给定大小为NxN的矩阵。任务是计算索引对(i,j)的数量,以使第j列的总和大于第i行的总和。
例子:
Input : N = 2, mat[][] = {{1, 2},
{3, 4}}
Output : 2
The 2 valid pairs are (1, 1) and (1, 2).
Input : N = 3, mat[][] = { { 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 } };
Output : 4
方法:
这个想法是预先分别计算每一行和每一列的行总和和列总和,然后计算可能的有效对(i,j)的数量,以使第j列的列总和大于i的行总和。 -扔。
下面是上述方法的实现:
C++
// C++ program to count the number of pairs
// (i,j) such that sum of elements in j-th column
// is greater than sum of elements in i-th row
#include
using namespace std;
#define N 3
// Function to count the number of pairs
// (i,j) such that sum of elements in j-th column
// is greater than sum of elements in i-th row
int countPairs(int a[N][N])
{
// Initialize row sum and column
// sum to zero
int sumr[N] = { 0 }, sumc[N] = { 0 };
// Calculate row sum and column sum
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++) {
sumr[i] += a[i][j];
sumc[j] += a[i][j];
}
int count = 0;
// Count the number of pairs that are valid
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++)
if (sumc[i] > sumr[j])
count++;
return count;
}
// Driver Code
int main()
{
int a[][N] = { { 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 } };
cout << countPairs(a);
return 0;
}
Java
// Java program to count the number of pairs
// (i,j) such that sum of elements in j-th column
// is greater than sum of elements in i-th row
import java.io.*;
class GFG
{
static int N = 3;
// Function to count the number of pairs
// (i,j) such that sum of elements in j-th column
// is greater than sum of elements in i-th row
static int countPairs(int a[][])
{
// Initialize row sum and column
// sum to zero
int sumr[] = new int[N] ;
int sumc[] = new int [N] ;
// Calculate row sum and column sum
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++)
{
sumr[i] += a[i][j];
sumc[j] += a[i][j];
}
int count = 0;
// Count the number of pairs that are valid
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++)
if (sumc[i] > sumr[j])
count++;
return count;
}
// Driver Code
public static void main (String[] args)
{
int a[][] = { { 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 } };
System.out.println (countPairs(a));
}
}
// This code is contributed by jit_t.
Python3
# Python 3 program to count the number of pairs
# (i,j) such that sum of elements in j-th column
# is greater than sum of elements in i-th row
N = 3
# Function to count the number of pairs
# (i,j) such that sum of elements in j-th column
# is greater than sum of elements in i-th row
def countPairs(a):
# Initialize row sum and column
# sum to zero
sumr = [0 for i in range(N)]
sumc = [0 for i in range(N)]
# Calculate row sum and column sum
for i in range(N):
for j in range(N):
sumr[i] += a[i][j]
sumc[j] += a[i][j]
count = 0
# Count the number of pairs that are valid
for i in range(N):
for j in range(N):
if (sumc[i] > sumr[j]):
count += 1
return count
# Driver Code
if __name__ == '__main__':
a = [[1, 2, 3],[4, 5, 6], [7, 8, 9]]
print(countPairs(a))
# This code is contributed by
# Surendra_Gangwar
C#
// C# program to count the number of pairs
// (i,j) such that sum of elements in j-th column
// is greater than sum of elements in i-th row
using System;
class GFG
{
static int N = 3;
// Function to count the number
// of pairs (i,j) such that sum
// of elements in j-th column is
// greater than sum of elements in i-th row
static int countPairs(int [,]a)
{
// Initialize row sum and column
// sum to zero
int []sumr = new int[N] ;
int []sumc = new int [N] ;
// Calculate row sum and column sum
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++)
{
sumr[i] += a[i, j];
sumc[j] += a[i, j];
}
int count = 0;
// Count the number of pairs that are valid
for (int i = 0; i < N; i++)
for (int j = 0; j < N; j++)
if (sumc[i] > sumr[j])
count++;
return count;
}
// Driver Code
public static void Main()
{
int [,]a = { { 1, 2, 3 },
{ 4, 5, 6 },
{ 7, 8, 9 } };
Console.WriteLine(countPairs(a));
}
}
// This code is contributed by Ryuga
输出:
4
时间复杂度: O(N 2 )