Find the subarray with least average

转自：http://www.geeksforgeeks.org/find-subarray-least-average/

Given an array arr[] of size n and integer k such that k <= n.

Input:  arr[] = {3, 7, 90, 20, 10, 50, 40}, k = 3Output: Subarray between indexes 3 and 5The subarray {20, 10, 50} has the least average among all subarrays of size 3.Input:  arr[] = {3, 7, 5, 20, -10, 0, 12}, k = 2Output: Subarray between [4, 5] has minimum average

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A Simple Solution is to consider every element as beginning of subarray of size k and compute sum of subarray starting with this element. Time complexity of this solution is O(nk).

An Efficient Solution is to solve the above problem in O(n) time and O(1) extra space. The idea is to use sliding window of size k. Keep track of sum of current k elements. To compute sum of current window, remove first element of previous window and add current element (last element of current window).

1) Initialize res_index = 0 // Beginning of result index2) Find sum of first k elements. Let this sum be 'curr_sum'3) Initialize min_sum = sum4) Iterate from (k+1)'th to n'th element, do following   for every element arr[i]      a) curr_sum = curr_sum + arr[i] - arr[i-k]      b) If curr_sum < min_sum           res_index = (i-k+1)5) Print res_index and res_index+k-1 as beginning and ending   indexes of resultant subarray.

Below is C++ implementation of above algorithm.

// A Simple C++ program to find minimum average subarray

#include<bits/stdc++.h>

usingnamespace std;

 

// Prints beginning and ending indexes of subarray

// of size k with minimum average

voidfindMinAvgSubarray(intarr[], int n, int k)

{

    // k must be smaller than or equal to n

    if(n < k)

       return;

 

    // Initialize  beginning index of result

    intres_index = 0;

 

    // Compute sum of first subarray of size k

    intcurr_sum = 0;

    for(int i=0; i<k; i++)

       curr_sum += arr[i];

 

    // Initialize minimum sum as current sum

    intmin_sum = curr_sum;

 

    // Traverse from (k+1)'th element to n'th element

    for(int i = k; i < n; i++)

    {

        // Add current item and remove first item of

        // previous subarray

        curr_sum += arr[i] - arr[i-k];

 

        // Update result if needed

        if(curr_sum < min_sum)

        {

            min_sum = curr_sum;

            res_index = (i-k+1);

        }

    }

 

    cout <<"Subarray between [" << res_index << ", "

        << res_index + k - 1<<"] has minimum average";

}

 

// Driver program

int main()

{

    intarr[] = {3, 7, 90, 20, 10, 50, 40};

    intk = 3; // Subarray size

    intn = sizeof arr / sizeof arr[0];

    findMinAvgSubarray(arr, n, k);

    return0;

}