LeetCode-Clumsy Factorial

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Description：
Normally, the factorial of a positive integer n is the product of all positive integers less than or equal to n. For example, factorial(10) = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1.

We instead make a clumsy factorial: using the integers in decreasing order, we swap out the multiply operations for a fixed rotation of operations: multiply (*), divide (/), add (+) and subtract (-) in this order.

For example, clumsy(10) = 10 * 9 / 8 + 7 - 6 * 5 / 4 + 3 - 2 * 1. However, these operations are still applied using the usual order of operations of arithmetic: we do all multiplication and division steps before any addition or subtraction steps, and multiplication and division steps are processed left to right.

Additionally, the division that we use is floor division such that 10 * 9 / 8 equals 11. This guarantees the result is an integer.

Implement the clumsy function as defined above: given an integer N, it returns the clumsy factorial of N.

Example 1:

Input: 4
Output: 7
Explanation: 7 = 4 * 3 / 2 + 1

Example 2:

Input: 10
Output: 12
Explanation: 12 = 10 * 9 / 8 + 7 - 6 * 5 / 4 + 3 - 2 * 1

Note:

• 1 <= N <= 10000
• -2^31 <= answer <= 2^31 - 1 (The answer is guaranteed to fit within a 32-bit integer.)

题意：计算一个正整数N的clumsy factorial，与正常阶乘不同的是，利用*/±来进行计算；要求返回给定整数N的clumsy factorial；

解法：因为题目规定了*/具有最高的计算优先级，所以我们不能够按照正常计算阶乘的那种方式计算；通过观察可以发现，如果我们把所有AB/C用一个新的数D代替的话，那么这个式子我们就不需要再去考虑运算的优先级了。这样的话我们每次用一个变量存储AB/C的值后，用前面计算所得的值减去当前计算的值即可；

Java

class Solution {
    public int clumsy(int N) {
        int res = 0;
        int sum = N * (-1);
        int ind = 0;
        for (int i = N - 1; i > 0; i--) {
            if (ind == 0) { // '*'
                sum *= i;
            } else if (ind == 1) { // '/'
                sum /= i;
            } else if (ind == 2) { // '+'
                res -= sum;
                res += i;
            } else { // '-'
                sum = i;
            }

            ind = (ind + 1) % 4;
        }
        if (ind <= 2) {
            res -= sum;
        }

        return res;
    }
}