Happy Number - LeetCode

examination questions

Write an algorithm to determine if a number is "happy".

A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers.

Example: 19 is a happy number

• 1² + 9² = 82
• 8² + 2² = 68
• 6² + 8² = 100
• 1² + 0² + 0² = 1

Please use the following function to solve the problem：

bool isHappy(int n) {

}

---

解题代码

#include <stdio.h>

bool isHappy(int n) {
    int arr[];
    int i = ;
    int sum = ;
    int temp1,temp2;

    while (true){
        do{
            temp1 = n / ;
            temp2 = n % ;
            n = temp1;
            sum = sum + temp2 * temp2;
        } while (temp1 > );

        if (sum != ){
            arr[i] = sum;
            n = sum;
            i++;
        }
        else{
            return true;
        }
        for (int j = ; j < i; j++){
            if (sum == arr[j-]){
                return false;
            }
        }
        sum = ;
    }
}

int main(){
    int n;
    scanf("%d",&n);
    if (isHappy(n)){
        printf("true\n");
    }
    else{
        printf("false\n");
    }
    return ;
}

LeetCode判断结果:

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" alt="" />

基本算法思想

把一个数拆分成单个数, 然后进行平方和, 对和进行比较, 如果满足和为1, 就是快乐数, 如果进入循环, 那么就不是快乐数.

代码注释分析

#include <stdio.h>

bool isHappy(int n) {
    int arr[]; //用于存储和不为1的值,仅仅是猜想有这么多个值
    int i = ; //记录和的个数
    int sum = ; //和值
    int temp1, temp2; //temp1为值, temp2为余数

    while (true){
        do{
            temp1 = n / ;
            temp2 = n % ;
            n = temp1;
            sum = sum + temp2 * temp2; //和
        } while (temp1 > ); //单个分解完成

        if (sum != ){ //如果不为1,就把该和值赋值给arr
            arr[i] = sum;
            n = sum;
            i++;
        }
        else{
            return true;
        }
        for (int j = ; j < i; j++){ //对和值进行循环匹配,如果和arr中的值相同,就退出,因为出现了循环
            if (sum == arr[j - ]){
                return false;
            }
        }
        sum = ;//第二次求和,必须先清零
    }
}

int main(){
    int n;
    scanf("%d", &n);
    if (isHappy(n)){
        printf("true\n");
    }
    else{
        printf("false\n");
    }
    return ;
}

优化

经过资料查询, 对于快乐数, 有以下规律:

不是快乐数的数称为不快乐数（unhappy number），所有不快乐数的数位平方和计算，最後都会进入 4 → 16 → 37 → 58 → 89 → 145 → 42 → 20 → 4 的循环中。

优化代码

#include <stdio.h>

bool isHappy(int n) {
    int sum = ;
    int temp1, temp2;

    while (true){
        do{
            temp1 = n / ;
            temp2 = n % ;
            n = temp1;
            sum = sum + temp2 * temp2;
        } while (temp1 > );

        if (sum == ){
            return true;
        }
        else{
            if (sum ==  || sum ==  || sum ==  || sum ==  || sum ==  || sum ==  || sum ==  || sum == ){
                return false;
            }
        }
        n = sum;
        sum = ;
    }
}

int main(){
    int n;
    scanf("%d", &n);
    if (isHappy(n)){
        printf("true\n");
    }
    else{
        printf("false\n");
    }
    return ;
}

LeetCode判断结果:

aaarticlea/png;base64,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" alt="" />