https://leetcode.com/problems/arranging-coins/

arranging-coins.go

// a1 + a2 + a3 + .. + an = n * (a1 + an) / 2
// 1 + 2 + 3 + 4 + 5
// 5 * (1 + 5) / 2 = 10

func arrangeCoins(n int) int {
    i, j := 1, n + 1
    
    for i < j {
        h := int(uint64(i + j) >> 1)
        sum := (h * (1 + h)) / 2
        
        if sum < n {
            i = h + 1
        } else {
            j = h
        }
    }
    
    if sum := (i * (1 + i)) / 2; sum > n {
        i--
    }
    
    return i
}