120. Triangle LeetCode Solution

In this guide, you will get 120. Triangle LeetCode Solution with the best time and space complexity. The solution to Triangle problem is provided in various programming languages like C++, Java, and Python. This will be helpful for you if you are preparing for placements, hackathons, interviews, or practice purposes. The solutions provided here are very easy to follow and include detailed explanations.

Table of Contents

1. Problem Statement
2. Complexity Analysis
3. Triangle solution in C++
4. Triangle solution in Java
5. Triangle solution in Python
6. Additional Resources

Problem Statement of Triangle

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.

Example 1:

Input: triangle = [[2],[3,4],[6,5,7],[4,1,8,3]]
Output: 11
Explanation: The triangle looks like:
2
3 4
6 5 7
4 1 8 3
The minimum path sum from top to bottom is 2 + 3 + 5 + 1 = 11 (underlined above).

Example 2:

Input: triangle = [[-10]]
Output: -10

Constraints:

1 <= triangle.length <= 200
triangle[0].length == 1
triangle[i].length == triangle[i – 1].length + 1
-104 <= triangle[i][j] <= 104

Follow up: Could you do this using only O(n) extra space, where n is the total number of rows in the triangle?

Complexity Analysis

• Time Complexity: O(n^2)
• Space Complexity: O(1)

120. Triangle LeetCode Solution in C++

class Solution {
 public:
  int minimumTotal(vector<vector<int>>& triangle) {
    for (int i = triangle.size() - 2; i >= 0; --i)
      for (int j = 0; j <= i; ++j)
        triangle[i][j] += min(triangle[i + 1][j], triangle[i + 1][j + 1]);
    return triangle[0][0];
  }
};
/* code provided by PROGIEZ */

120. Triangle LeetCode Solution in Java

class Solution {
  public int minimumTotal(List<List<Integer>> triangle) {
    for (int i = triangle.size() - 2; i >= 0; --i)
      for (int j = 0; j <= i; ++j)
        triangle.get(i).set(j, triangle.get(i).get(j) + Math.min(triangle.get(i + 1).get(j),
                                                                 triangle.get(i + 1).get(j + 1)));
    return triangle.get(0).get(0);
  }
}
// code provided by PROGIEZ

120. Triangle LeetCode Solution in Python

class Solution:
  def minimumTotal(self, triangle: list[list[int]]) -> int:
    for i in reversed(range(len(triangle) - 1)):
      for j in range(i + 1):
        triangle[i][j] += min(triangle[i + 1][j],
                              triangle[i + 1][j + 1])

    return triangle[0][0]
 # code by PROGIEZ

Additional Resources

• Explore all LeetCode problem solutions at Progiez here
• Explore all problems on LeetCode website here

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