Consider an X x Y array of 1's and 0s. The X axis represents "influences" meaning that X influences Y. So, for example, if $array[3,7] is 1 that means that 3 influences 7. An "influencer" is someone who influences every other person, but is not influenced by any other member. Given such an array, write a function to determine whether or not an "influencer" exists in the array.

public static int influencer(final int[][] jobs, final int r, final int c) { int[] degree_in = new int[jobs.length]; int[] degree_out = new int[jobs.length]; for (int i = 0; i < r; ++i) { for (int j = 0; j < c; ++j) { if(jobs[i][j] == 1) { // i influences j degree_out[i]++; degree_in[j]++; } } } for (int i = 0; i < r; ++i) { if (degree_out[i] == r - 1 && degree_in[i] == 0) { return i; } } return -1; }

//if vec[i][j] == 0 then i is not an influence //if vec[i][j] == 1 then j is not an influence //so time complexity is O(n) bool find_influences(vector > &vec) { int n = vec.size(); vector not_influence(n); for (int i = 0; i = 0; --j) { if (!vec[i][j]) { break; } not_influence[j] = 1; } if (j < 0) { return true; } } not_influence[i] = 1; } return false; }

X should be equal to Y, right?

Here is a different view. Please comment if you find any issues with the logic. 1st. condition: An influencer can not be influenced by any one. Let's say the in a matrix of [x.y], there is an influencer with index 2. So, the column=2 (3rd column) in the matrix must be all 0s, since the influencer can not be influenced. Step 1: Find a column with all 0s. If found, remember the column index or there is no influencer. Let's say, it is m Second condition: An influencer must have influenced everyone. So, in our example: row=2 (third row) must be all 1s except for column=2, since influencer can not even influence self. Step 2: Check row=m and find that all values are 1 except for [m][m]. If found, we have an influencer.

Take the XOR product of the original matrix with the transposed matrix and sum by row. If any row counts equal the rank then they are influencers.

Run a BFS or DFS. For each node keep going to influencer. Find a node which can be reach by all nodes. Sort of finding sink node.

Not_Influencers[n] = 0; //Make all elements 0 for (i = 0 ; i< n ; i++){ if(Not_Influencers[i] == 1) continue; row_sum = find_row_sum(a[i]); if(row_sum == n-1 && find_col_sum(i) == 0) return Found; for(j = i; j < i; j++) if (a[j] == 1) Not_Influencers[j] = 1; }

the XOR suggestion I think is incomplete. The condition sum(row_influencer) = 1 and sum(column_influencer) = N so a simple matrix multiplication with the transposed should give for the vector v[influencer] = N and v[N-influencer] = 1. I assume influencer influences himself.

def find_influencer(matrix): for row in range(len(matrix)): following_none = not any(matrix[row]) if not following_none: continue all_following = True for r_no in range(len(matrix)): if not row == r_no: continue if not matrix[r_no][row]: all_following = False break if all_following: return row return -1

This was a tough one that forces you to consider how best to traverse the array and eliminate possibilities as soon as possible.

Consider the input as Graph given in adjaceny matrix representation. Find whether a semi-eulerian path is present in the graph or not.