So i need help with finding a certain term in the fibonacci sequence. I have a program that is pretty close to it, but it will always find the term before the one i actually want.For example, if i want to show the 12th term it will show 89 instead of 144. This is also based on user input, so the user will choose what term to display. Heres the program i have.
#include <iostream>
using namespace std;
float fibSequence(float x);
int main(){
int x;
cout << "Term in fibonacci number: ";
cin >> x;
cout << "Fibonacci term: " << fibSequence(x) << endl;
}
float fibSequence(float x){
int prev = 1;
int prev2 = 0;
int current = x;
for(int i = 2; i <= x; i++){
current = prev + prev2;
prev = prev2;
prev2 = current;
}
return current;
}
And for the life of me i cannot figure out why. Like always, any help is appreciated!
You have an error in your assignment order. It should be:
current = prev + prev2;
prev2 = prev;
prev = current;
edit:
you could also switch the initial values:
int prev = 0;
int prev2 = 1;
but i assume prev2 is meant to be 'older' than prev
Related
This is the code that I have written and I am giving you sample inputs and outputs to this just to clear my question even more
Sample input
2 (value of t, which are test cases)
3 (number of inputs )
2 4 2
3
0
2
3
I am getting output as
1
1
I should be getting output as
1
0
#include<iostream>
#include<vector>
#define ll long long
using namespace std;
int main()
{
int t;
cin >> t;
while (t--)
{
vector<ll int> x;
ll int n;
cin >> n;
ll int i, ent;
for (i = 0; i < n; i++)
{
cin >> ent;
x.push_back(ent);
}
vector<ll int>::iterator y,z;
for(y=(x.begin());y!=(x.end()-1);y++)
for (z = (x.begin() + 1); z != (x.end()); z++)
{
int count=0;
if (*y + *z == *y * (*z))
count++;
}
cout << count<<endl;
}
return 0;
}
Updated code: But still having the same problem
#include<iostream>
#include<vector>
#define ll long long
int main()
{
int t;
std ::cin >> t;
while (t--)
{
std :: vector<ll int> x;
ll int n;
std :: cin >> n;
ll int i, ent;
for (i = 0; i < n; i++)
{
std :: cin >> ent;
x.push_back(ent);
}
std::vector<ll int>::iterator y,z;
int count = 0;
for(y=(x.begin());y!=(x.end()-1);y++)
for (z = (x.begin()+1); z != (x.end()); z++)
{
if (*y + *z == *y * (*z))
count++;
}
std ::cout << count<< std ::endl;
}
return 0;
}
Your first problem is that you're accessing the variable count outside its scope. It is declared in the scope of the inner for() loop, and you're trying to print it outside of it. Move its declaration above the for() loops
Now, to answer your question. In the second iteration of the while() loop (vector 0, 2, 3),
in one of the for() loops' iterations, *x and *z will be equal to 2. What you should have done to avoid it is to initialize z as z = y + 1
Your code as written should produce that output (if it even complies...) g++ won't compile it because you reference count after the loop it was created in. count is scoped to that loop so it doesn't exist outside. Anyway I assume you're using some compiler switches or a compiler that allows that.
You effectively make one list of numbers and loop through it checking the mathematical relation you coded (ie when two numbers added together is the same as them multiplied together.) Your first loop goes from the first value to the second last value (because you check for equality against end() - 1) I'm not sure if that's what you really wanted or not. Your second loop starts at the second value and then goes till the last value. So in your second test case your second number is 2 and 2 will be used for the parameter *y and then it is the first value in the second loop so you're doing the check with 2 and 2 and 2+2 == 4 == 2*2 so the check passes and count is incremented. Try the code below to get some insight into what you're doing (note that I removed the declaration of count from inside the loop and moved it just above the declaration of y and z which was required for me to compile it with my system):
{
cout << "y:" << *y <<" z:" << *z << endl;
if (*y + *z == *y * (*z)){
cout << "match " << *y << " " << *z << endl;
count++;
}
}
Name conflict between std::count and your local count. Remove using namespace std; and you will have more meaningful error message: as unknown identifier count, as count should be declared outside of the loop:
int count=0;
for(y=(x.begin());y!=(x.end()-1);y++)
for (z = (x.begin() + 1); z != (x.end()); z++)
{
if (*y + *z == *y * (*z))
count++;
}
std::cout << count << std::endl;
Note: std::cout << function_name outputs 1 with implicit bool conversion.
Note: logic of the code itself might still have issues
I am writing code to get the last digit of very large fibonacci numbers such as fib(239), etc.. I am using strings to store the numbers, grabbing the individual chars from end to beginning and then converting them to int and than storing the values back into another string. I have not been able to test what I have written because my program keeps abruptly closing after the std::cin >> n; line.
