60. Permutation Sequence
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The set [1,2,3,…,n]
contains a total of n! unique permutations.
By listing and labeling all of the permutations in order,
We get the following sequence (ie, for n = 3):
"123"
"132"
"213"
"231"
"312"
"321"
Given n and k, return the kth permutation sequence.
Note: Given n will be between 1 and 9 inclusive.
思路:这题的第一想法肯定是回溯一遍,列出所有结果,然后输出第k个,但是显然是tlc的,这里我们可以讲一下思路,对于n=5的,最高位没差一下,中间的差值就有4!个,次高位就是3! 个。根据此规律我们就没有必要回溯列出所有的了
代码如下(已通过leetcode)
public class Solution {
public String getPermutation(int n, int k) {
StringBuilder res = new StringBuilder();
boolean[] flag = new boolean[n];
int temp = 1;
for (int i = 1; i <= n; i++)
temp = temp * i;
int[] data = new int[n + 1];
data[n] = temp;
data[0] = 1;
for (int i = n - 1; i >= 1; i--)
data[i] = data[i + 1] / (i + 1);
int numsLeft = n;
for (int i = 0; i < n; i++) {
if (numsLeft > 1) {
int mThUnused = (k - 1) / data[numsLeft - 1];
int counter = -1;
int head = 0;
for (; head < n && counter < mThUnused; head++) {
if (!flag[head])
counter++;
}
flag[head - 1] = true;
res.append(head);
k = k - mThUnused * data[numsLeft - 1];
numsLeft--;
} else
for (int j = 0; j < n; j++)
if (!flag[j]) {
res.append(j + 1);
break;
}
}
return res.toString();
}
}
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