06 Zigzag Conversion


The string "PAYPALISHIRING" is written in a zigzag pattern on a given number of rows like this:

P   A   H   N
Y   I   R

And then read line by line: "PAHNAPLSIIGYIR"

First Thought

This zigzag form actually does not need to be written out. The string can be divided into groups by one zigzag, whose length is rownum*2 - 2. Then every line can be calculated out.

For the first line, they are the head of each zigzag.

For the rest but not last, there would be two characters: counted from the front and counted from the end.

For the last line, they are the middle one.

Which gives us the code


Several details were missed by me in the beginning:

  1. The tail, which does not form a full zigzag should be calculated specially
  2. When numRow == 1, numRow * 2 - 2 == 0 and it should be treated specially
class Solution {
    string convert(string s, int numRows) {
        string ans, c;
        int setnum = numRows * 2 - 2;
        if (setnum == 0) {
            return s;
        int sets = s.size() / setnum;

        for (int j = 0; j < s.length(); j += setnum) {
            ans.append(c = s[j]);
        for (int i = 1; i < numRows-1; ++i) {
            int j;
            for (j = 0; j < sets; ++j) {
                ans.append(c = s[j * setnum + i]);
                ans.append(c = s[j * setnum + setnum - i]);
            if (j * setnum + i < s.size())
                ans.append(c = s[j * setnum + i]);
            if (j * setnum + setnum - i < s.size())
                ans.append(c = s[j * setnum + setnum - i]);     
        for (int j = setnum / 2; j < s.length(); j += setnum) {
            ans.append(c = s[j]);
        return ans;


Time Complexity

Each character are just visited randomly once, so it is always $O(n)$.

Space Complexity

A new string is needed to store the output, so it is always $O(n)$.

penway Wang
penway Wang
Mechanic Technical Director

My research interests include computer vision, artificial intelligence and software engineering. I am a FSAE race car crew member at the same time, designing suspension system.