Given a 2D array of strings arr[][4], representing the scores of M football matches played in a tournament involving N teams, the task is to print the names of the teams in ascending order of their ranks.
- The rules of a match are as follows:
- Each team plays 2 matches.
- The winning team gets 2 points and the losing team gets 0.
- In the case of a tie, both teams share a point each.
- If GD, GA, and GF stand for Goal Difference, Goals Against, and Goals For respectively. The rank of a team is decided in the following priority order:
- Points > GD > GF > Lexicographical order of names.
Examples:
Input: arr[][] = { { “Spain”, “England”, “3″, “0″ }, { “England”, “France”, “1″, “1″ }, { “Spain”, “France”, “0”, “2” } }, N = 3, M = 3
Output: France Spain England
Explanation: Points Table after 3 matches apiece:
Teams Matches
PlayedGF GA GD Points Ranking Spain
2
3
2
1
2
2
England
2
1
4
-3
1
3
France
2
3
1
2
3
1
Input: arr[][] = { { “Spain”, “England”, “3″, “0″ }, { “England”, “France”, “1″, “1″ }, { “Spain”, “Spain”, “0”, “2” } }, N = 3, M = 3
Output: Invalid Input
Approach: The problem can be solved using sorting a dictionary by multiple attributes.
Follow the steps below to solve the problem:
- Traverse the list arr[][] and print “Invalid” if arr[i][0] is equal to arr[i][1] and break.
- Initialize a dictionary say table to store the GA, GF, and GD for a particular teams.
- Traverse the list arr[][] and perform the following operations:
- Increment GF for arr[i][0], table[arr[i][0]][0] by arr[i][2] and GA for the arr[i][0], table[arr[i][0]][1] by arr[i][3].
- Increment GF for arr[i][1], table[arr[i][1]][0] by arr[i][3] and GA for the arr[i][1], table[arr[i][1]][1] by arr[i][2].
- Update GD for arr[i][0], table[arr[i][0]] by table[arr[i][0][2] – table[arr[i][0][3].
- Update GD for arr[i][1], table[arr[i][1]] by table[arr[i][1][2] – table[arr[i][1][3].
- If arr[i][2] == arr[i][3], then increment table[arr[i][0][0] and table[arr[i][1]][0] both by 1.
- If arr[i][2] > arr[i][3], then increment table[arr[i][0][0] by 2.
- If arr[i][2] < arr[i][3], then increment table[arr[i][1][0] by 2.
- Now, sort the dictionary table based on the priority points > GD > GF and names as:
- table = sorted(table.items(), key=lambda r: (-r[1][0], -r[1][1], -r[1][2], r[0]))
- Finally, print the names of the teams in sorted table.
Below is the implementation of the above approach:
Python3
# Python program for the above approach # Function to find the ranking of teamsdef RankTeams(arr): # Traverse the list arr for i in range(len(arr)): # arr[i][0] is equal to arr[i][1] if(arr[i][0] == arr[i][1]): print("Invalid") return # Convert the goal to integer arr[i][2] = int(arr[i][2]) arr[i][3] = int(arr[i][3]) # Stores the list of GD, GA, and GF table = {} # Traverse the list for i in range(len(arr)): # Store the list of GA, GF # and GD of first team li1 = [0] * 4 # Store the list of GA, GF # and GD of second team li2 = [0] * 4 # If arr[i][0] is in table if arr[i][0] in table: li1 = table[arr[i][0]] # If arr[i][1] is in table if arr[i][1] in table: li2 = table[arr[i][1]] # Increment GF by arr[i][2] li1[2] += arr[i][2] # Increment GA by arr[i][3] li1[3] += arr[i][3] # Increment GF by arr[i][3] li2[2] += arr[i][3] # Increment GA by arr[i][2] li2[3] += arr[i][2] # Update GD li1[1] = li1[2] - li1[3] li2[1] = li2[2] - li2[3] # If tie if(arr[i][2] == arr[i][3]): li1[0] += 1 li2[0] += 1 # If arr[i][0] wins elif(arr[i][2] > arr[i][3]): li1[0] += 2 # If arr[i][1] wins elif(arr[i][2] < arr[i][3]): li2[0] += 2 # Update list in table table[arr[i][0]] = li1 table[arr[i][1]] = li2 # Traverse the sortd table in the given priority for key, value in sorted(table.items(), key = lambda r: (-r[1][0], -r[1][1], -r[1][2], r[0])): # Print the team name print(key, end ='\n') # Driver Code # Inputarr = [['Spain', 'England', '3', '0'], ['England', 'France', '1', '1'], ['Spain', 'France', '0', '2']] RankTeams(arr) |
France Spain England
Time Complexity: O(N * log(N))
Auxiliary Space: O(N)
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.
