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LeetCode 120, Medium. Topics: Array, Dynamic Programming. View on LeetCode. Generate this problem as a practice environment: tested reference solution, 16 parametrized pytest cases, and a playground notebook:

Problem

Given a triangle array, return the minimum path sum from top to bottom. 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.

Examples

Constraints

  • 1 <= triangle.length <= 200
  • triangle[0].length == 1
  • triangle[i].length == triangle[i - 1].length + 1
  • -10^4 <= triangle[i][j] <= 10^4
Follow up: Could you do this using only O(n) extra space, where n is the total number of rows in the triangle?

Solution

Reference implementation from solution.py on GitHub, full suite in test_solution.py:

Complexity

Tags

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Last modified on September 7, 2026