Here is what I have so far.
#include <iostream>
#include <string>
using std::cin;
using std::cout;
using namespace std;
char get_fibonacci_last_digit_naive(int n) {
cout << "in func";
if (n <= 1)
return (char)n;
string previous= "0";
string current= "1";
for (int i = 0; i < n - 1; ++i) {
//long long tmp_previous = previous;
string tmp_previous= previous;
previous = current;
//current = tmp_previous + current; // could also use previous instead of current
// for with the current length of the longest of the two strings
//iterates from the end of the string to the front
for (int j=current.length(); j>=0; --j) {
// grab consectutive positions in the strings & convert them to integers
int t;
if (tmp_previous.at(j) == '\0')
// tmp_previous is empty use 0 instead
t=0;
else
t = stoi((string&)(tmp_previous.at(j)));
int c = stoi((string&)(current.at(j)));
// add the integers together
int valueAtJ= t+c;
// store the value into the equivalent position in current
current.at(j) = (char)(valueAtJ);
}
cout << current << ":current value";
}
return current[current.length()-1];
}
int main() {
int n;
std::cin >> n;
//char& c = get_fibonacci_last_digit_naive(n); // reference to a local variable returned WARNING
// http://stackoverflow.com/questions/4643713/c-returning-reference-to-local-variable
cout << "before call";
char c = get_fibonacci_last_digit_naive(n);
std::cout << c << '\n';
return 0;
}
The output is consistently the same. No matter what I enter for n, the output is always the same. This is the line I used to run the code and its output.
$ g++ -pipe -O2 -std=c++14 fibonacci_last_digit.cpp -lm
$ ./a.exe
10
There is a newline after the 10 and the 10 is what I input for n.
I appreciate any help. And happy holidays!
I'm posting this because your understanding of the problem seems to be taking a backseat to the choice of solution you're attempting to deploy. This is an example of an XY Problem, a problem where the choice of solution method and problems or roadblocks with its implementation obfuscates the actual problem you're trying to solve.
You are trying to calculate the final digit of the Nth Fibonacci number, where N could be gregarious. The basic understanding of the fibonacci sequence tells you that
fib(0) = 0
fib(1) = 1
fib(n) = fib(n-1) + fib(n-2), for all n larger than 1.
The iterative solution to solving fib(N) for its value would be:
unsigned fib(unsigned n)
{
if (n <= 1)
return n;
unsigned previous = 0;
unsigned current = 1;
for (int i=1; i<n; ++i)
{
unsigned value = previous + current;
previous = current;
current = value;
}
return current;
}
which is all well and good, but will obviously overflow once N causes an overflow of the storage capabilities of our chosen data type (in the above case, unsigned on most 32bit platforms will overflow after a mere 47 iterations).
But we don't need the actual fib values for each iteration. We only need the last digit of each iteration. Well, the base-10 last-digit is easy enough to get from any unsigned value. For our example, simply replace this:
current = value;
with this:
current = value % 10;
giving us a near-identical algorithm, but one that only "remembers" the last digit on each iteration:
unsigned fib_last_digit(unsigned n)
{
if (n <= 1)
return n;
unsigned previous = 0;
unsigned current = 1;
for (int i=1; i<n; ++i)
{
unsigned value = previous + current;
previous = current;
current = value % 10; // HERE
}
return current;
}
Now current always holds the single last digit of the prior sum, whether that prior sum exceeded 10 or not really isn't relevant to us. Once we have that the next iteration can use it to calculate the sum of two single positive digits, which cannot exceed 18, and again, we only need the last digit from that for the next iteration, etc.. This continues until we iterate however many times requested, and when finished, the final answer will present itself.
Validation
We know the first 20 or so fibonacci numbers look like this, run through fib:
0:0
1:1
2:1
3:2
4:3
5:5
6:8
7:13
8:21
9:34
10:55
11:89
12:144
13:233
14:377
15:610
16:987
17:1597
18:2584
19:4181
20:6765
Here's what we get when we run the algorithm through fib_last_digit instead:
0:0
1:1
2:1
3:2
4:3
5:5
6:8
7:3
8:1
9:4
10:5
11:9
12:4
13:3
14:7
15:0
16:7
17:7
18:4
19:1
20:5
That should give you a budding sense of confidence this is likely the algorithm you seek, and you can forego the string manipulations entirely.
