Codeforces 712 C. Memory and De-Evolution （思维）

Posted 2022-08-13 小坏蛋_千千

Description

Memory is now interested in the de-evolution of objects, specifically triangles. He starts with an equilateral triangle of side length x, and he wishes to perform operations to obtain an equilateral triangle of side length y.

In a single second, he can modify the length of a single side of the current triangle such that it remains a non-degenerate triangle (triangle of positive area). At any moment of time, the length of each side should be integer.

What is the minimum number of seconds required for Memory to obtain the equilateral triangle of side length y?

 

Input

The first and only line contains two integers x and y (3 ≤ y < x ≤ 100 000) — the starting and ending equilateral triangle side lengths respectively.

 

Output

Print a single integer — the minimum number of seconds required for Memory to obtain the equilateral triangle of side length y if he starts with the equilateral triangle of side length x.

 

Examples input

6 3

 

Examples output

4

 

题意

一开始有一个边长为 $x$ 的等边三角形，我们每一次可以把它其中一条边减掉任意长度，但是每一次减完以后必须要保证三边依然可以组成三角形，问至少需要多少次才可以将原图形变为边长为 $y$ 的等边三角形。

 

思路

正着不好想我们可以反过来看，将边长为 $y$ 的等边三角形变为边长为 $x$ 的等边三角形至少需要操作多少次。

假设三角形三边长分别为 $a,b,c$ ，且此时 $a≤b≤c$ ，那么显然我们可以将最短边 $a$ 增大到 $b+c-1$ 的长度，如此反复，直到最短边大于等于 x x <script type="math/tex" id="MathJax-Element-9">x</script> 即可。

 

AC 代码

#include<bits/stdc++.h>
#define IO ios::sync_with_stdio(false);\\
    cin.tie(0);\\
    cout.tie(0);
using namespace std;
typedef long long LL;
const int maxn = 1e6+10;

int x,y;
int a[3];
int ans;
int main()

    IO;
    cin>>x>>y;
    a[0] = a[1] = a[2] = y;
    while(a[0]<=x)
    
        a[0] = a[1] + a[2] -1;
        sort(a,a+3);
        ++ans;
    
    cout<<ans<<endl;
    return 0;