Algorithm
You are given two integers n and m. You have to construct the array a of length n consisting of non-negative integers (i.e. integers greater than or equal to zero) such that the sum of elements of this array is exactly m and the value ∑i=1n−1|ai−ai+1| is the maximum possible. Recall that |x| is the absolute value of x.
In other words, you have to maximize the sum of absolute differences between adjacent (consecutive) elements. For example, if the array a=[1,3,2,5,5,0] then the value above for this array is |1−3|+|3−2|+|2−5|+|5−5|+|5−0|=2+1+3+0+5=11. Note that this example doesn't show the optimal answer but it shows how the required value for some array is calculated.
You have to answer t independent test cases.
The first line of the input contains one integer t (1≤t≤104) — the number of test cases. Then t test cases follow.
The only line of the test case contains two integers n and m (1≤n,m≤109) — the length of the array and its sum correspondingly.
For each test case, print the answer — the maximum possible value of ∑i=1n−1|ai−ai+1| for the array a consisting of n non-negative integers with the sum m.
5 1 100 2 2 5 5 2 1000000000 1000000000 1000000000
0 2 10 1000000000 2000000000
In the first test case of the example, the only possible array is [100] and the answer is obviously 0.
In the second test case of the example, one of the possible arrays is [2,0] and the answer is |2−0|=2.
In the third test case of the example, one of the possible arrays is [0,2,0,3,0] and the answer is |0−2|+|2−0|+|0−3|+|3−0|=10.
Code Examples
#1 Code Example with C++ Programming
Code -
C++ Programming
#include<bits/stdc++.h>
using namespace std;
int main(){
int t;
cin>>t;
int n, m;
while (t--) {
cin>>n>>m;
if(n == 1){
cout<<0<<endl;
continue;
}
if(n == 2){
cout<<m<<endl;
continue;
}
cout<<(2 * m)<<endl;
}
return 0;
}Input
1 100
2 2
5 5
2 1000000000
1000000000 1000000000
Output
2
10
1000000000
2000000000
Demonstration
Codeforcess solution 1353-A A. Most Unstable Array ,C++, Java, Js and Python, 1353-A,Codeforcess solution