陣列中兩兩異或大於m的個數
阿新 • • 發佈:2019-01-02
給定整數m以及n各數字A1,A2,..An,將數列A中所有元素兩兩異或,共能得到n(n-1)/2個結果,請求出這些結果中大於m的有多少個
1. aDigit=1, mDigit=1時,字典中第k位為0,異或結果為1,需要繼續搜尋更低位,第k位為1,異或結果為0,小於mDigit,不用理會; 2. aDigit=0, mDigit=1時,字典中第k位為1,異或結果為1,需要繼續搜尋更低位,第k位為0,異或結果為0,小於mDigit,不用理會; 3. aDigit=1, mDigit=0時,字典中第k位為0,異或結果為1,與對應分支所有數異或,結果都會大於m,第k位為1,異或結果為0,遞迴獲得結果; 4. aDigit=0, mDigit=0時,public class Main { private static class TrieTree { TrieTree[] next = new TrieTree[2]; int count = 1; } private static long solve(int[] a, int m) { TrieTree trieTree = buildTrieTree(a); long result = 0; for (int i = 0; i < a.length; i++) { result += queryTrieTree(trieTree, a[i], m, 31); } return result / 2; } private static long queryTrieTree(TrieTree trieTree, int a, int m, int index) { if(trieTree == null) return 0; TrieTree current = trieTree; for (int i = index; i >= 0; i--) { int aDigit = (a >> i) & 1; int mDigit = (m >> i) & 1; if(aDigit == 1 && mDigit == 1) { if(current.next[0] == null) return 0; current = current.next[0]; } else if (aDigit == 0 && mDigit == 1) { if(current.next[1] == null) return 0; current = current.next[1]; } else if (aDigit == 1 && mDigit == 0) { long p = queryTrieTree(current.next[1], a, m, i - 1); long q = current.next[0] == null ? 0 : current.next[0].count; return p + q; } else if (aDigit == 0 && mDigit == 0) { long p = queryTrieTree(current.next[0], a, m, i - 1); long q = current.next[1] == null ? 0 : current.next[1].count; return p + q; } } return 0; } private static TrieTree buildTrieTree(int[] a) { TrieTree trieTree = new TrieTree(); for (int i = 0; i < a.length; i++) { TrieTree current = trieTree; for (int j = 31; j >= 0; j--) { int digit = (a[i] >> j) & 1; if(current.next[digit] == null) { current.next[digit] = new TrieTree(); } else { current.next[digit].count ++; } current = current.next[digit]; } } return trieTree; } }