6. ZigZag Conversion

The string "PAYPALISHIRING" is written in a zigzag pattern on a given number of rows like this: (you may want to display this pattern in a fixed font for better legibility)

P   A   H   N
A P L S I I G
Y   I   R

And then read line by line:  "PAHNAPLSIIGYIR"

Write the code that will take a string and make this conversion given a number of rows:

string convert(string text, int nRows);

convert("PAYPALISHIRING", 3) should return "PAHNAPLSIIGYIR".

题目的意思是把字符串上下上下走之字形状,然后按行输出,比如包含数字0~22的字符串, 给定行数为5,走之字形如下:

现在要按行输出字符,即:0 8 16 1 7 9 15 17 2…….

如果把以上的数字字符看做是字符在原数组的下标, 给定行数为n = 5, 可以发现以下规律:

(1)第一行和最后一行下标间隔都是interval = n*2-2 = 8 ;                                              

(2)中间行的间隔是周期性的,第i行的间隔是: interval–2*i,  2*i,  interval–2*i, 2*i, interval–2*i, 2*i, …

class Solution {
public:
	string convert(string s, int numRows) {
		if (numRows == 1){
			return s;
		}
		int len = s.size();
		string res(len, ' ');
		int interval = 2 * numRows - 2;
		int k = 0;
		for (int i = 0; i < len; i += interval){
			res[k++] = s[i];
		}
		for (int i = 1; i < numRows - 1; i++){
			int iter = 2 * i;
			for (int j = i; j < len; j += iter){
				res[k++] = s[j];
				iter = interval - iter;
			}
		}
		for (int i = numRows - 1; i < len; i += interval){
			res[k++] = s[i];
		}
		return res;
	}
};