120. Triangle.md

120. 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.

Solution

在triangle变量原处修改值就可以甚至只用O(1)的额外空间，我真机智。

java方法见code2

Code

class Solution(object):
    def minimumTotal(self, triangle):
        """
        :type triangle: List[List[int]]
        :rtype: int
        """
        height = len(triangle)
        for i in range(1,height):
            cur = triangle[i]
            cur[0] = cur[0] + triangle[i-1][0]
            for t in range(i-1):
                cur[t+1] = cur[t+1] + min(triangle[i-1][t],triangle[i-1][t+1])
            cur[-1] = cur[-1] + triangle[i-1][-1]
        # print(triangle)
        return min(triangle[-1])
        

Code2

class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        
        // 默认初始化为0
        int[] A = new int[triangle.size()+1];
        for(int i=triangle.size()-1;i>=0;i--)
            for(int j=0;j<triangle.get(i).size();j++)
            {
                A[j] = Math.min(A[j],A[j+1]) + triangle.get(i).get(j);
            }
        return A[0];        
    }
}

// 3.20 我怎么写了个自顶向下的呢哈哈哈哈哈傻的
class Solution {
    public int minimumTotal(List<List<Integer>> triangle) {
        
        int len = triangle.size();
        if(len==0)
            return 0;
        
        int[] res = new int[len];
        res[0] = triangle.get(0).get(0);
        
        for(int i=1;i<len;i++)
        {
            for(int j=i;j>=0;j--)
            {
                if(j==0)
                    res[j] += triangle.get(i).get(j);
                else if(j==i)
                    res[j] = triangle.get(i).get(j) + res[i-1];
                else
                    res[j] = Math.min(res[j],res[j-1])+triangle.get(i).get(j);
            }
        }
        int min = Integer.MAX_VALUE;
        for(int num : res)
            min = Math.min(min,num);
        return min;
    }
}