n2-to-n

n2-to-n.cpp

typedef unsigned __int64 u64;

//
// i\j 0 1 2 3 4
//  0  0 2 5 9
//  1  1 4 8
//  2  3 7
//  3  6
//  4
//
u64 ijton(u64 i, u64 j) {
    return (i + j) * (i + j + 1) / 2 + j;
}

// i\j 0 1 2 3 4
//  0  0 2 5 9
//  1  1 4 8
//  2  3 7
//  3  6
//  4
pair<u64,u64> ntoij(u64 n) {
    u64 w = (u64)((sqrt(8.0 * n + 1.0) - 1.0) / 2.0);
    u64 t = w * (w + 1) / 2;
    return make_pair(w - (n - t), n - t);
}

test.cpp

void ijton_tests() {
    #define EXPECT_EQ(expected, actual, error) \
            do if (expected != actual) cout << error; while (0)

    // i\j 0 1 2 3 4
    //  0  0 2 5 9
    //  1  1 4 8
    //  2  3 7
    //  3  6
    //  4

    EXPECT_EQ(0, ijton(0,0), "Error ijton(i,j) on 0,0\n");

    EXPECT_EQ(1, ijton(1,0), "Error ijton(i,j) on 1,0\n");
    EXPECT_EQ(2, ijton(0,1), "Error ijton(i,j) on 0,1\n");
    
    EXPECT_EQ(3, ijton(2,0), "Error ijton(i,j) on 2,0\n");
    EXPECT_EQ(4, ijton(1,1), "Error ijton(i,j) on 1,1\n");
    EXPECT_EQ(5, ijton(0,2), "Error ijton(i,j) on 0,2\n");
}

void ntoij_tests() {
    #define EXPECT_EQ(expected, actual, error) \
            do if (expected != actual) cout << error; while (0)

    // i\j 0 1 2 3 4
    //  0  0 2 5 9
    //  1  1 4 8
    //  2  3 7
    //  3  6
    //  4

    pair<u64,u64> p(0,0);
    EXPECT_EQ(p, ntoij(0), "Error ntoij(n) on 0\n");

    p = pair<u64,u64>(1,0);
    EXPECT_EQ(p, ntoij(1), "Error ntoij(n) on 1\n");
    p = pair<u64,u64>(0,1);
    EXPECT_EQ(p, ntoij(2), "Error ntoij(n) on 2\n");

    p = pair<u64,u64>(2,0);
    EXPECT_EQ(p, ntoij(3), "Error ntoij(n) on 3\n");
    p = pair<u64,u64>(1,1);
    EXPECT_EQ(p, ntoij(4), "Error ntoij(n) on 4\n");
    p = pair<u64,u64>(0,2);
    EXPECT_EQ(p, ntoij(5), "Error ntoij(n) on 5\n");
}