Codeforce 712A Memory and Crow
2017-02-10 21:19
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A. Memory and Crow
time limit per test:2 seconds
memory limit per test:256 megabytes
input:standard input
output:standard output
There are n integers b1, b2, ..., bn written in a row. For all
i from 1 to
n, values ai are defined by the crows performing the following procedure:
The crow sets ai initially
0.
The crow then adds bi to
ai, subtracts
bi + 1, adds the
bi + 2 number, and so on until the
n'th number. Thus, ai = bi - bi + 1 + bi + 2 - bi + 3....
Memory gives you the values a1, a2, ..., an, and he now wants you to find the initial numbers
b1, b2, ..., bn written in the row? Can you do it?
Input
The first line of the input contains a single integer n (2 ≤ n ≤ 100 000) — the number of integers written in the row.
The next line contains n, the
i'th of which is ai ( - 109 ≤ ai ≤ 109) —
the value of the i'th number.
Output
Print n integers corresponding to the sequence
b1, b2, ..., bn. It's guaranteed that the answer is unique and fits in 32-bit integer type.
Examples
Input
Output
Input
Output
Note
In the first sample test, the crows report the numbers
6, - 4, 8, - 2, and
3 when he starts at indices 1,
2, 3, 4 and
5 respectively. It is easy to check that the sequence 2
4 6 1 3 satisfies the reports. For example,
6 = 2 - 4 + 6 - 1 + 3, and - 4 = 4 - 6 + 1 - 3.
In the second sample test, the sequence 1,
- 3, 4, 11,
6 satisfies the reports. For example, 5 = 11 - 6 and
6 = 6.
解题思路:
【题意】
有n个数b1, b2, ..., bn
a1, a2, ..., an是通过等式ai = bi - bi + 1 + bi + 2 - bi + 3....(±)bn得到的
现给你a1, a2, ..., an这n个数,问b1, b2, ..., bn是多少
【类型】
公式推导
【分析】
由此可见,数组b中的第i项等于数组a中的第i项与第i+1项之和
特别地,数组b中的第n项等于数组a中的第n项
【时间复杂度&&优化】
O(n)
题目链接→Codeforces Problem 712A Memory and Crow
time limit per test:2 seconds
memory limit per test:256 megabytes
input:standard input
output:standard output
There are n integers b1, b2, ..., bn written in a row. For all
i from 1 to
n, values ai are defined by the crows performing the following procedure:
The crow sets ai initially
0.
The crow then adds bi to
ai, subtracts
bi + 1, adds the
bi + 2 number, and so on until the
n'th number. Thus, ai = bi - bi + 1 + bi + 2 - bi + 3....
Memory gives you the values a1, a2, ..., an, and he now wants you to find the initial numbers
b1, b2, ..., bn written in the row? Can you do it?
Input
The first line of the input contains a single integer n (2 ≤ n ≤ 100 000) — the number of integers written in the row.
The next line contains n, the
i'th of which is ai ( - 109 ≤ ai ≤ 109) —
the value of the i'th number.
Output
Print n integers corresponding to the sequence
b1, b2, ..., bn. It's guaranteed that the answer is unique and fits in 32-bit integer type.
Examples
Input
5 6 -4 8 -2 3
Output
2 4 6 1 3
Input
5 3 -2 -1 5 6
Output
1 -3 4 11 6
Note
In the first sample test, the crows report the numbers
6, - 4, 8, - 2, and
3 when he starts at indices 1,
2, 3, 4 and
5 respectively. It is easy to check that the sequence 2
4 6 1 3 satisfies the reports. For example,
6 = 2 - 4 + 6 - 1 + 3, and - 4 = 4 - 6 + 1 - 3.
In the second sample test, the sequence 1,
- 3, 4, 11,
6 satisfies the reports. For example, 5 = 11 - 6 and
6 = 6.
解题思路:
【题意】
有n个数b1, b2, ..., bn
a1, a2, ..., an是通过等式ai = bi - bi + 1 + bi + 2 - bi + 3....(±)bn得到的
现给你a1, a2, ..., an这n个数,问b1, b2, ..., bn是多少
【类型】
公式推导
【分析】
由此可见,数组b中的第i项等于数组a中的第i项与第i+1项之和
特别地,数组b中的第n项等于数组a中的第n项
【时间复杂度&&优化】
O(n)
题目链接→Codeforces Problem 712A Memory and Crow
1 #include <bits/stdc++.h> 2 using namespace std; 3 int main() 4 { 5 int n,a,b; 6 while(cin>>n) 7 { 8 for(int i=1;i<=n;i++) 9 { 10 cin>>a; 11 if(i>1) 12 cout<<a+b<<" "; 13 b=a; 14 } 15 cout<<a<<endl; 16 } 17 return 0; 18 }
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