Write a function to count the total strobogrammatic numbers that exist in the range of low <= num <= high.
For example,
Given low = "50", high = "100", return 3. Because 69, 88, and 96 are three strobogrammatic numbers.
Note:
Because the range might be a large number, the low and high numbers are represented as string.
[分析]
思路1:比较容易想到的思路,利用题II的思路构造出low.length 和high.length之间的所有strobogrammatic number, 然后计数在low-high范围内的那些数字个数。
思路2:参考 https://leetcode.com/discuss/50624/clean-and-easy-understanding-java-solution 在构造过程中判断并计数,且构造方式是从两边往中间,而思路1是从中间忘两边。在leetcode的运行时间优于思路1
思路3:受思路2启发,改造思路1,也在构造过程中判断,修改过程各种bug调试好久,而且运行时间远高于思路1和思路2,无言~
public class Solution { // Method 2: ref Map<Character, Character> map = new HashMap<>(); { map.put('1', '1'); map.put('8', '8'); map.put('6', '9'); map.put('9', '6'); map.put('0', '0'); } String low = "", high = ""; public int strobogrammaticInRange(String low, String high) { this.low = low; this.high = high; int result = 0; for(int n = low.length(); n <= high.length(); n++){ int[] count = new int[1]; strobogrammaticInRange(new char[n], count, 0, n-1); result += count[0]; } return result; } private void strobogrammaticInRange(char[] arr, int[] count, int lo, int hi){ if(lo > hi){ String s = new String(arr); if((arr[0] != '0' || arr.length == 1) && compare(low, s) && compare(s, high)){ count[0]++; } return; } for(Character c: map.keySet()){ arr[lo] = c; arr[hi] = map.get(c); if((lo == hi && c == map.get(c)) || lo < hi) strobogrammaticInRange(arr, count, lo+1, hi-1); } } private boolean compare(String a, String b){ if(a.length() != b.length()) return a.length() < b.length(); int i = 0; while(i < a.length() &&a.charAt(i) == b.charAt(i)) i++; return i == a.length() ? true: a.charAt(i) <= b.charAt(i); } // Method 1 public int strobogrammaticInRange1(String low, String high) { int count = 0; int minLen = low.length(), maxLen = high.length(); for (int n = minLen; n <= maxLen; n++) { List<String> candidates = recur(n, n); if (n == minLen || n == maxLen) { for (String cand : candidates) { if (isLess(low, cand) && isLess(cand, high)) count++; } } else { count += candidates.size(); } } return count; } public List<String> recur(int k, int n) { List<String> result = new ArrayList<String>(); if (k <= 0) { result.add(""); return result; } if (k == 1) { result.add("0"); result.add("1"); result.add("8"); return result; } List<String> subResult = recur(k - 2, n); for (String substr : subResult) { if (k < n) result.add('0' + substr + '0'); result.add('1' + substr + '1'); result.add('8' + substr + '8'); result.add('6' + substr + '9'); result.add('9' + substr + '6'); } return result; } private boolean isLess(String a, String b) { if (a.length() != b.length()) return a.length() <= b.length() ? true : false; int i = 0; while (i < a.length() && a.charAt(i) == b.charAt(i)) i++; return i == a.length() ? true : a.charAt(i) <= b.charAt(i); } }
public class Solution { // Method 3 String low = null, high = null; public int strobogrammaticInRange(String low, String high) { this.low = low; this.high = high; int count = 0; int minLen = low.length(), maxLen = high.length(); for (int n = minLen; n <= maxLen; n++) { List<String> candidates = recur(n, n, minLen, maxLen); count += candidates.size(); } return count; } Map<Character, Character> map = new HashMap<>(); { map.put('1', '1'); map.put('8', '8'); map.put('6', '9'); map.put('9', '6'); } public List<String> recur(int k, int n, int minLen, int maxLen) { List<String> result = new ArrayList<String>(); if (k <= 0) { result.add(""); return result; } if (k == 1) { if (k < n || isLessOrEqual(this.low, "0") && isLessOrEqual("0", this.high)) result.add("0"); if (k < n || isLessOrEqual(this.low, "1") && isLessOrEqual("1", this.high)) result.add("1"); if (k < n || isLessOrEqual(this.low, "8") && isLessOrEqual("8", this.high)) result.add("8"); return result; } List<String> subResult = recur(k - 2, n, minLen, maxLen); for (String substr : subResult) { if (k < n) result.add('0' + substr + '0'); for (Character c : map.keySet()) { String cand = c + substr + map.get(c); if (k == n) { if ((minLen < n && n < maxLen) || isLessOrEqual(this.low, cand) && isLessOrEqual(cand, this.high)) result.add(cand); } else { result.add(cand); } } } return result; } private boolean isLessOrEqual(String a, String b) { if (a.length() != b.length()) return a.length() <= b.length() ? true : false; int i = 0; while (i < a.length() && a.charAt(i) == b.charAt(i)) i++; return i == a.length() ? true : a.charAt(i) <= b.charAt(i); } }