modified_binary_search.c File Reference

Modified binary search algorithm More...

#include <stdio.h>
#include <stdlib.h>

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Functions
int	binarySearch (const int **mat, int i, int j_low, int j_high, int x)
	This function does Binary search for x in i-th row from j_low to j_high. More...
void	modifiedBinarySearch (const int **mat, int n, int m, int x)
	Function to perform binary search on the mid values of row to get the desired pair of rows where the element can be found. More...
int	main ()
	Main function. More...

Detailed Description

Modified binary search algorithm

Function Documentation

binarySearch()

int binarySearch	(	const int **	mat,
		int	i,
		int	j_low,
		int	j_high,
		int	x
	)

This function does Binary search for x in i-th row from j_low to j_high.

Parameters

mat	2D matrix to search within
i	row to search in
j_low	start column index
j_high	end column index
x	value to search for

Returns

column where x was found

-1 if value not found

{
    while (j_low <= j_high)
    {
        int j_mid = (j_low + j_high) / 2;
 
        // Element found
        if (mat[i][j_mid] == x)
        {
            printf("Found at (%d,%d)\n", i, j_mid);
            return j_mid;
        }
        else if (mat[i][j_mid] > x)
            j_high = j_mid - 1;
        else
            j_low = j_mid + 1;
    }
 
    // element not found
    printf("element not found\n");
    return -1;
}

main()

int main

(

void

)

Main function.

{
    int x;     // element to be searched
    int m, n;  // m = columns, n = rows
 
    scanf("%d %d %d\n", &n, &m, &x);
 
    int **mat = (int **)malloc(n * sizeof(int *));
    for (int i = 0; i < m; i++) mat[i] = (int *)malloc(m * sizeof(int));
 
    for (int i = 0; i < n; i++)
    {
        for (int j = 0; j < m; j++)
        {
            scanf("%d", &mat[i][j]);
        }
    }
 
    modifiedBinarySearch(mat, n, m, x);
 
    for (int i = 0; i < n; i++) free(mat[i]);
    free(mat);
    return 0;
}

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modifiedBinarySearch()

void modifiedBinarySearch	(	const int **	mat,
		int	n,
		int	m,
		int	x
	)

Function to perform binary search on the mid values of row to get the desired pair of rows where the element can be found.

Parameters

[in]	mat	matrix to search for the value in
	n	number of rows in the matrix
	m	number of columns in the matrix
	x	value to search for

{  // If Single row matrix
    if (n == 1)
    {
        binarySearch(mat, 0, 0, m - 1, x);
        return;
    }
 
    // Do binary search in middle column.
    // Condition to terminate the loop when the 2 desired rows are found.
    int i_low = 0, i_high = n - 1, j_mid = m / 2;
    while ((i_low + 1) < i_high)
    {
        int i_mid = (i_low + i_high) / 2;
        // element found
        if (mat[i_mid][j_mid] == x)
        {
            printf("Found at (%d,%d)\n", i_mid, j_mid);
            return;
        }
        else if (mat[i_mid][j_mid] > x)
            i_high = i_mid;
        else
            i_low = i_mid;
    }
    // If element is present on the mid of the two rows
    if (mat[i_low][j_mid] == x)
        printf("Found at (%d,%d)\n", i_low, j_mid);
    else if (mat[i_low + 1][j_mid] == x)
        printf("Found at (%d,%d)\n", i_low + 1, j_mid);
 
    // Search element on 1st half of 1st row
    else if (x <= mat[i_low][j_mid - 1])
        binarySearch(mat, i_low, 0, j_mid - 1, x);
 
    // Search element on 2nd half of 1st row
    else if (x >= mat[i_low][j_mid + 1] && x <= mat[i_low][m - 1])
        binarySearch(mat, i_low, j_mid + 1, m - 1, x);
 
    // Search element on 1st half of 2nd row
    else if (x <= mat[i_low + 1][j_mid - 1])
        binarySearch(mat, i_low + 1, 0, j_mid - 1, x);
 
    // search element on 2nd half of 2nd row
    else
        binarySearch(mat, i_low + 1, j_mid + 1, m - 1, x);
}

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