Running this code on a Mac I get:
libc++abi.dylib: terminating with uncaught exception of type std::out_of_range: basic_string before callin funcAbort trap: 6
The most obvious problem with the code itself is in the following line:
for (int j=current.length(); j>=0; --j) {
Reasons:
If you are doing things like current.at(j), this will crash immediately. For example, the string "blah" has length 4, but there is no character at position 4.
The length of tmp_previous may be different from current. Calling tmp_previous.at(j) will crash when you go from 8 to 13 for example.
Additionally, as others have pointed out, if the the only thing you're interested in is the last digit, you do not need to go through the trouble of looping through every digit of every number. The trick here is to only remember the last digit of previous and current, so large numbers are never a problem and you don't have to do things like stoi.
As an alternative to a previous answer would be the string addition.
I tested it with the fibonacci number of 100000 and it works fine in just a few seconds. Working only with the last digit solves your problem for even larger numbers for sure. for all of you requiring the fibonacci number as well, here an algorithm:
std::string str_add(std::string a, std::string b)
{
// http://ideone.com/o7wLTt
size_t n = max(a.size(), b.size());
if (n > a.size()) {
a = string(n-a.size(), '0') + a;
}
if (n > b.size()) {
b = string(n-b.size(), '0') + b;
}
string result(n + 1, '0');
char carry = 0;
std::transform(a.rbegin(), a.rend(), b.rbegin(), result.rbegin(), [&carry](char x, char y)
{
char z = (x - '0') + (y - '0') + carry;
if (z > 9) {
carry = 1;
z -= 10;
} else {
carry = 0;
}
return z + '0';
});
result[0] = carry + '0';
n = result.find_first_not_of("0");
if (n != string::npos) {
result = result.substr(n);
}
return result;
}
std::string str_fib(size_t i)
{
std::string n1 = "0";
std::string n2 = "1";
for (size_t idx = 0; idx < i; ++idx) {
const std::string f = str_add(n1, n2);
n1 = n2;
n2 = f;
}
return n1;
}
int main() {
const size_t i = 100000;
const std::string f = str_fib(i);
if (!f.empty()) {
std::cout << "fibonacci of " << i << " = " << f << " | last digit: " << f[f.size() - 1] << std::endl;
}
std::cin.sync(); std::cin.get();
return 0;
}
Try it with first calculating the fibonacci number and then converting the int to a std::string using std::to_string(). in the following you can extract the last digit using the [] operator on the last index.
int fib(int i)
{
int number = 1;
if (i > 2) {
number = fib(i - 1) + fib(i - 2);
}
return number;
}
int main() {
const int i = 10;
const int f = fib(i);
const std::string s = std::to_string(f);
if (!s.empty()) {
std::cout << "fibonacci of " << i << " = " << f << " | last digit: " << s[s.size() - 1] << std::endl;
}
std::cin.sync(); std::cin.get();
return 0;
}
Avoid duplicates of the using keyword using.
Also consider switching from int to long or long long when your numbers get bigger. Since the fibonacci numbers are positive, also use unsigned.
For a given n, I am trying to find the smallest number that is divisible by n, and also has sum of digits as n.
For example: For n = 10, Output should be 190, For n = 11, Output should be 209
I have adopted the Breadth First Traversal Approach to solve my problem.
#include <iostream>
#include <queue>
#include <string>
using namespace std;
class State{
public:
int sum,rem;
string str;
State(int s,int r,string st){
sum = s;
rem = r;
str = st;
}
};
int main() {
int n,newSum,newRem;
queue<State> q;
cin>>n;
bool visited[n+1][n+1] = {0};
State curr = State(0,0,"");
q.push(curr);
visited[0][0] = 1;
while(!q.empty()){
curr = q.front();
q.pop();
if(curr.sum==n && curr.rem==0){
cout<<curr.str<<endl;
break;
}
for(int j=0; j<=9; j++){
newSum = curr.sum + j;
newRem = (curr.rem*10+j)%n;
if(newSum > n){
break;
}
else if(!visited[newSum][newRem]){
curr = State(curr.sum+j, ((curr.rem*10)+j)%n,curr.str+to_string(j));
q.push(curr);
visited[newSum][newRem] = 1;
}
}
}
return 0;
}
My code, returns a number that satisfies the condition, but it is not the smallest possible number.
For n = 10, my code gives 12340
For n = 11, my code gives 1010207
Ideone link: http://ideone.com/c4W48N
You should try running through with a debugger, it shows up the problem very quickly.
In this line:
curr = State(curr.sum+j, ((curr.rem*10)+j)%n,curr.str+to_string(j));
q.push(curr);
You are assigning a new value to the curr variable, which you are then using next time around the loop. This means instead of trying 1, 2, 3, etc, you are trying 1, 12, 123, etc.
