[LeetCode] Triangle

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最新推荐文章于 2020-05-23 10:06:18 发布 · 86 阅读

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本文介绍了一个算法，用于解决从三角形顶部到底部的最小路径和问题。通过动态规划方法，我们可以在O(n)额外空间复杂度下找到最优路径。详细解释了算法实现过程，包括初始化、迭代计算和最终结果的确定。

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TriangleOct 30 '12

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.

class Solution {
public:
    int minimumTotal(vector<vector<int> > &triangle) {
        int s = triangle.size();
        if (s == 0)return 0;
        int *a = new int[s];
        memset(a, 0, 4*s);
        a[0] = triangle[0][0];
        for (int i = 1; i < triangle.size(); ++i) {
            a[triangle[i].size() - 1] = a[triangle[i].size()-2] + 
                triangle[i][triangle[i].size()-1];
            for (int j =  triangle[i].size()-2; j >=1; --j) {
                a[j] = min(a[j-1], a[j]) + triangle[i][j];
            }
            a[0] += triangle[i][0];

        }
        int res = a[0];
        for (int i = 1; i < s; i++) {
            if (res > a[i]) res = a[i];
        }
        delete []a;
        return res;
    }
};