[LeetCode] Triangle

最新推荐文章于 2020-05-23 10:06:18 发布

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文章标签：

#LeetCode #Array #Shortest Path #Topological Order #Dynamic Programming

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本文介绍了一种求解从三角形顶部到底部的最小路径和的方法，通过动态规划算法来实现，具体步骤包括初始化状态数组、逆序更新状态数组等。

Total Accepted: 8954 Total Submissions: 33737

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).

// compute shortest path in topological order
public class Solution {
    public int minimumTotal(ArrayList<ArrayList<Integer>> triangle) {
        int[] dp = new int[triangle.size()];
        
        for (int i = 0; i < triangle.size(); i++) {
            if (i == 0) {
                dp[0] = triangle.get(0).get(0);
                continue;
            }
            
            // backward
            for (int j = i; j >= 0; j--) {
                int val1 = Integer.MAX_VALUE;
                int val2 = Integer.MAX_VALUE;
                
                if (j != 0)     val1 = dp[j-1];
                if (j != i)     val2 = dp[j];
                
                dp[j] = triangle.get(i).get(j).intValue() + (val1 < val2 ? val1 : val2);         
            }
        }
        
        int min = Integer.MAX_VALUE;
        
        for (int i = 0; i < triangle.size(); i++) {
            if (dp[i] < min) min = dp[i];
        }
        
        return min;
    }
}