LeetCode 6. ZigZag ConversionZ字形转换
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 s, int numRows);
Example 1:
Input: s = "PAYPALISHIRING", numRows = 3
Output: "PAHNAPLSIIGYIR"
Example 2:
Input: s = "PAYPALISHIRING", numRows = 4
Output: "PINALSIGYAHRPI"
Explanation:
直接跳转法(横着走)
按照规律走,对于第一行和最后一行,我们能够能发现,一个元素到他的下一个元素的距离为2 * numRow - 2。
对于中间的元素,我们能都发现他的下一元素与其步长有关。我们可以从每列的第一个元素A开始算起,到满列的元素C的距离为2 * numRow - 2。达到下一个满列元素之前必然会遇到一个元素B。即A->B->C的总距离为2 * numRow - 2。同时有A->B 的距离加上 B->C的距离等于总距离。因此步长为step(B -> C) = 2 * numRows - 2 - step(A->B)。
上述很容易通过画出图以及下标来进行验证。这样时间复杂度为O(n),空间复杂度为O(n^2)
public String convert(String s, int numRows) {
if(numRows == 1){
return s;
}
StringBuilder res = new StringBuilder();
int len = s.length();
for(int i = 0; i < len; i = i + 2 * numRows - 2){
res.append(s.charAt(i));
}
for(int i = 1; i < numRows - 1; i++){
int step = 2*i;
int index = i;
while(index < len){
res.append(s.charAt(index));
step = 2 * numRows - 2 - step;
index += step;
}
}
for(int i = numRows - 1; i < len; i = i + 2 * numRows - 2){
res.append(s.charAt(i));
}
return res.toString();
}
拉链法(竖着走)
拼接法是按着原来的字符串的顺序走。与拉链法类似。设置一个长度为numRows的数组,每个数组对应着一个链表。然后将字符串的每个字符加入到对应的位置。按链表的方式输出字符串。这样时间复杂度为O(n),空间复杂度为O(n^2)
public String convert(String s, int numRows) {
if (numRows == 1) return s;
List<StringBuilder> rows = new ArrayList<>();
for (int i = 0; i < Math.min(numRows, s.length()); i++)
rows.add(new StringBuilder());
int curRow = 0;
boolean goingDown = false;
for (char c : s.toCharArray()) {
rows.get(curRow).append(c);
if (curRow == 0 || curRow == numRows - 1) goingDown = !goingDown;
curRow += goingDown ? 1 : -1;
}
StringBuilder ret = new StringBuilder();
for (StringBuilder row : rows) ret.append(row);
return ret.toString();
}
ringBuilder();
for (StringBuilder row : rows) ret.append(row);
return ret.toString();
}