#include #include 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, 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, 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 = (int **)malloc(n * sizeof(int *)); for (x = 0; x < n; x++) mat[x] = (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 (x = 0; x < n; x++) free(mat[x]); free(mat); return 0; }