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| 1 | +# 1583. Count Unhappy Friends |
| 2 | + |
| 3 | +- Difficulty: Medium. |
| 4 | +- Related Topics: Array, Simulation. |
| 5 | +- Similar Questions: . |
| 6 | + |
| 7 | +## Problem |
| 8 | + |
| 9 | +You are given a list of `preferences` for `n` friends, where `n` is always **even**. |
| 10 | + |
| 11 | +For each person `i`, `preferences[i]` contains a list of friends **sorted** in the **order of preference**. In other words, a friend earlier in the list is more preferred than a friend later in the list. Friends in each list are denoted by integers from `0` to `n-1`. |
| 12 | + |
| 13 | +All the friends are divided into pairs. The pairings are given in a list `pairs`, where `pairs[i] = [xi, yi]` denotes `xi` is paired with `yi` and `yi` is paired with `xi`. |
| 14 | + |
| 15 | +However, this pairing may cause some of the friends to be unhappy. A friend `x` is unhappy if `x` is paired with `y` and there exists a friend `u` who is paired with `v` but: |
| 16 | + |
| 17 | + |
| 18 | + |
| 19 | +- `x` prefers `u` over `y`, and |
| 20 | + |
| 21 | +- `u` prefers `x` over `v`. |
| 22 | + |
| 23 | + |
| 24 | +Return **the number of unhappy friends**. |
| 25 | + |
| 26 | + |
| 27 | +Example 1: |
| 28 | + |
| 29 | +``` |
| 30 | +Input: n = 4, preferences = [[1, 2, 3], [3, 2, 0], [3, 1, 0], [1, 2, 0]], pairs = [[0, 1], [2, 3]] |
| 31 | +Output: 2 |
| 32 | +Explanation: |
| 33 | +Friend 1 is unhappy because: |
| 34 | +- 1 is paired with 0 but prefers 3 over 0, and |
| 35 | +- 3 prefers 1 over 2. |
| 36 | +Friend 3 is unhappy because: |
| 37 | +- 3 is paired with 2 but prefers 1 over 2, and |
| 38 | +- 1 prefers 3 over 0. |
| 39 | +Friends 0 and 2 are happy. |
| 40 | +``` |
| 41 | + |
| 42 | +Example 2: |
| 43 | + |
| 44 | +``` |
| 45 | +Input: n = 2, preferences = [[1], [0]], pairs = [[1, 0]] |
| 46 | +Output: 0 |
| 47 | +Explanation: Both friends 0 and 1 are happy. |
| 48 | +``` |
| 49 | + |
| 50 | +Example 3: |
| 51 | + |
| 52 | +``` |
| 53 | +Input: n = 4, preferences = [[1, 3, 2], [2, 3, 0], [1, 3, 0], [0, 2, 1]], pairs = [[1, 3], [0, 2]] |
| 54 | +Output: 4 |
| 55 | +``` |
| 56 | + |
| 57 | + |
| 58 | +**Constraints:** |
| 59 | + |
| 60 | + |
| 61 | + |
| 62 | +- `2 <= n <= 500` |
| 63 | + |
| 64 | +- `n` is even. |
| 65 | + |
| 66 | +- `preferences.length == n` |
| 67 | + |
| 68 | +- `preferences[i].length == n - 1` |
| 69 | + |
| 70 | +- `0 <= preferences[i][j] <= n - 1` |
| 71 | + |
| 72 | +- `preferences[i]` does not contain `i`. |
| 73 | + |
| 74 | +- All values in `preferences[i]` are unique. |
| 75 | + |
| 76 | +- `pairs.length == n/2` |
| 77 | + |
| 78 | +- `pairs[i].length == 2` |
| 79 | + |
| 80 | +- `xi != yi` |
| 81 | + |
| 82 | +- `0 <= xi, yi <= n - 1` |
| 83 | + |
| 84 | +- Each person is contained in **exactly one** pair. |
| 85 | + |
| 86 | + |
| 87 | + |
| 88 | +## Solution |
| 89 | + |
| 90 | +```javascript |
| 91 | +/** |
| 92 | + * @param {number} n |
| 93 | + * @param {number[][]} preferences |
| 94 | + * @param {number[][]} pairs |
| 95 | + * @return {number} |
| 96 | + */ |
| 97 | +var unhappyFriends = function(n, preferences, pairs) { |
| 98 | + var preferenceMap = Array(n).fill(0).map(() => Array(n)); |
| 99 | + for (var i = 0; i < preferences.length; i++) { |
| 100 | + for (var j = 0; j < preferences[i].length; j++) { |
| 101 | + preferenceMap[i][preferences[i][j]] = j; |
| 102 | + } |
| 103 | + } |
| 104 | + var pairMap = Array(n); |
| 105 | + for (var m = 0; m < pairs.length; m++) { |
| 106 | + pairMap[pairs[m][0]] = pairs[m][1]; |
| 107 | + pairMap[pairs[m][1]] = pairs[m][0]; |
| 108 | + } |
| 109 | + var res = 0; |
| 110 | + for (var k = 0; k < n; k++) { |
| 111 | + judge(preferenceMap, pairMap, k, n) && res++; |
| 112 | + } |
| 113 | + return res; |
| 114 | +}; |
| 115 | + |
| 116 | +var judge = function(preferenceMap, pairMap, i, n) { |
| 117 | + for (var k = 0; k < n; k++) { |
| 118 | + if (k === i || k === pairMap[i]) continue; |
| 119 | + if (preferenceMap[i][pairMap[i]] > preferenceMap[i][k] |
| 120 | + && preferenceMap[k][pairMap[k]] > preferenceMap[k][i]) { |
| 121 | + return true; |
| 122 | + } |
| 123 | + } |
| 124 | + return false; |
| 125 | +}; |
| 126 | +``` |
| 127 | + |
| 128 | +**Explain:** |
| 129 | + |
| 130 | +nope. |
| 131 | + |
| 132 | +**Complexity:** |
| 133 | + |
| 134 | +* Time complexity : O(n * n). |
| 135 | +* Space complexity : O(n * n). |
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