[LeetCode] Strobogrammatic Number II
A strobogrammatic number is a number that looks the same when rotated 180 degrees (looked at upside down).
Find all strobogrammatic numbers that are of length = n.
For example,
Given n = 2, return ["11","69","88","96"].
Run some examples
n = 0, null;
n = 1, [0, 1, 8]
n = 2, [11, 69, 88, 96]
n = 3, [101, 609, 808, 906,
111, 619, 818, 916,
181, 689, 888, 986]
n = 4, [1001, 6009, 8008, 9006,
1111, 6119, 8118, 9116,
1691, 6699, 8698, 9696,
1881, 6889, 8888, 9886,
1961, 6969, 8968, 9966]
Brainstorming:
For a given n, each of its result in the list are generated by doing the following.
For each of the result of length n - 2 :
add 1 on its left and 1 on its right;
add 6 on its left and 9 on its right;
add 8 on its left and 8 on its right;
add 9 on its left and 6 on its right;
add 0 on its left and 0 on its right; (special case: 0 can not be added to either end when constructing the final result)
Recursive solution:
Runtime: The number of results in relation to n is 3 * 2^(n-1) for n >= 1 when n is odd;
5 * 2^(n-2) for n >=2 when n is even;
so the run time is exponential O(2^n). It is optimal since there are exponential number of solutions.
Space complexity: for odd n, 3 * (2^(n-1) + 2^(n-3) + .........+ 1 ) O(2^n);
similar when n is even.
public class Solution {
public List<String> findStrobogrammatic(int n) {
List<StringBuilder> sbList = findRecursive(n, n);
List<String> ans = new ArrayList<>();
for(StringBuilder sb: sbList) {
ans.add(sb.toString());
}
return ans;
}
private List<StringBuilder> findRecursive(int currLen, int targetLen)
{
List<StringBuilder> r = new ArrayList<StringBuilder>();
if(currLen == 0)
{
r.add(new StringBuilder(""));
return r;
}
if(currLen == 1)
{
r.add(new StringBuilder("0"));
r.add(new StringBuilder("1"));
r.add(new StringBuilder("8"));
return r;
}
List<StringBuilder> shorter = findRecursive(currLen - 2, targetLen);
for(StringBuilder sb : shorter)
{
if(currLen != targetLen)
{
r.add(new StringBuilder("0").append(sb).append("0"));
}
r.add(new StringBuilder("1").append(sb).append("1"));
r.add(new StringBuilder("6").append(sb).append("9"));
r.add(new StringBuilder("8").append(sb).append("8"));
r.add(new StringBuilder("9").append(sb).append("6"));
}
return r;
}
}
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