You are also recalculating items you have just calculated.
You can replace this with
State newState = State(newSum, newRem, curr.str + to_string(j));
q.push(newState);
or more simply again:
q.push(State(newSum, newRem, curr.str+to_string(j)));
Ok, so I have a regular Node list, with members info and next.
I need to use a function, recursively, to calculate the average, and then compare if each node is bigger than the average or not.
int Acount(NodeType* Node, int sum, int& avg){
if (Node == NULL){//last call
avg = sum / avg;
return 0;
}
else {
return (Acount(Node->next, sum + Node->info, ++avg) + (Node->info > avg ? 1 : 0));
}
}
Which is quite simple. Problem is the value returned is always 0.
The problem appears to be with
(Node->info > avg ? 1 : 0));
I've done the tests and when I do the following:
return (Acount(Node->next, sum + Node->info, ++avg) + Node->info;
or
return (Acount(Node->next, sum + Node->info, ++avg) + avg;
Results meet expectations. As in, I'm getting the sum of the Node->info in the first case, and I'm getting average*number of nodes in the second case.
Point of this, I've proved that the function is working perfectly.
Yet when it comes to
(Node->info > avg ? 1 : 0));
Appears to be problematic, which is quite peculiar. if I place for example:
(Node->info == 5 ? 1 : 0));
And there is only one 5 in the nodes, then the function returns 1. So everything is working as intended, yet I keep getting a 0.
The following are the main functions and additional functions for the Node.
#include <iostream>
using std::cout;
using std::cin;
using std::endl;
struct NodeType{
int info;
NodeType *next;
};
//pre: first node passed is not NULL
int Acount(NodeType* Node, int sum, int& avg){
if (Node == NULL){//last call
avg = sum / avg;
return 0;
}
else {
return (Acount(Node->next, sum + Node->info, ++avg) + (Node->info > avg ? 1 : 0));
}
}
void fill(NodeType*& Node){
NodeType *temp;
Node = new NodeType;
Node->info = 0;
Node->next = NULL;
temp = Node;
for (int i = 1; i < 10; i++){
temp->next = new NodeType;
temp = temp->next;
temp->info = i;
temp->next = NULL;
}
}
void print(NodeType* Node){
NodeType *temp = Node;
while (temp != NULL){
cout << temp->info << " ";
temp = temp->next;
}
cout << endl;
}
void Delete(NodeType* Node){
NodeType *temp;
while (Node != NULL){
temp = Node;
Node = Node->next;
delete temp;
}
}
void main(){
int sum = 0, avg = 0;
NodeType *Node;
fill(Node);
print(Node);
cout << Acount(Node, sum, avg) << endl;
Delete(Node);
}
In C++ there is no concept of left-to-right (or right-to-left) evaluation order of expressions. Operator priorities will control associativity, but in the case of f1() + f2() there is no guarantee that f1() is invoked before f2() (and viceversa). It may depend on the compiler or other.
My suggestion is to split the expression into 2 distinct statements as follows:
int tmp = Acount(Node->next, sum + Node->info, ++avg);
return tmp + (Node->info > avg ? 1 : 0);
I am not sure if your code has defined behaviour. But, this line
return (Acount(Node->next, sum + Node->info, ++avg) + (Node->info > avg ? 1 : 0));
depends on if the left summand or the right summand is calculated first.
If it is the left one, then Acount goes down the recursion an incrementing avg until avg equals the number of elements in the list (here 10 when starting from zero called by the main routine). Note, that avg is passed by reference. Thus, when the recursion goes back up, this term in the right summand
Node->info > avg
will never be true because Node->info is set in the fill routine to values smaller then the number of elements.
I don't think your method will work.
In this statement:
return (Acount(Node->next, sum + Node->info, ++avg) + (Node->info > avg ? 1 : 0))
You don't know when the second term has be evaluated. It's not defined in C++.
I was recently working on the following problem.
http://www.codechef.com/problems/D2
The Chef is planning a buffet for the DirectiPlex inauguration party, and everyone is invited. On their way in, each guest picks up a sheet of paper containing a random number (this number may be repeated). The guests then sit down on a round table with their friends.
The Chef now decides that he would like to play a game. He asks you to pick a random person from your table and have them read their number out loud. Then, moving clockwise around the table, each person will read out their number. The goal is to find that set of numbers which forms an increasing subsequence. All people owning these numbers will be eligible for a lucky draw! One of the software developers is very excited about this prospect, and wants to maximize the number of people who are eligible for the lucky draw. So, he decides to write a program that decides who should read their number first so as to maximize the number of people that are eligible for the lucky draw. Can you beat him to it?
