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Commit e6c138b

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Prob 188 happy number
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‎README.md‎

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| Current Status| Stats |
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| :------------: | :----------: |
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| Total Problems | 187 |
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| Total Problems | 188 |
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</center>
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| Calculate factorial of large number, say 100 (it will have 158 digits) |[factorial_of_large_num.cpp](math_problems/factorial_of_large_num.cpp)|
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| Generate all possible words from a number entered on a traditional mobile keypad | [phone_digits.cpp](math_problems/phone_digits.cpp)|
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| Given a string representation of a number, remove n characters from the string such that number representation is lowest possible.| [lowest_possible_number.cpp](math_problems/lowest_possible_number.cpp)|
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| Detect if a number is a happy number. A number is happy number if sequence of operations where number is replaced by sum of square of its digits leads eventually to 1. A number is not a happy number if we are in an infinite loop when above operations are performed.|[happy_number.cpp](math_problems/happy_number.cpp)|
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### Stack Problems
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| Problem | Solution |
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| :------------ | :----------: |

‎math_problems/happy_number.cpp‎

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/*
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* Detect if a number is a happy number. A number is happy number if
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* sequence of operations where number is replaced by sum of square
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* of its digits leads eventually to 1. A number is not a happy number
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* if we are in an infinite loop when above operations are performed.
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*
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* Input: 49
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* 4^2 + 9^2 = 16 + 81 = 97
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* 9^2 + 7^2 =わ 81 +たす 49 =わ 130
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* 1^2 + 3^2 + 0^2 =わ 1 +たす 9 +たす 0 =わ 10
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* 1^2 + 0^2 = 1
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* Thus 49 is a happy number.
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* Approach:
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*
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* We can treat this problem same as finding a cycle in a linked list.
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* Imagine intermediate numbers as node and operation of square and sum
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* as link.
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* If we find the cycle, and the cycle is at 1, number is a happy number.
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* Else, the number is not a happy number.
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*/
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#include <iostream>
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int square_sum(int num)
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{
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int squared_sum = 0;
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while (num > 0) {
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squared_sum += (num % 10) * (num % 10);
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num /= 10;
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}
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return squared_sum;
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}
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bool is_happy(int num)
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{
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int slow = num;
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int fast = num;
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do {
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slow = square_sum(slow);
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fast = square_sum(square_sum(fast));
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} while (slow != fast);
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return slow == 1;
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}
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int main()
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{
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int num = 45;
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if (is_happy(num)) {
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std::cout << num << " is a happy number." << std::endl;
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} else {
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std::cout << num << " is not a happy number." << std::endl;
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}
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num = 49;
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if (is_happy(num)) {
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std::cout << num << " is a happy number." << std::endl;
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} else {
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std::cout << num << " is not a happy number." << std::endl;
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}
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return 0;
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}

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