题目描述：

LeetCode 675. Cut Off Trees for Golf Event

You are asked to cut off trees in a forest for a golf event. The forest is represented as a non-negative 2D map, in this map:

1. 0 represents the obstacle can't be reached.
2. 1 represents the ground can be walked through.
3. The place with number bigger than 1 represents a tree can be walked through, and this positive number represents the tree's height.

You are asked to cut off all the trees in this forest in the order of tree's height - always cut off the tree with lowest height first. And after cutting, the original place has the tree will become a grass (value 1).

You will start from the point (0, 0) and you should output the minimum steps you need to walk to cut off all the trees. If you can't cut off all the trees, output -1 in that situation.

You are guaranteed that no two trees have the same height and there is at least one tree needs to be cut off.

Example 1:

Input: 
[
 [1,2,3],
 [0,0,4],
 [7,6,5]
]
Output: 6

Example 2:

Input: 
[
 [1,2,3],
 [0,0,0],
 [7,6,5]
]
Output: -1

Example 3:

Input: 
[
 [2,3,4],
 [0,0,5],
 [8,7,6]
]
Output: 6
Explanation: You started from the point (0,0) and you can cut off the tree in (0,0) directly without walking.

Hint: size of the given matrix will not exceed 50x50.

题目大意：

二维非负整数数组表示森林，0表示障碍物，1表示草地，其余数字表示树木（值表示高度）。

高度从小到大遍历所有树木，求最小总步数。

树木的高度均不相等。

解题思路：

排序（Sort） + 宽度优先搜索（BFS）

按照树木的高度从小到大排序，从0, 0出发，依次向下一棵树木移动，并利用BFS计算移动过程中的步数。

Java代码：

public class Solution {
    private List<List<Integer>> forest;
    private int w, h;
    private int[] dx = new int[]{1, 0, -1, 0};
    private int[] dy = new int[]{0, 1, 0, -1};
    public int cutOffTree(List<List<Integer>> forest) {
        this.forest = forest;
        w = forest.size();
        h = forest.get(0).size();
        int ans = 0;
        List<int[]> trees = new LinkedList<>();
        for (int x = 0; x < w; x++) {
            for (int y = 0; y < h; y++) {
                int v = forest.get(x).get(y);
                if (v <= 1) continue;
                trees.add(new int[]{x, y, v});
            };
        }
        trees.sort((x, y) -> x[2] - y[2]);
        int sx = 0, sy = 0;
        for (int[] tree : trees) {
            int tx = tree[0], ty = tree[1];
            int dist = findDist(sx, sy, tx, ty);
            if (dist < 0) return -1;
            ans += dist;
            sx = tx;
            sy = ty;
        }
        return ans;
    }
    public int findDist(int sx, int sy, int tx, int ty) {
        LinkedList<int[]> queue = new LinkedList<>();
        queue.add(new int[]{sx, sy, 0});
        Set<Integer> vset = new HashSet<>();
        vset.add(sx * h + sy);
        while (!queue.isEmpty()) {
            int[] first = queue.poll();
            int x = first[0], y = first[1], s = first[2];
            if (x == tx && y == ty) return s;
            for (int i = 0; i < dx.length; i++) {
                int nx = x + dx[i];
                int ny = y + dy[i];
                if (nx < 0 || nx >= w || ny < 0 || ny >= h)
                    continue;
                if (forest.get(nx).get(ny) == 0) continue;
                if (vset.contains(nx * h + ny)) continue;
                vset.add(nx * h + ny);
                queue.add(new int[]{nx, ny, s + 1});
            }
        }
        return -1;
    }
}

 

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