Question
Given a triangle, find the minimum path sum from top to bottom. Each step you may move to adjacent numbers on the row below.
For example, given the following triangle
[
[2],
[3,4],
[6,5,7],
[4,1,8,3]
]
The minimum path sum from top to bottom is 11 (i.e., 2 + 3 + 5 + 1 = 11).
Note:
Bonus point if you are able to do this using only O(n) extra space, where n is the total number of rows in the triangle.
Stats
| Frequency | 1 |
| Difficulty | 3 |
| Adjusted Difficulty | 1 |
| Time to use | -------- |
Ratings/Color = 1(white) 2(lime) 3(yellow) 4/5(red)
Analysis
This is a math question.
Solution
It’s an easy question. Instead of normal DP transition function, this one is so-called bottom-up approach.
Code
public int minimumTotal(ArrayList<ArrayList<Integer>> triangle) {
int len = triangle.size();
if (len == 0) return 0;
int[] m = new int[len];
m[0] = triangle.get(0).get(0);
for (int i = 1; i < len; i ++) {
ArrayList<Integer> cur = triangle.get(i);
for (int j = i; j >= 0; j --) {
if (j == i) m[j] = m[j-1] + cur.get(j);
else if (j == 0) m[j] = m[0] + cur.get(0);
else m[j] = Math.min(m[j-1], m[j]) + cur.get(j);
}
}
int min = Integer.MAX_VALUE;
for (Integer k: m)
min = Math.min(min, k);
return min;
}