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Print the names of the teams in increasing order of their rankings
• Difficulty Level : Hard
• Last Updated : 08 Apr, 2021

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:

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)
Output:
France
Spain
England

Time Complexity: O(N * log(N))
Auxiliary Space: O(N)

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