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modified_Binary_Search.c
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#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;
}