遍历网格 [英] Looping through a grid

问题描述

我使用这两个简单的循环从高到低，从右到左搜索网格.

I use these two simple loops to search through a grid from height to bottom, right to left.

for(int y=0; y<height; y++){
  for(int x=width; x>=0; x--){
  }
}

基本上，我想像下图中的数字那样横向搜索网格，直到它覆盖所有单元格.我的方法效果不好，因此我在这里寻求帮助.

Basically, I want to search through the grid sideways like the numbers in the picture below until it covers all the cells. My approach hasn't worked out well so I'm asking for help here.

我该如何尽快完成此任务?我相信仅使用两个循环就可以做到这一点，但我无法弄清楚.

How can I accomplish this the quickest way possible? I believe this should be possible to do using just two loops but I can't figure it out.

推荐答案

以下将完成此操作:

 final int h = 4;
 final int w = 3;
 for (int d = 0; d < w + h; d++) {
     for (int y = 0; y < h; y++) {
         int x = w - d + y;
         if (x < 0 || x >= w) continue;
         System.out.printf("%d %d\n", x, y);
     }
 }

在这里， h 是高度，而 w 是网格的宽度.

Here, h is the height and w is the width of the grid.

该算法基于以下观察结果:对于每个对角线，到顶部边缘和到右侧边缘的距离之和保持恒定.

The algorithm is based on the observation that for each diagonal, the sum of the distances to the top edge and to the right edge remains constant.

外部循环遍历对角线；内部循环，在对角线上的所有单元格上.

The outer loop iterates over the diagonals; the inner loop, over all cells on the diagonal.

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