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Minimum number of bins required to place N items ( Using Best Fit algorithm )

• Last Updated : 09 Apr, 2021

Given an array weight[] consisting of weights of N items and a positive integer C representing the capacity of each bin, the task is to find the minimum number of bins required such that all items are assigned to one of the bins.

Examples:

Input: weight[] = {4, 8, 1, 4, 2, 1}, C = 10
Output: 2
Explanation: The minimum number of bins required to accommodate all items is 2.
The first bin contains the items with weights {4, 4, 2}.
The second bin contains the items with weights {8, 1, 1}.

Input: weight[] = {9, 8, 2, 2, 5, 4}, C = 10
Output: 4

Approach: The given problem can be solved by using the best-fit algorithm. The idea is to place the next item in the bin, where the smallest empty space is left. Follow the steps below to solve the problem:

• Initialize a variable, say count as 0 that stores the minimum number of bins required.
• Sort the given array weight[] in decreasing order.
• Initialize a multiset, say M to store the empty spaces left in the occupied bins presently.
• Traverse the array weight[] and for each element perform the following steps:
• If there exists the smallest empty space which is at least arr[i] is present in the M, then erase that space from M and insert the remaining free space to M.
• Otherwise, increment the count by 1 and insert the empty space of the new bin in M.
• After completing the above steps, print the value of count as the minimum number of bins required.

Below is the implementation of the above approach:

C++

 `// C++ program for the above approach ` ` `  `#include ` `using` `namespace` `std; ` ` `  `// Function to find the minimum number ` `// of bins required to fill all items ` `void` `bestFit(``int` `arr[], ``int` `n, ``int` `W) ` `{ ` `    ``// Stores the required number ` `    ``// of bins ` `    ``int` `count = 0; ` ` `  `    ``// Sort the array in decreasing order ` `    ``sort(arr, arr + n, greater<``int``>()); ` ` `  `    ``// Stores the empty spaces in ` `    ``// existing bins ` `    ``multiset<``int``> M; ` ` `  `    ``// Traverse the given array ` `    ``for` `(``int` `i = 0; i < n; i++) { ` ` `  `        ``// Check if exact space is ` `        ``// present in the set M ` `        ``auto` `x = M.find(arr[i]); ` ` `  `        ``// Store the position of the ` `        ``// upperbound of arr[i] in M ` `        ``auto` `y = M.upper_bound(arr[i]); ` ` `  `        ``// If arr[i] is present, then ` `        ``// use this space and erase it ` `        ``// from the map M ` `        ``if` `(x != M.end()) { ` `            ``M.erase(x); ` `        ``} ` ` `  `        ``// If upper bound of arr[i] is ` `        ``// present, use this space and ` `        ``// insert the left space ` `        ``else` `if` `(y != M.end()) { ` `            ``M.insert(*y - arr[i]); ` `            ``M.erase(y); ` `        ``} ` ` `  `        ``// Otherwise, increment the count ` `        ``// of bins and insert the ` `        ``// empty space in M ` `        ``else` `{ ` `            ``count++; ` `            ``M.insert(W - arr[i]); ` `        ``} ` `    ``} ` ` `  `    ``// Print the result ` `    ``cout << count; ` `} ` ` `  `// Driver Code ` `int` `main() ` `{ ` `    ``int` `items[] = { 4, 8, 1, 4, 2, 1 }; ` `    ``int` `W = 10; ` `    ``int` `N = ``sizeof``(items) / ``sizeof``(items[0]); ` ` `  `    ``// Function Call ` `    ``bestFit(items, N, W); ` ` `  `    ``return` `0; ` `} `

Output:

```2
```

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

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