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 s, int numRows);

Example 1:
<preclass=”crayon:false”>Input: s = “PAYPALISHIRING”, numRows = 3 Output: “PAHNAPLSIIGYIR”

Example 2:

Input: s = "PAYPALISHIRING", numRows = 4
Output: "PINALSIGYAHRPI"
Explanation:

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

Solution: Simulation

Store the zigzag results for each row and then output row by row.

Time complexity: O(n)

Space complexity: O(n)

// Author: Huahua
class Solution {
public:
  string convert(string s, int nRows) {
    if (nRows == 1) return s;

    vector<string> ss(nRows);
    int l = s.length();
    int x = 0, y = 0, i = 0;
    bool down = true;
    while (i < l) {
      ss[y] += s[i];
      if (down) {
        ++y;
        if (y == nRows) {
            down = false;
            y -=2;
        }
      } else {
        --y;
        if (y < 0) {
            down = true;
            y = 1;
        }
      }
      i++;
    }

    string ans;
    for(const string& r : ss)
      ans += r;
    return ans;
  }
};

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