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.
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.
Solution:
O(n) extra space:public class Solution { public int minimumTotal(ArrayList<ArrayList<Integer>> triangle) { int [] minValue = new int[1]; minValue[0] = triangle.size()>0 ? triangle.get(0).get(0) : 0; for(int i=1; i < triangle.size(); i++) { int[] temp = new int [i+1]; for (int j=0; j<=i; j++) { temp[j] = j>0 ? minValue[j-1] : Integer.MAX_VALUE; temp[j] = j<i ? Math.min(minValue[j],temp[j]) : temp[j]; temp[j] = temp[j] + triangle.get(i).get(j); } minValue=temp; } int min= minValue[0]; for (int i=0; i<minValue.length; i++) min =minValue[i]<min ? minValue[i] : min; return min; }
O(1) extra space (using the input as temporary storage):
public class Solution { public int minimumTotal(ArrayList<ArrayList<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); } }
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