在二进制矩阵中找到具有最大位差的行对 · GeeksForGeeks 中文系列教程

# 在二进制矩阵中找到具有最大位差的行对 > 原文： [https://www.geeksforgeeks.org/find-pair-rows-binary-matrix-maximum-bit-difference/](https://www.geeksforgeeks.org/find-pair-rows-binary-matrix-maximum-bit-difference/) 给定一个二进制矩阵。任务是在二进制矩阵中找到最大位差的一对行例子： ``` Input: mat[][] = {{1, 1, 1, 1}, {1, 1, 0, 1}, {0, 0, 0, 0}}; Output : (1, 3) Bit difference between row numbers 1 and 3 is maximum with value 4\. Bit difference between 1 and 2 is 1 and between 2 and 3 is 3. Input: mat[][] = {{1 ,1 ,1 ,1 } {1 ,0, 1 ,1 } {0 ,1 ,0 ,0 } {0, 0 ,0 ,0 }} Output : (2, 3) Bit difference between rows 2 and 3 is maximum which is 4. Input: mat[][] = {{1 ,0 ,1 ,1 } {1 ,1 ,1 ,1 } {0 ,1 ,0 ,1 } {1, 0 ,0 ,0 }} Output : (1, 3) or (2 ,4 ) or (3 ,4 ) They all are having maximum bit difference that is 3 ``` **此问题的简单解决方案**是，一一挑选二进制矩阵的每一行，并与矩阵的其余行计算最大位差。最后返回那些具有最大位差的行。使用 [Trie 数据结构](https://www.geeksforgeeks.org/trie-insert-and-search/)的**有效解决方案**。下面是算法。 ``` 1). Create an empty Trie. Every node of Trie contains two children for 0 and 1 bits. 2). Insert First Row of Binary matrix into Trie 3).Traverse rest of the rows of given Binary Matrix a). For Each Row First we search maximum bit difference with rows that we insert before that in Trie and count bit difference b). For every search we update maximum bit_diff count if needed else not store pair of index that have maximum bit difference c). At Last Print Pair ``` ``` // C++ program to Find Pair of row in Binary matrix // that has maximum Bit difference #include<bits/stdc++.h> using namespace std; // Maximum size of matrix const int MAX = 100; struct TrieNode { int leaf; //store index of visited row struct TrieNode *Child[2]; }; // Utility function to create a new Trie node TrieNode * getNode() { TrieNode * newNode = new TrieNode; newNode->leaf = 0; newNode->Child[0] = newNode->Child[1] = NULL; return newNode; } // utility function insert new row in trie void insert(TrieNode *root, int Mat[][MAX], int n, int row_index) { TrieNode * temp = root; for (int i=0; i<n; i++) { // Add a new Node into trie if(temp->Child[ Mat[row_index][i] ] == NULL) temp->Child[ Mat[row_index][i] ] = getNode(); // move current node to point next node in trie temp = temp->Child[ Mat[row_index][i] ]; } // store index of currently inserted row temp->leaf = row_index +1 ; } // utility function calculate maximum bit difference of // current row with previous visited row of binary matrix pair<int, int> maxBitDiffCount(TrieNode * root, int Mat[][MAX], int n, int row_index) { TrieNode * temp = root; int count = 0; // Find previous visited row of binary matrix // that has starting bit same as current row for (int i= 0 ; i < n ; i++) { // First look for same bit in trie if (temp->Child[ Mat[row_index][i] ] != NULL) temp = temp->Child[ Mat[row_index][i] ]; // Else looking for opposite bit else if (temp->Child[1 - Mat[row_index][i]] != NULL) { temp = temp->Child[1- Mat[row_index][i]]; count++; } } int leaf_index = temp->leaf; int count1 = 0 ; temp = root; // Find previous visited row of binary matrix // that has starting bit opposite to current row for (int i= 0 ; i < n ; i++) { // First looking for opposite bit if (temp->Child[ 1 - Mat[row_index][i] ] !=NULL) { temp = temp->Child[ 1- Mat[row_index][i] ]; count1++; } // Else look for same bit in trie else if (temp->Child[ Mat[row_index][i] ] != NULL) temp = temp->Child[ Mat[row_index][i] ]; } pair <int ,int> P = count1 > count ? make_pair(count1, temp->leaf): make_pair(count, leaf_index); // return pair that contain both bit difference // count and index of row with we get bit // difference return P; } // Returns maximum bit difference pair of row void maxDiff( int mat[][MAX], int n, int m) { TrieNode * root = getNode(); // Insert first matrix row in trie insert(root, mat, m, 0); int max_bit_diff = INT_MIN; pair <int ,int> P, temp ; // Traverse all rest row of binary matrix for (int i = 1 ; i < n; i++) { // compute bit difference with previous visited // rows of matrix temp = maxBitDiffCount(root, mat, m ,i); // update maximum bit difference if (max_bit_diff < temp.first ) { max_bit_diff = temp.first; P = make_pair( temp.second, i+1); } // insert current row value into Trie insert(root, mat, m, i ); } // print maximum bit difference pair in row cout << "(" << P.first <<", "<< P.second << ")"; } // Driver program int main() { int mat[][MAX] = {{0 ,1 ,0 ,1, 0 }, {1, 0, 1 ,1 ,0 }, {0 ,0 ,1 ,0, 1 } }; maxDiff(mat, 3, 5) ; return 0; } ``` 输出： ``` 1 , 3 ``` 本文由 [**Nishant_singh（Pintu）**](https://practice.geeksforgeeks.org/user-profile.php?user=_code) 提供。如果您喜欢 GeeksforGeeks 并希望做出贡献，则还可以使用 [tribution.geeksforgeeks.org](http://www.contribute.geeksforgeeks.org) 撰写文章，或将您的文章邮寄至 tribution@geeksforgeeks.org。查看您的文章出现在 GeeksforGeeks 主页上，并帮助其他 Geeks。