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package g0401_0500.s0441_arranging_coins;
// #Easy #Math #Binary_Search #Binary_Search_I_Day_6
// #2022_07_16_Time_2_ms_(95.97%)_Space_41.8_MB_(28.06%)
public class Solution {
public int arrangeCoins(int n) {
if (n < 0) {
throw new IllegalArgumentException(
"Input Number is invalid. Only positive numbers are allowed");
}
if (n <= 1) {
return n;
}
if (n <= 3) {
return n == 3 ? 2 : 1;
}
// Binary Search space will start from 2 to n/2.
long start = 2;
long end = n / 2;
while (start <= end) {
long mid = start + (end - start) / 2;
long coinsFilled = mid * (mid + 1) / 2;
if (coinsFilled == n) {
return (int) mid;
}
if (coinsFilled < n) {
start = mid + 1;
} else {
end = mid - 1;
}
}
// Since at this point start > end, start will start pointing to a value greater
// than the desired result. We will return end as it will point to the correct
// int value.
return (int) end;
}
}