遍历数组对角线 [英] Traverse an array diagonally
问题描述
我有一个大阵任意大小的。这是一个方阵。我试图掌握如何遍历其对角线像 /
而非 \\
(我已经知道如何去做)。我有以下的code迄今:
I have a large array of arbitrary size. It's a square array. I'm trying to grasp how to traverse it diagonally like a /
rather than a \
(what I already know how to do). I have the following code thus far:
char[][] array = new char[500][500];
//array full of random letters
String arrayLine = "";
for (int y = 0; y < array.length; y++) {
for (int x = 0; x < array.length; x++) {
for (???) {
arrayLine = arrayLine + array[???][???];
}
}
System.out.println(arrayLine);
}
我有三个回路,因为这是我怎么做的另一条对角线:
I have three loops, because this is how I did the other diagonal:
for (int y = 0; y < array.length; y++) {
for (int x = 0; x < array.length; x++) {
for (int z = 0; z < array.length-y-x; z++) {
arrayLine = arrayLine + array[y+z][x+z];
}
}
System.out.println(arrayLine);
}
在我的努力,我继续下去的边界之外,并得到一个ElementOutOfBounds例外。说数组如下(3x3的,而不是500×500):
In my attempts, I keep going outside the boundaries and get an ElementOutOfBounds exception. Say the array is as below (a 3x3 instead of 500x500):
A B C
D E F
G H I
我要打印出以下字符串:
I want to print out the following as strings:
A
BD
CEG
FH
I
一个previous SO问题曾与整型数组类似的问题,而解决方案是基于关闭数组元素的总和。但我有个字符的工作,所以我不能想到一个方法来得到它。
A previous SO question had a similar problem with integer arrays, and the solution is based off of the sum of array elements. But I'm working with chars, so I can't think of a methodology to get it.
推荐答案
想想细胞的坐标:
. 0 1 2
0 A B C
1 D E F
2 G H I
有关任何对角线,所有的元素都具有共同的东西:一个元素的坐标的总和是一个常数。下面是常量:
For any diagonal, all of the elements have something in common: the sum of an element's coordinates is a constant. Here are the constants:
0 = 0+0 (A)
1 = 1+0 (B) = 0+1 (D)
2 = 2+0 (C) = 1+1 (E) = 0+2 (G)
3 = 2+1 (F) = 1+2 (H)
4 = 2+2 (I)
最小不变的是最小的坐标和,0.1最大恒是国内最大的坐标和。由于每个坐标分量可以达到 array.length - 1
,最大常数 2 *(array.length - 1)
。
所以,我们要做的事情就是迭代常量。对于每一个常数,遍历其坐标总和不变的元素。这可能是最简单的方法:
So the thing to do is iterate over the constants. For each constant, iterate over the elements whose coordinates sum to the constant. This is probably the simplest approach:
for (int k = 0; k <= 2 * (array.length - 1); ++k) {
for (int y = 0; y < array.length; ++y) {
int x = k - y;
if (x < 0 || x >= array.length) {
// Coordinates are out of bounds; skip.
} else {
System.out.print(array[y][x]);
}
}
System.out.println();
}
不过,这最终会遍历了很多超出边界坐标,因为它在所有可能的是
坐标总是迭代,即使只有一个对角线包含所有可能的是
坐标。让我们修改是
循环,因此只能参观是
坐标所需电流 K
。
However, that will end up iterating over a lot of out-of-bounds coordinates, because it always iterates over all possible y
coordinates, even though only one diagonal contains all possible y
coordinates. Let's change the y
loop so it only visits the y
coordinates needed for the current k
.
对于超出边界坐标的一个条件是 X&LT; 0
。替换 X
并解决的定义:
One condition for out-of-bounds coordinates is x < 0
. Substitute the definition of x
and solve:
x < 0
k - y < 0
k < y
y > k
所以,当 Y'GT;氏/ code>,
X
将是负面的。因此,我们只想循环,而 Y'LT; = K
So when y > k
, x
will be negative. Thus we only want to loop while y <= k
.
其他条件超出边界坐标为 X&GT; = array.length
。解决:
The other condition for out-of-bounds coordinates is x >= array.length
. Solve:
x >= array.length
k - y >= array.length
k - array.length >= y
y <= k - array.length
所以,当 Y'LT; = K - array.length
, X
将过大。因此,我们要在0或来启动
,以较大者为准。是
K - array.length + 1
So when y <= k - array.length
, x
will be too large. Thus we want to start y
at 0 or k - array.length + 1
, whichever is larger.
for (int k = 0; k <= 2 * (array.length - 1); ++k) {
int yMin = Math.max(0, k - array.length + 1);
int yMax = Math.min(array.length - 1, k);
for (int y = yMin; y <= yMax; ++y) {
int x = k - y;
System.out.print(array[y][x]);
}
System.out.println();
}
请注意:我只证明了这code正确。我没有测试它。
Note: I have only proven this code correct. I have not tested it.
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