a #dynamic_programming problem.
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Same as in [[Leetcode House-Robber]], there are four stages to optimization:
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#### Stage 1: ordinary recursion
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#### Stage 2: recursion with caching
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### Solution
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