# Triangle Problem

## Description

LeetCode Problem 120.

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:

``````1
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Input: triangle = [,[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:

``````1
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Input: triangle = [[-10]]
Output: -10
``````

Constraints:

• 1 <= triangle.length <= 200
• triangle.length == 1
• triangle[i].length == triangle[i - 1].length + 1
• -10^4 <= triangle[i][j] <= 10^4

## Sample C++ Code

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int minimumTotal(vector<vector<int> > &triangle) {
int n = triangle.size();
vector<int> minlen(triangle.back());
for (int layer = n-2; layer >= 0; layer--)  {
// For each layer
for (int i = 0; i <= layer; i++) {
// Check its every 'node'
// Find the lesser of its two children,
// and sum the current value in the triangle with it.
minlen[i] = min(minlen[i], minlen[i+1]) + triangle[layer][i];
}
}
return minlen;
}
``````