Cs50 Tideman Solution -

locked[i][j] : A boolean matrix (graph) representing if there is a directed arrow from i to j . pair : A struct containing winner and loser . Detailed Solution Walkthrough

int margin1 = preferences[pairs[j].winner][pairs[j].loser] - preferences[pairs[j].loser][pairs[j].winner]; int margin2 = preferences[pairs[j+1].winner][pairs[j+1].loser] - preferences[pairs[j+1].loser][pairs[j+1].winner]; if (margin1 < margin2)

Before locking a pair, you must search the graph to see if the loser can already reach the winner through existing paths. Implementing the Recursion Helper Function

if (locked[start][i] && creates_cycle(i, end)) return true; Cs50 Tideman Solution

has_incoming = true; break;

The CS50 Tideman problem is a popular problem set from the Harvard University's CS50 introductory computer science course. In this problem, students are tasked with implementing a voting system called Tideman, named after the American mathematician and computer scientist Ralph Tideman. The goal of the problem is to create a program that can accurately determine the winner of an election using the Tideman voting system.

To manually test, try a 3-candidate case where a cycle would occur: locked[i][j] : A boolean matrix (graph) representing if

Ensure that the pair with the highest margin of victory moves to index 0 . 5. Lock Pairs (The Cycle Check)

Create a helper function called has_cycle(int winner, int loser) .

. This is the "Ranked" part of Ranked Pairs. If Candidate A beats B by 10 votes, and Candidate C beats D by only 2 votes, Candidate A's victory is processed first. 4. Lock the pairs (The "Cycle" Check) To manually test, try a 3-candidate case where

if (preferences[i][j] > preferences[j][i])

(the margin by which the winner defeated the loser). Sorting ensures that the most significant mandates are "locked" into the graph first. 3. Lock Pairs and Avoid Cycles This is the core and most difficult part of the algorithm. lock_pairs