Php Program for Number of pairs with maximum sum
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 sum function 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 sums function 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!