Given N, the row number of Pascal’s triangle(row starting from 0). Find the count of odd numbers in N-th row of Pascal’s Triangle.
Input : 11 Output : 8 Input : 20 Output : 4
Approach : It appears the answer is always a power of 2. In fact, the following theorem exists :
THEOREM : The number of odd entries in row N of Pascal’s Triangle is 2 raised to the number of 1’s in the binary expansion of N.
Example: Since 83 = 64 + 16 + 2 + 1 has binary expansion (1010011), then row 83 has pow(2, 4) = 16 odd numbers.
Below is the implementation of above approach :
Time Complexity : O(L), where L is the length of binary representation of given N.
Reference : https://www.math.hmc.edu/funfacts/ffiles/30001.4-5.shtml
- Pascal's Triangle
- Sum of all elements up to Nth row in a Pascal triangle
- Calculate nCr using Pascal's Triangle
- Leibniz harmonic triangle
- XNOR of two numbers
- Sum of numbers with exactly 2 bits set
- Find two numbers from their sum and XOR
- Maximum XOR using K numbers from 1 to n
- Count of numbers having only 1 set bit in the range [0, n]
- Find k numbers which are powers of 2 and have sum N | Set 1
- Numbers whose bitwise OR and sum with N are equal
- Count numbers whose sum with x is equal to XOR with x
- Check if two numbers are bit rotations of each other or not
- Add two numbers without using arithmetic operators
- Print first n numbers with exactly two set bits
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