TheAlgorithms-C/Searches/modifiedBinarySearch.c

#include<stdio.h>

int n,m;    //size of the matrix

// This function does Binary search for x in i-th row from j_low to j_high. 
void binarySearch(int mat[n][m], int i, int j_low,int j_high, int x)
{
    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 ;
        }
        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");
}
 
// Function to perform binary search on the mid values of row to get the desired pair of rows
// where the element can be found
void modifiedBinarySearch(int mat[n][m], int n, int m, int x)
{  // 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);
}

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