Write a PHP program for a given array arr[], count the number of pairs arr[i], arr[j] such that arr[i] + arr[j] is maximum and i < j.
Example:
Input : arr[] = {1, 1, 1, 2, 2, 2}
Output: 3
Explanation: The maximum possible pair sum where i<j is 4, which is given by 3 pairs, so the answer is 3 the pairs are (2, 2), (2, 2) and (2, 2)Input: arr[] = {1, 4, 3, 3, 5, 1}
Output: 1
Explanation: The pair 4, 5 yields the maximum sum i.e, 9 which is given by 1 pair only
Php Program for Number of pairs with maximum sum using Naive Approach:
Traverse a loop i from 0 to n, i.e length of the array and another loop j from i+1 to n to find all possible pairs with i<j. Find the pair with the maximum possible sum, again traverse for all pairs and keep the count of the number of pairs which gives the pair sum equal to maximum .
Below is the Implementation of the above Approach:
PHP
<?php// PHP program to count pairs// with maximum sum.// function to find the number// of maximum pair sumfunction sum( $a, $n){ // traverse through all // the pairs $maxSum = PHP_INT_MIN; for($i = 0; $i < $n; $i++) for($j = $i + 1; $j < $n; $j++) $maxSum = max($maxSum, $a[$i] + $a[$j]); // traverse through all // pairs and keep a count // of the number of // maximum pairs $c = 0; for($i = 0; $i < $n; $i++) for($j = $i + 1; $j < $n; $j++) if ($a[$i] + $a[$j] == $maxSum) $c++; return $c;} // Driver Code $array = array(1, 1, 1, 2, 2, 2); $n = count($array); echo sum($array, $n); // This code is contributed by anuj_67.?> |
3
Time complexity: O(n2)
Auxiliary Space: O(1)
Efficient Method:
- Maximum element is always part of solution.
- If maximum element appears more than once, then result is maxCount * (maxCount – 1)/2. We basically need to choose 2 elements from maxCount (maxCountC2).
- If maximum element appears once, then result is equal to count of second maximum element. We can form a pair with every second max and max.
Below is the Implementation of the above Approach:
PHP
<?php// PHP program to count// pairs with maximum sum.// function to find the number// of maximum pair sumsfunction sum( $a, $n){ // Find maximum and second // maximum elements. Also // find their counts. $maxVal = $a[0]; $maxCount = 1; $secondMax = PHP_INT_MIN; $secondMaxCount; for ( $i = 1; $i < $n; $i++) { if ($a[$i] == $maxVal) $maxCount++; else if ($a[$i] > $maxVal) { $secondMax = $maxVal; $secondMaxCount = $maxCount; $maxVal = $a[$i]; $maxCount = 1; } else if ($a[$i] == $secondMax) { $secondMax = $a[$i]; $secondMaxCount++; } else if ($a[$i] > $secondMax) { $secondMax = $a[$i]; $secondMaxCount = 1; } } // If maximum element appears // more than once. if ($maxCount > 1) return $maxCount * ($maxCount - 1) / 2; // If maximum element // appears only once. return $secondMaxCount;}// Driver Code$array = array(1, 1, 1, 2, 2, 2, 3 );$n = count($array);echo sum($array, $n);// This code is contributed by anuj_67.?> |
3
Time complexity: O(n)
Auxiliary Space: O(1)
Please refer complete article on Number of pairs with maximum sum for more details!
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