center of vector

ex2.centrovector.cpp

// centrovector.cpp
// juanfc 2014-02-25
//
// Consider a vector V that contains N natural values (an array of naturals of
// size N, being N any constant). Define the centre c of vector V as the index
// between 1 and N–2 that follows:
//
// This property is not always met; in that case we say that there is no centre.
// Design procedure centreOfVector that receives a vector V as parmeter and
// returns two values as parameters: first one says if there is a centre and
// second one, if so, the value of that index.

// Supposing N = 5:
//   1st Example:
//     V is: 6 2 3 0 1
//     Then centre is 1 (cell with 2) because:
//      - Left sum:  (1-0)*V[0] = 1*6 = 6
//      - Right sum: (2-1)*V[2]+(3-1)*V[3]+(4-1)*V[4] = 1*3+2*0+3*1 = 6
//   2nd Example:
//     V is: 1 2 1 1 0
//     No centre


#include <iostream>
using namespace std;

const int N = 10;

typedef int TVector[N];




int main()
{
    void centreOfVector(TVector v, bool& is, int& c);
    int centreOfVector(TVector v);

    bool ok;
    int c;
    centreOfVector((TVector){6, 2, 3, 0, 1}, ok, c);
    if (ok)
        cout << "{6, 2, 3, 0, 1} has a center in " << c << endl;
    else
        cout << "{6, 2, 3, 0, 1} has Not a center" << endl;

    centreOfVector((TVector){1, 2, 1, 1, 0}, ok, c);
    if (ok)
        cout << "{1, 2, 1, 1, 0} has a center in " << c << endl;
    else
        cout << "{1, 2, 1, 1, 0} has NOT a center" << endl;

    cout << centreOfVector((TVector){6, 2, 3, 0, 1}) << endl;
    cout << centreOfVector((TVector){1, 2, 1, 1, 0}) << endl;


    return 0;
}

void centreOfVector(TVector v, bool& is, int& c)
{
    int sumUpto(TVector a, int c);
    int sumFrom(TVector a, int c);

    c = 0;
    is = false;
    while (c < N and not (is = sumUpto(v, c) == sumFrom(v, c))) {
        ++c;
    }
}

// also possible returning the index, -1 if not.
int centreOfVector(TVector v)
{
    int sumUpto(TVector a, int c);
    int sumFrom(TVector a, int c);

    int c = 0;
    while (c < N and sumUpto(v, c) != sumFrom(v, c) ) {
        ++c;
    }
    if (c >= N)
        c = -1;

    return c;
}

int sumUpto(TVector a, int c)
{
    int s = 0;
    for (int i = 0; i < c; i++)
        s += a[i] * (c - i);
    return s;
}

int sumFrom(TVector a, int c)
{
    int s = 0;
    for (int i = c + 1; i < N; i++)
        s += a[i] * (i - c);
    return s;
}