招银2018[编程题]小招喵跑步

Posted 2021-01-02 wqpkita

小招喵喜欢在数轴上跑来跑去，假设它现在站在点n处，它只会3种走法，分别是：
1.数轴上向前走一步，即n=n+1 
2.数轴上向后走一步,即n=n-1 
3.数轴上使劲跳跃到当前点的两倍，即n=2*n
现在小招喵在原点，即n=0，它想去点x处，快帮小招喵算算最快的走法需要多少步？

#include <iostream>
//#include <algorithm>
using namespace std;

#define min(a, b) (((a)<(b))?(a):(b))

int minSteps(int n) {
    int result = 0;
    if (n < 0) n = -1 * n;

    //动态规划方法
    if (n == 0) return 0;
    if (n == 1) return 1;
    int *steps = new int[n + 1];
    steps[0] = 0;
    steps[1] = 1;
    for (int i = 2; i <= n; i++) {
        if (i % 2 == 0)
            steps[i] = min(steps[i - 1], steps[i / 2]) + 1;
        else
            steps[i] = min(steps[i - 1], steps[(i + 1) / 2] + 1) + 1;
    }
    result = steps[n];
    delete[]steps;
    return result;
}

int main() {
    int n;
    cin >> n;
    cout << minSteps(n) << endl;
    return 0;
}