Triangle

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.

思路：记录最后一行sum，然后求出最小值

注意事项：由于下一行比上一行多一个值，所以要从后向前覆盖

java代码：

1. public int minimumTotal(List<List<Integer>> triangle) {
2. if(triangle==null) return 0;
3. int high = triangle.size();
4. if(high==0) return 0;
5. int[] result = new int[high];
6. int final_value = Integer.MAX_VALUE;
7. for(int i=0;i<high;i++) {
8. int j=0;
9. List<Integer> line = triangle.get(i);
10. for(j=line.size()-1;j>=0;j--) {
11. if(i==0) {
12. result[j] =line.get(j);
13. } else {
14. if(j==0) result[0] = result[0] + line.get(0);
15. else if(j==line.size()-1) {
16. result[j] = result[j-1] + line.get(j);
17. }
18. else {
19. if(result[j-1] > result[j])
20. result[j] = result[j] + line.get(j);
21. else
22. result[j] = result[j-1] + line.get(j);
23. }
24. }
25. if(i==high-1) {
26. if(result[j] < final_value) {
27. final_value = result[j];
28. }
29. }
30. }
31. }
32. return final_value;
33. }

C++代码： 从后向前

1. int minimumTotal(vector<vector<int> > &triangle) {
2. if(triangle.empty()) return 0;
3. vector<int> flag;
4. int high = triangle.size();
5. flag.resize(triangle[high-1].size());
6. for(int i=high-1;i>=0;i--) {
7. int width = triangle[i].size();
8. for(int j=0;j<width;j++) {
9. if(i==high-1) flag[j] = triangle[i][j];
10. else flag[j] = triangle[i][j] + min(flag[j],flag[j+1]);
11. }
12. }
13. return flag[0];
14. }