Podano je polje n različnih elementov. Poiščite največji zmnožek najmanjšega števila dveh števil v matriki in absolutne razlike njunih položajev, tj. poiščite največjo vrednost abs(i - j) * min(arr[i] arr[j]), kjer se i in j spreminjata od 0 do n-1.
sistemsko programsko opremo
Primeri:
Input : arr[] = {3 2 1 4} Output: 9 // arr[0] = 3 and arr[3] = 4 minimum of them is 3 and // absolute difference between their position is // abs(0-3) = 3. So product is 3*3 = 9 Input : arr[] = {8 1 9 4} Output: 16 // arr[0] = 8 and arr[2] = 9 minimum of them is 8 and // absolute difference between their position is // abs(0-2) = 2. So product is 8*2 = 16 Recommended Practice Poiščite največjo vrednost Poskusite! A preprosta rešitev kajti ta problem je vzeti vsak element enega za drugim in primerjati ta element z elementi na desni strani. Nato izračunajte zmnožek najmanjšega izmed njih in absolutne razlike med njihovimi indeksi ter maksimirajte rezultat. Časovna zahtevnost za ta pristop je O(n^2).
An učinkovita rešitev za rešitev problema v linearni časovni kompleksnosti. Vzamemo dva iteratorja Levo=0 in Desno=n-1 primerjajte elemente arr[levo] in arr[desno].
left = 0 right = n-1 maxProduct = -INF While (left < right) If arr[Left] < arr[right] currProduct = arr[Left]*(right-Left) Left++ . If arr[right] < arr[Left] currProduct = arr[Right]*(Right-Left) Right-- . maxProduct = max(maxProduct currProduct)
Spodaj je izvedba zgornje ideje.
C++// C++ implementation of code #include
// Java implementation of code import java.util.*; class GFG { // Function to calculate maximum value of // abs(i - j) * min(arr[i] arr[j]) in arr[] static int Maximum_Product(int arr[] int n) { // Initialize result int maxProduct = Integer.MIN_VALUE; // product of current pair int currProduct; // loop until they meet with each other int Left = 0 right = n - 1; while (Left < right) { if (arr[Left] < arr[right]) { currProduct = arr[Left] * (right - Left); Left++; } // arr[right] is smaller else { currProduct = arr[right] * (right - Left); right--; } // maximizing the product maxProduct = Math.max(maxProduct currProduct); } return maxProduct; } // Driver code public static void main(String[] args) { int arr[] = {8 1 9 4}; int n = arr.length; System.out.print(Maximum_Product(arr n)); } } // This code is contributed by Anant Agarwal.
# Python implementation of code # Function to calculate # maximum value of # abs(i - j) * min(arr[i] # arr[j]) in arr[] def Maximum_Product(arrn): # Initialize result maxProduct = -2147483648 # product of current pair currProduct=0 # loop until they meet with each other Left = 0 right = n-1 while (Left < right): if (arr[Left] < arr[right]): currProduct = arr[Left]*(right-Left) Left+=1 else: # arr[right] is smaller currProduct = arr[right]*(right-Left) right-=1 # maximizing the product maxProduct = max(maxProduct currProduct) return maxProduct # Driver code arr = [8 1 9 4] n = len(arr) print(Maximum_Product(arrn)) # This code is contributed # by Anant Agarwal.
// C# implementation of code using System; class GFG { // Function to calculate maximum // value of abs(i - j) * min(arr[i] // arr[j]) in arr[] static int Maximum_Product(int []arr int n) { // Initialize result int maxProduct = int.MinValue; // product of current pair int currProduct; // loop until they meet // with each other int Left = 0 right = n - 1; while (Left < right) { if (arr[Left] < arr[right]) { currProduct = arr[Left] * (right - Left); Left++; } // arr[right] is smaller else { currProduct = arr[right] * (right - Left); right--; } // maximizing the product maxProduct = Math.Max(maxProduct currProduct); } return maxProduct; } // Driver code public static void Main() { int []arr = {8 1 9 4}; int n = arr.Length; Console.Write(Maximum_Product(arr n)); } } // This code is contributed by nitin mittal.
// PHP implementation of code // Function to calculate // maximum value of // abs(i - j) * min(arr[i] // arr[j]) in arr[] function Maximum_Product($arr $n) { $INT_MIN = 0; // Initialize result $maxProduct = $INT_MIN; // product of current pair $currProduct; // loop until they meet // with each other $Left = 0; $right = $n - 1; while ($Left < $right) { if ($arr[$Left] < $arr[$right]) { $currProduct = $arr[$Left] * ($right - $Left); $Left++; } // arr[right] is smaller else { $currProduct = $arr[$right] * ($right - $Left); $right--; } // maximizing the product $maxProduct = max($maxProduct $currProduct); } return $maxProduct; } // Driver Code $arr = array(8 1 9 4); $n = sizeof($arr) / sizeof($arr[0]); echo Maximum_Product($arr $n); // This code is contributed // by nitin mittal. ?> <script> // Javascript implementation of code // Function to calculate // maximum value of // abs(i - j) * min(arr[i] // arr[j]) in arr[] function Maximum_Product(arr n) { let INT_MIN = 0; // Initialize result let maxProduct = INT_MIN; // Product of current pair let currProduct; // Loop until they meet // with each other let Left = 0 right = n - 1; while (Left < right) { if (arr[Left] < arr[right]) { currProduct = arr[Left] * (right - Left); Left++; } // arr[right] is smaller else { currProduct = arr[right] * (right - Left); right--; } // Maximizing the product maxProduct = Math.max(maxProduct currProduct); } return maxProduct; } // Driver Code let arr = new Array(8 1 9 4); let n = arr.length; document.write(Maximum_Product(arr n)); // This code is contributed by Saurabh Jaiswal </script>
Izhod
16
Časovna zahtevnost: O(N log N) tukaj je N dolžina niza.
Prostorska kompleksnost: O(1) ker ni uporabljenega dodatnega prostora.
Kako to deluje?
Pomembno je pokazati, da ne zamudimo nobenega potencialnega para v zgornjem linearnem algoritmu, tj. pokazati moramo, da dejanje levo++ ali desno-- ne vodi do primera, ko bi dobili višjo vrednost maxProduct.
Upoštevajte, da vedno množimo z (desno - levo).
- Če pride[levo]< arr[right] then smaller values of desno za trenutno levo so neuporabne, saj ne morejo ustvariti višje vrednosti maxProduct (ker množimo z arr[levo] z (desno - levo)). Kaj pa, če bi bil arr[levo] večji od katerega koli elementa na njegovi levi strani. V tem primeru je moral biti s trenutno pravico najden boljši par za ta element. Zato lahko varno povečamo levo, ne da bi zamudili boljši par s trenutno levo.
- Podobni argumenti veljajo, kadar arr[right]< arr[left].