A number is a gapful number when −
- It has at least three digits, and
- It is exactly divisible by the number formed by putting its first and last digits together
For example −
The number 1053 is a gapful number because it has 4 digits and it is exactly divisible by 13. Similarly, 135 is a gapful number because it has 3 digits and it is exactly divisible by 15.
Our job is to write a program that returns the nearest gapful number to the number we provide as input.
For example, for all 2-digit numbers, it would be 100. For 103, it would be 105.
We will break the problem into two functions −
isGapful() function
It receives a number string and returns a boolean as in the below code −
const isGapful = (numStr) => {
const int = parseInt(numStr);
return int % parseInt(numStr[0] + numStr[numStr.length - 1]) === 0;
};nearestGapful() function
This is our main function that receives a number, returns the nearest gapful number. Here’s the code −
const nearestGapful = (num) => {
if(typeof num !== 'number'){
return -1;
}
if(num <= 100){
return 100;
}
let prev = num - 1, next = num + 1;
while(!isGapful(String(prev)) && !isGapful(String(next))){
prev--;
next++;
};
return isGapful(String(prev)) ? prev : next;
};The isGapful() function returns a boolean based on whether the number is gapful or not in constant time, the nearestGapful() function loops until it finds a number that is gapful and returns it.
Following is the complete code −
Example
const n = 134;
//receives a number string and returns a boolean
const isGapful = (numStr) => {
const int = parseInt(numStr);
return int % parseInt(numStr[0] + numStr[numStr.length - 1]) === 0;
};
//main function -- receives a number, returns a number
const nearestGapful = (num) => {
if(typeof num !== 'number'){
return -1;
}
if(num <= 100){
return 100;
}
let prev = num - 1, next = num + 1;
while(!isGapful(String(prev)) && !isGapful(String(next))){
prev--;
next++;
};
return isGapful(String(prev)) ? prev : next;
};
console.log(nearestGapful(n));Output
The output in the console will be −
135