Leetcode 396. Rotate Function

最新推荐文章于 2022-04-22 16:29:48 发布

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最新推荐文章于 2022-04-22 16:29:48 发布

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本文介绍了一种求解数组经过旋转后得到的最大特定值的方法。提供了两种解决方案：一种是使用O(n)的时间复杂度和数学推导的方式；另一种是直观但时间复杂度为O(n^2)的解法。通过这两种方法，文章详细解释了如何计算数组旋转后的最大加权和。

O(n) Math solution.

/**
 * F(k)     = 0 * Bk[0] + 1 * Bk[1] + ... + (n-1) * Bk[n-1]
 *          = 0 * Bk-1[n-1] + 1 * Bk-1[0] + ... + (n-1) * Bk-1[n-2]
 * F(k-1)   = 0 * Bk-1[0] + 1 * Bk-1[1] + ... + (n-1) * Bk-1[n-1] 
 * 
 * F(k) - F(k-1) = 1*Bk-1([0]-[1]) + 2*Bk-1([1]-[2]) + (n-1)*Bk-1([n-2]-[n-1]) = sum_of_array - nBk-1[n-1] = sum_of_array - nBk[0]
 * 
 * B1[0] = A[len-1]
 * B2[0] = A[len-2]
 * ...
 * Blen-1[0] = A[1]
 */ 
public class Solution {
    public int maxRotateFunction(int[] A) {
        int len = A.length;
        
        // Calculate the sum of the array and F(0)
        int sum = 0;
        int f = 0;
        for (int i=0; i<len; i++) {
            sum += A[i];
            f += (i * A[i]);
        }
        
        // From length-1 to 1 calculate Fk, save the max value
        int max = f;
        for (int j=len-1; j>=1; j--) {
            f = f + sum - len * A[j];
            max = Math.max(f, max);
        }
        
        return max;
    }
}

Straightforward O(n^2) solution.

public class Solution {
    public int maxRotateFunction(int[] A) {
        if (A == null || A.length == 0) {
            return 0;
        }
        
        int n = A.length;
        int max = Integer.MIN_VALUE;
        
        for (int k=0; k<n; k++) {
            // Rotate the array
            int[] temp = rotate(A, k);
            // Calculate the F(k)
            int curr = calculateF(temp);
            // Compare and set max value
            max = Math.max(curr, max);
        }
        
        return max;
    }
    
    // Rotate the given by k clockwise
    public int[] rotate(int[] A, int k) {
        int len = A.length;
        int[] rotated = new int[len];
        
        // Move last k elements in A to the head of the new created array
        for (int i=0; i<k; i++) {
            rotated[i] = A[len-k+i];
        }
        
        // Move first len - k elements to the tail of the rotated array
        for (int i=0; i<len-k; i++) {
            rotated[k+i] = A[i];
        }
        
        return rotated;
    }
    
    // Calculate the F value for rotated array
    public int calculateF(int[] rotated) {
        int sum = 0;
        
        for (int i=0; i<rotated.length; i++) {
            sum += (i * rotated[i]);
        }
        
        return sum;
    }
}