2021-03-28: Define a number: a number that can be expressed as the sum of several (number>1) consecutive positive numbers. For example: 5 = 2+3, 5 is such a number; 12 = 3+4+5, 12 is such a number. 1 is not such a number, because the number is required to be greater than 1, and the sum of consecutive positive numbers. 2 = 1 + 1, and 2 is not because the right side of the equal sign is not a continuous positive number. Given a parameter N, return whether it can be expressed as a number of consecutive positive numbers.
Fu Da's answer 2021-03-28:
1. Natural wisdom.
Sliding window. Midpoint to 1. L shifts to the left, and increases; R shifts to the left, and decreases. If sum = N, it is true.
2. Reverse the results based on the results and find the rules.
N is the power of 2 and cannot be expressed as the sum of consecutive positive numbers; N is not the power of 2 but is the number of the sum of consecutive positive numbers.
The code is written in golang. code show as below:
package main
import "fmt"
func main() {
for i := 1; i <= 64; i++ {
fmt.Println(i, isMSum1(i), isMSum2(i))
}
}
func isMSum1(num int) bool {
if num == 1 {
return false
}
R := (num + 1) >> 1
L := R - 1
sum := R
for {
if sum == num {
return true
} else if sum > num {
sum -= R
R--
} else {
if L == 0 {
break
}
sum += L
L--
}
}
return false
}
func isMSum2(num int) bool {
return num != (num & (^num + 1))
//return num != (num & (-num))
//return (num & (num - 1)) != 0
}The execution results are as follows: