Merge Equals CodeForces - 962D(优先队列)

本文针对Codeforces上的D题“MergeEquals”进行了解析,并提供了一种使用优先队列和结构体来解决该问题的方法。文章详细介绍了算法思路,包括如何处理数列中两两相同值的合并操作。

CF真是锻炼STL用法的好地方

http://codeforces.com/problemset/problem/962/D
用map实现的做法—》https://blog.youkuaiyun.com/qq_40831340/article/details/81913330
D. Merge Equals
time limit per test2 seconds
memory limit per test256 megabytes
inputstandard input
outputstandard output
You are given an array of positive integers. While there are at least two equal elements, we will perform the following operation. We choose the smallest value x that occurs in the array 2 or more times. Take the first two occurrences of x in this array (the two leftmost occurrences). Remove the left of these two occurrences, and the right one is replaced by the sum of this two values (that is, 2⋅x).

Determine how the array will look after described operations are performed.

For example, consider the given array looks like [3,4,1,2,2,1,1]. It will be changed in the following way: [3,4,1,2,2,1,1] → [3,4,2,2,2,1] → [3,4,4,2,1] → [3,8,2,1].

If the given array is look like [1,1,3,1,1] it will be changed in the following way: [1,1,3,1,1] → [2,3,1,1] → [2,3,2] → [3,4].

Input
The first line contains a single integer n (2≤n≤150000) — the number of elements in the array.

The second line contains a sequence from n elements a1,a2,…,an (1≤ai≤109) — the elements of the array.

Output
In the first line print an integer k — the number of elements in the array after all the performed operations. In the second line print k integers — the elements of the array after all the performed operations.

Examples
inputCopy
7
3 4 1 2 2 1 1
outputCopy
4
3 8 2 1
inputCopy
5
1 1 3 1 1
outputCopy
2
3 4
inputCopy
5
10 40 20 50 30
outputCopy
5
10 40 20 50 30
Note
The first two examples were considered in the statement.

In the third example all integers in the given array are distinct, so it will not change.


题意:给你n个数,将其中的两两相同的值合并成一个新数放回数列中,直到没有可以合并的数,然后按照原有顺序输出新数列
思路:首先存放数列可以用队列,保持原有顺序,但是题上要求按照小的取,于是想到优先队列存结构体,在结构体中把当前数字的位置保存下来,将数字从对队列中两两往出取,最后会只剩一个,单独判断一下就好,最后结果存在结构体数组中,按照位置排序输出就好

#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
set<int> s;
struct node{
    ll num;
    ll pos;
    bool operator <(const node& a)const {
        return num==a.num? pos>a.pos:num>a.num;
    }
}no[150005];
priority_queue <node > q;
int aa[150005];
bool cmp(node a,node b){
    return a.pos<b.pos;
}
int main(){
    ll n;
    cin>>n;
    ll a;
    for(int i=1;i<=n;i++){
        cin>>a;
        no[i].num = a;
        no[i].pos = i;
        q.push(no[i]);
    }
    //cout<<s.size()<<endl;
/*  if(s.size()==n){
        for(int i=1;i<=n;i++) cout<<aa[i]<<" ";
        cout<<endl;
    }*/
    ll k = 0;
    node x,y;
    while(!q.empty()){
        if(q.size()==1){//特判队列只剩一个元素的情况
            no[k++] = q.top();

            q.pop();
        }
        else{
            x = q.top(); q.pop();
            y = q.top(); q.pop();
            if(x.num != y.num){
                no[k++] = x;

                q.push(y);
            }
            else{
                y.num = y.num*2;
                q.push(y);
            }
        }
    }
    cout<<k<<endl;
    sort(no,no+k,cmp);
    for(int i=0;i<k;i++){
        cout<<no[i].num<<" ";
    }
    cout<<endl;
    return 0;
}
### 解题思路 最长公共前后缀可使用 KMP 算法。若要合并 `a` 串和 `b` 串,构造一个 `b,a` 的串,对其求 `next` 数组,最后一位的 `next` 数组值就是最长公共前后缀的长度,随后模拟合并。但直接这样做会超时,因为原串很长而后面的串很短时,复杂度为 $O(n^2)$。可通过限定原串与新串合并时的范围来优化。不过可能会出现 `WA` 的情况,比如合并 `101` 和 `010` 时,新组合的串 `010101` 最后一位的 `next` 数组值大于单个串长,此时在两个串中间插入一个不可能存在的字符串来阻断两个串,防止这种情况发生。 ### 代码示例 ```python def get_next(s): n = len(s) next_arr = [0] * n j = 0 for i in range(1, n): while j > 0 and s[i] != s[j]: j = next_arr[j - 1] if s[i] == s[j]: j += 1 next_arr[i] = j return next_arr n = int(input()) words = [] for _ in range(n): words.append(input()) ans = words[0] for i in range(1, n): new_word = words[i] m = len(ans) k = len(new_word) # 限定合并范围 merge_range = min(m, k) temp = new_word + '#' + ans[-merge_range:] next_arr = get_next(temp) overlap = next_arr[-1] ans += new_word[overlap:] print(ans) ``` ### 代码解释 - `get_next` 函数:用于计算字符串的 `next` 数组,是 KMP 算法的核心部分。 - 主程序:首先读取输入的单词数量 `n` 和每个单词,将第一个单词作为初始结果。然后遍历后续的单词,每次合并时,构造临时字符串,计算 `next` 数组得到重叠部分的长度,最后将不重叠的部分添加到结果字符串中。 ### 复杂度分析 - 时间复杂度:优化后接近 $O(n)$,$n$ 为所有单词的总长度。 - 空间复杂度:$O(n)$,主要用于存储 `next` 数组和结果字符串。
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