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每日一题——372. 超级次方

372. 超级次方

你的任务是计算 ab 对 1337 取模,a 是一个正整数,b 是一个非常大的正整数且会以数组形式给出。


投降了,cv了官方题解

public class Solution {
    const int MOD = 1337;

    public int SuperPow(int a, int[] b) {
        int ans = 1;
        for (int i = b.Length - 1; i >= 0; --i) {
            ans = (int) ((long) ans * Pow(a, b[i]) % MOD);
            a = Pow(a, 10);
        }
        return ans;
    }

    public int Pow(int x, int n) {
        int res = 1;
        while (n != 0) {
            if (n % 2 != 0) {
                res = (int) ((long) res * x % MOD);
            }
            x = (int) ((long) x * x % MOD);
            n /= 2;
        }
        return res;
    }
}

 

快速幂 – OI Wiki (oi-wiki.org)

数论题杀我,这道题考察的知识我之前从来没接触过

算是恶补了一下了

先给你们看看我研读了之后还是错误的写法

public class Solution {
    public int SuperPow(int a, int[] b) {
        int Mod = 1337;
        ulong divisor = 0;
        string temp = null;
        int ans = 1;

        for (int i = 0; i < b.Length; i++)
        {
            temp += b[i];
        }
        divisor = ulong.Parse(temp);

        //取模的运算不干涉乘法
        a %= Mod;

        while (divisor > 0)
        {
            if (divisor % 2 == 1) 
            {
                ans = ans * a % Mod;
            }
            a = a * a % Mod;
            divisor >>= 1;
        }


        return ans;
    }
}

a^n,当n很大的时候一个一个乘速度就很慢了

所谓的快速幂

就是不一个一个乘

而是把任务分割下去

把n表示为二进制

分割成a的2^k次幂的序列

又因为2^k能从前项推导

这样就能大量的节约事件了

详细可以看看上面的网址

这里举个例子来解释上面的代码

a是2,b是3

那么b的二进制就是011

每次都做一次右移的位运算,就相当于每次都除一次2

如果b是奇数的话,那就多取模一次

然后外面继续乘法和取模运算

直到最后

我是很干脆的把b直接遍历存放到了ulong里

但是来了个测试用例把我难倒了

78267
[1,7,7,4,3,1,7,0,1,4,4,9,2,8,5,0,0,9,3,1,2,5,9,6,0,9,9,0,9,6,0,5,3,7,9,8,8,9,8,2,5,4,1,9,3,8,0,5,9,5,6,1,1,8,9,3,7,8,5,8,5,5,3,0,4,3,1,5,4,1,7,9,6,8,8,9,8,0,6,7,8,3,1,1,1,0,6,8,1,1,6,6,9,1,8,5,6,9,0,0,1,7,1,7,7,2,8,5,4,4,5,2,9,6,5,0,8,1,0,9,5,8,7,6,0,6,1,8,7,2,9,8,1,0,7,9,4,7,6,9,2,3,1,3,9,9,6,8,0,8,9,7,7,7,3,9,5,5,7,4,9,8,3,0,1,2,1,5,0,8,4,4,3,8,9,3,7,5,3,9,4,4,9,3,3,2,4,8,9,3,3,8,2,8,1,3,2,2,8,4,2,5,0,6,3,0,9,0,5,4,1,1,8,0,4,2,5,8,2,4,2,7,5,4,7,6,9,0,8,9,6,1,4,7,7,9,7,8,1,4,4,3,6,4,5,2,6,0,1,1,5,3,8,0,9,8,8,0,0,6,1,6,9,6,5,8,7,4,8,9,9,2,4,7,7,9,9,5,2,2,6,9,7,7,9,8,5,9,8,5,5,0,3,5,8,9,5,7,3,4,6,4,6,2,3,5,2,3,1,4,5,9,3,3,6,4,1,3,3,2,0,0,4,4,7,2,3,3,9,8,7,8,5,5,0,8,3,4,1,4,0,9,5,5,4,4,9,7,7,4,1,8,7,5,2,4,9,7,9,1,7,8,9,2,4,1,1,7,6,4,3,6,5,0,2,1,4,3,9,2,0,0,2,9,8,4,5,7,3,5,8,2,3,9,5,9,1,8,8,9,2,3,7,0,4,1,1,8,7,0,2,7,3,4,6,1,0,3,8,5,8,9,8,4,8,3,5,1,1,4,2,5,9,0,5,3,1,7,4,8,9,6,7,2,3,5,5,3,9,6,9,9,5,7,3,5,2,9,9,5,5,1,0,6,3,8,0,5,5,6,5,6,4,5,1,7,0,6,3,9,4,4,9,1,3,4,7,7,5,8,2,0,9,2,7,3,0,9,0,7,7,7,4,1,2,5,1,3,3,6,4,8,2,5,9,5,0,8,2,5,6,4,8,8,8,7,3,1,8,5,0,5,2,4,8,5,1,1,0,7,9,6,5,1,2,6,6,4,7,0,9,5,6,9,3,7,8,8,8,6,5,8,3,8,5,4,5,8,5,7,5,7,3,2,8,7,1,7,1,8,7,3,3,6,2,9,3,3,9,3,1,5,1,5,5,8,1,2,7,8,9,2,5,4,5,4,2,6,1,3,6,0,6,9,6,1,0,1,4,0,4,5,5,8,2,2,6,3,4,3,4,3,8,9,7,5,5,9,1,8,5,9,9,1,8,7,2,1,1,8,1,5,6,8,5,8,0,2,4,4,7,8,9,5,9,8,0,5,0,3,5,5,2,6,8,3,4,1,4,7,1,7,2,7,5,8,8,7,2,2,3,9,2,2,7,3,2,9,0,2,3,6,9,7,2,8,0,8,1,6,5,2,3,0,2,0,0,0,9,2,2,2,3,6,6,0,9,1,0,0,3,5,8,3,2,0,3,5,1,4,1,6,8,7,6,0,9,8,0,1,0,4,5,6,0,2,8,2,5,0,2,8,5,2,3,0,2,6,7,3,0,0,2,1,9,0,1,9,9,2,0,1,6,7,7,9,9,6,1,4,8,5,5,6,7,0,6,1,7,3,5,9,3,9,0,5,9,2,4,8,6,6,2,2,3,9,3,5,7,4,1,6,9,8,2,6,9,0,0,8,5,7,7,0,6,0,5,7,4,9,6,0,7,8,4,3,9,8,8,7,4,1,5,6,0,9,4,1,9,4,9,4,1,8,6,7,8,2,5,2,3,3,4,3,3,1,6,4,1,6,1,5,7,8,1,9,7,6,0,8,0,1,4,4,0,1,1,8,3,8,3,8,3,9,1,6,0,7,1,3,3,4,9,3,5,2,4,2,0,7,3,3,8,7,7,8,8,0,9,3,1,2,2,4,3,3,3,6,1,6,9,6,2,0,1,7,5,6,2,5,3,5,0,3,2,7,2,3,0,3,6,1,7,8,7,0,4,0,6,7,6,6,3,9,8,5,8,3,3,0,9,6,7,1,9,2,1,3,5,1,6,3,4,3,4,1,6,8,4,2,5]

200位数组是不可能直接放到ulong里面的

所以我又犯了难

 

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