Dada una array binaria. La tarea es encontrar el par de filas en la array binaria que tiene la máxima diferencia de bits. Ejemplos:
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
La solución simple de este problema es que elija cada fila de la array binaria una por una y calcule la diferencia máxima de bits con el resto de las filas de la array. En las últimas filas devueltas aquellas que tienen la diferencia máxima de bits.
Una solución eficiente utilizando Trie Data Structure . A continuación se muestra el algoritmo.
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
Implementación:
CPP
// 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;
}
Producción
(1, 3)
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Artículo escrito por GeeksforGeeks-1 y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA