CODE 13: Triangle

最新推荐文章于 2019-01-13 06:57:34 发布

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最新推荐文章于 2019-01-13 06:57:34 发布

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分类专栏： leetcode

本文链接：https://blog.youkuaiyun.com/luzheqi/article/details/11712665

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本文介绍了一个算法来解决最小路径和问题，即在给定的三角形中找到从顶部到底部的最小路径总和。每个步骤只能移动到相邻的数字下一行。文章提供了一个Java解决方案，并讨论了使用O(n)额外空间的优化。

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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.

	public int minimumTotal(ArrayList<ArrayList<Integer>> triangle) {
		// Start typing your Java solution below
		// DO NOT write main() function
		if (null == triangle || 0 == triangle.size()) {
			return 0;
		}

		int layerNumer = triangle.size();
		ArrayList<Integer> tmpLengths = new ArrayList<Integer>();
		tmpLengths.add(triangle.get(0).get(0));
		for (int i = 1; i < layerNumer; i++) {
			ArrayList<Integer> layer = triangle.get(i);
			layer.set(0, layer.get(0) + tmpLengths.get(0));
			for (int k = 1; k < layer.size(); k++) {
				if (k == layer.size() - 1) {
					layer.set(k, layer.get(k) + tmpLengths.get(k - 1));
				} else {
					if (tmpLengths.get(k) > tmpLengths.get(k - 1)) {
						layer.set(k, tmpLengths.get(k - 1) + layer.get(k));
					} else {
						layer.set(k, tmpLengths.get(k) + layer.get(k));
					}
				}
			}
			tmpLengths.clear();
			tmpLengths.addAll(layer);
		}
		int min = tmpLengths.get(0);
		for (int i = 1; i < layerNumer; i++) {
			if (tmpLengths.get(i) < min) {
				min = tmpLengths.get(i);
			}
		}
		return min;
	}