Input
The first line contains t, the number of test cases (about 15). Then t test cases follow. Each test case consists of two lines:
The first line contains a number N, the number of guests invited to the party.
The second line contains N numbers a1, a2, ..., an separated by spaces, which are the numbers written on the sheets of paper in clockwise order.
Output
For each test case, print a line containing a single number which is the maximum number of guests that can be eligible for participating the the lucky draw.
Constraints
1 ≤ N ≤ 10000
You may assume that each number number on the sheet of paper; ai is randomly generated, i.e. can be with equal probability any number from an interval [0,U], where U is some upper bound (1 ≤ U ≤ 106).
Example
Input:
3
2
0 0
3
3 2 1
6
4 8 6 1 5 2
Output:
1
2
4
On checking the solutions I found this code:
#include <iostream>
#include <vector>
#include <stdlib.h>
#include <algorithm>
#define LIMIT 37
using namespace std;
struct node {
int val;
int index;
};
int N;
int binary(int number, vector<int>& ans) {
int start = 0;
int n = ans.size();
int end = n - 1;
int mid;
if (start == end)
return 0;
while (start != end) {
mid = (start + end) / 2;
if (ans[mid] == number)
break;
if (ans[mid] > number)
end = mid;
else
start = mid + 1;
}
mid = (start + end) / 2;
return mid;
}
void display(vector<int>& list) {
cout << endl;
for (int i = 0; i < list.size(); i++)
cout << list[i] << " ";
cout << endl;
}
int maxsubsequence(vector<int>& list) {
vector<int> ans;
int N = list.size();
ans.push_back(list[0]);
int i;
// display(list);
for (i = 1; i < N; i++) {
int index = binary(list[i], ans);
/*if(index+1<ans.size())
continue;*/
if (list[i] < ans[index])
ans[index] = list[i];
if (list[i] > ans[index])
ans.push_back(list[i]);
// display(ans);
}
return ans.size();
}
int compute(int index, int* g) {
vector<int> list;
list.push_back(g[index]);
int itr = (index + 1) % N;
while (itr != index) {
list.push_back(g[itr]);
itr = (itr + 1) % N;
}
return maxsubsequence(list);
}
int solve(int* g, vector<node> list) {
int i;
int ret = 1;
for (i = 0; i < min(LIMIT, (int)list.size()); i++) {
// cout<<list[i].index<<endl;
ret = max(ret, compute(list[i].index, g));
}
return ret;
}
bool cmp(const node& o1, const node& o2)
{ return (o1.val < o2.val); }
int g[10001];
int main() {
int t;
cin >> t;
while (t--) {
cin >> N;
vector<node> list;
int i;
for (i = 0; i < N; i++) {
node temp;
cin >> g[i];
temp.val = g[i];
temp.index = i;
list.push_back(temp);
}
sort(list.begin(), list.end(), cmp);
cout << solve(g, list) << endl;
}
return 0;
}
Can someone explain this to me. I am well aware of calculating LIS in nlog(n).
What I am not able to understand is this part:
int ret = 1;
for (i = 0; i < min(LIMIT, (int)list.size()); i++) {
// cout<<list[i].index<<endl;
ret = max(ret, compute(list[i].index, g));
}
and the reason behind sorting
sort(list.begin(),list.end(),cmp);
This algorithm is simply guessing at the starting point and computing the LIS for each of these guesses.
The first value in a LIS is likely to be a small number, so this algorithm simply tries the LIMIT smallest values as potential starting points.
The sort function is used to identify the smallest values.
The for loop is used to check each starting point in turn.
WARNING
Note that this algorithm may fail for certain inputs. For example, consider the sequence
0,1,2,..,49,9900,9901,...,99999,50,51,52,...,9899
The algorithm will try just the first 37 starting points and miss the best starting point at 50.
You can test this by changing the code to:
int main() {
int t;
t=1;
while (t--) {
N=10000;
vector<node> list;
int i;
for (i = 0; i < N; i++) {
node temp;
if (i<50)
g[i]=i;
else if (i<150)
g[i]=9999-150+i;
else
g[i]=i-100;
temp.val = g[i];
temp.index = i;
list.push_back(temp);
}
sort(list.begin(), list.end(), cmp);
cout << solve(g, list) << endl;
}
return 0;
}
This will generate different answers depending on whether LIMIT is 37 or 370.
In practice, for randomly generated sequences it will have a good chance of working (although I don't know how to compute the probability exactly).