Question Definition
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.
Java Solution
public int minimumTotal(List<List<Integer>> triangle) {
if(triangle.size() == 0 || triangle.get(0).size() == 0) return 0;
int[] maxs = new int[triangle.size()];
maxs[0] = triangle.get(0).get(0);
for(int level = 1; level < triangle.size(); level++){
List<Integer> l = triangle.get(level);
maxs[l.size() - 1] = maxs[l.size() - 2] + l.get(l.size() - 1);
for(int i = l.size() - 2; i > 0; i--){
maxs[i] = Math.min(maxs[i], maxs[i - 1]) + l.get(i);
}
maxs[0] = maxs[0] + l.get(0);
}
int min = maxs[0];
for(int num : maxs){
if(min > num)
min = num;
}
return min;
}
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