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LeetCode 120.Triangle

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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 

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[
     [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.

Explanation

动态规划的基本题。主要就是要给每个pos都有一个找到最小值，逐层找到最后一个。

Code

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public class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        if (triangle == null || triangle.size() == 0) return -1;
        if (triangle.get(0) == null || triangle.get(0).size() == 0) return -1;
        int n = triangle.size();
        int[][] f = new int[n][n];
        f[0][0] = triangle.get(0).get(0);
        for (int i=1; i<n; i++) {
            f[i][0] = f[i-1][0] + triangle.get(i).get(0);
            f[i][i] = f[i-1][i-1] + triangle.get(i).get(i);
        }
        for (int i=1; i<n; i++) {
            for(int j=1; j<i; j++) {
                f[i][j] = Math.min(f[i-1][j-1], f[i-1][j]) + triangle.get(i).get(j);
            }
        }
        int best = f[n-1][0];
        for (int i=1; i<n; i++) {
            best = Math.min(best, f[n-1][i]);
        }
        return best;
    }
}