# Calculate the number of set bits for every number from 0 to N

Given a non-negative integer N, the task is to find the count of set bits for every number from 0 to N.

Examples:

Input: N = 3
Output: 0 1 1 2
0, 1, 2 and 3 can be written in binary as 0, 1, 10 and 11.
The number of 1’s in their binary representation are 0, 1, 1 and 2.

Input: N = 5
Output: 0 1 1 2 1 2

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Naive approach: Run a loop from 0 to N and using inbuilt bit count function __builtin_popcount(), find the number of set bits in all the required integers.

Below is the implementation of the above approach:

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the count ` `// of set bits in all the ` `// integers from 0 to n ` `void` `findSetBits(``int` `n) ` `{ ` `    ``for` `(``int` `i = 0; i <= n; i++) ` `        ``cout << __builtin_popcount(i) << ``" "``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 5; ` ` `  `    ``findSetBits(n); ` ` `  `    ``return` `0; ` `} `

 `// Java implementation of the approach ` `class` `GFG  ` `{ ` ` `  `// Function to find the count ` `// of set bits in all the ` `// integers from 0 to n ` `static` `void` `findSetBits(``int` `n) ` `{ ` `    ``for` `(``int` `i = ``0``; i <= n; i++) ` `        ``System.out.print(Integer.bitCount(i) + ``" "``); ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String[] args)  ` `{ ` `    ``int` `n = ``5``; ` ` `  `    ``findSetBits(n); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

 `# Python 3 implementation of the approach ` `def` `count(n): ` `    ``count ``=` `0` `    ``while` `(n):  ` `        ``count ``+``=` `n & ``1` `        ``n >>``=` `1` `    ``return` `count ` ` `  `# Function to find the count ` `# of set bits in all the ` `# integers from 0 to n ` `def` `findSetBits(n): ` `    ``for` `i ``in` `range``(n ``+` `1``): ` `        ``print``(count(i), end ``=` `" "``) ` `     `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` `    ``n ``=` `5` ` `  `    ``findSetBits(n) ` ` `  `# This code is contributed by Surendra_Gangwar `

Output:
```0 1 1 2 1 2
```

Efficient approach: Let us write the binary representation of numbers in the range (0, 6).

0 in binary – 000
1 in binary – 001
2 in binary – 010
3 in binary – 011
4 in binary – 100
5 in binary – 101
6 in binary – 110

Since, any even number can be written as (2 * i) and any odd number can be written as (2 * i + 1) where i is a natural number.
2, 4 and 3, 6 have equal number of 1’s in their binary representation as multiplying any number is equivalent to shifting it left by 1 (read here).
Similarly, any even number 2 * i and i will have equal number of 1’s in its binary representation.
Number of 1’s in 5(101) is equal to number of 1’s in 2’s binary representation + 1. So in case of any odd number (2 * i + 1), it will be (number of 1’s in the binary representation of i) + 1.

Below is the implementation of the above approach:

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to find the count ` `// of set bits in all the ` `// integers from 0 to n ` `void` `findSetBits(``int` `n) ` `{ ` ` `  `    ``// dp[i] will store the count ` `    ``// of set bits in i ` `    ``int` `dp[n + 1]; ` ` `  `    ``// Initialise the dp array ` `    ``memset``(dp, 0, ``sizeof``(dp)); ` ` `  `    ``// Count of set bits in 0 is 0 ` `    ``cout << dp << ``" "``; ` ` `  `    ``// For every number starting from 1 ` `    ``for` `(``int` `i = 1; i <= n; i++) { ` ` `  `        ``// If current number is even ` `        ``if` `(i % 2 == 0) { ` ` `  `            ``// Count of set bits in i is equal to ` `            ``// the count of set bits in (i / 2) ` `            ``dp[i] = dp[i / 2]; ` `        ``} ` ` `  `        ``// If current element is odd ` `        ``else` `{ ` ` `  `            ``// Count of set bits in i is equal to ` `            ``// the count of set bits in (i / 2) + 1 ` `            ``dp[i] = dp[i / 2] + 1; ` `        ``} ` ` `  `        ``// Print the count of set bits in i ` `        ``cout << dp[i] << ``" "``; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` `    ``int` `n = 5; ` ` `  `    ``findSetBits(n); ` ` `  `    ``return` `0; ` `} `

 `// Java implementation of the approach ` `class` `GFG ` `{ ` ` `  `// Function to find the count ` `// of set bits in all the ` `// integers from 0 to n ` `static` `void` `findSetBits(``int` `n) ` `{ ` ` `  `    ``// dp[i] will store the count ` `    ``// of set bits in i ` `    ``int` `[]dp = ``new` `int``[n + ``1``]; ` ` `  `    ``// Count of set bits in 0 is 0 ` `    ``System.out.print(dp[``0``] + ``" "``); ` ` `  `    ``// For every number starting from 1 ` `    ``for` `(``int` `i = ``1``; i <= n; i++)  ` `    ``{ ` ` `  `        ``// If current number is even ` `        ``if` `(i % ``2` `== ``0``)  ` `        ``{ ` ` `  `            ``// Count of set bits in i is equal to ` `            ``// the count of set bits in (i / 2) ` `            ``dp[i] = dp[i / ``2``]; ` `        ``} ` ` `  `        ``// If current element is odd ` `        ``else` `        ``{ ` ` `  `            ``// Count of set bits in i is equal to ` `            ``// the count of set bits in (i / 2) + 1 ` `            ``dp[i] = dp[i / ``2``] + ``1``; ` `        ``} ` ` `  `        ``// Print the count of set bits in i ` `        ``System.out.print(dp[i] + ``" "``); ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String []args) ` `{ ` `    ``int` `n = ``5``; ` ` `  `    ``findSetBits(n); ` `} ` `} ` ` `  `// This code is contributed by Rajput-Ji `

 `# Python3 implementation of the approach  ` ` `  `# Function to find the count of set bits  ` `# in all the integers from 0 to n  ` `def` `findSetBits(n) : ` ` `  `    ``# dp[i] will store the count  ` `    ``# of set bits in i  ` `    ``# Initialise the dp array ` `    ``dp ``=` `[``0``] ``*` `(n ``+` `1``);  ` `     `  `    ``# Count of set bits in 0 is 0  ` `    ``print``(dp[``0``], end ``=` `" "``);  ` ` `  `    ``# For every number starting from 1  ` `    ``for` `i ``in` `range``(``1``, n ``+` `1``) : ` ` `  `        ``# If current number is even  ` `        ``if` `(i ``%` `2` `=``=` `0``) : ` ` `  `            ``# Count of set bits in i is equal to  ` `            ``# the count of set bits in (i / 2)  ` `            ``dp[i] ``=` `dp[i ``/``/` `2``];  ` ` `  `        ``# If current element is odd  ` `        ``else` `: ` ` `  `            ``# Count of set bits in i is equal to  ` `            ``# the count of set bits in (i / 2) + 1  ` `            ``dp[i] ``=` `dp[i ``/``/` `2``] ``+` `1``;  ` ` `  `        ``# Print the count of set bits in i  ` `        ``print``(dp[i], end ``=` `" "``);  ` ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``n ``=` `5``;  ` ` `  `    ``findSetBits(n);  ` ` `  `# This code is contributed by AnkitRai01 `

 `// C# implementation of the approach ` `using` `System; ` `     `  `class` `GFG ` `{ ` ` `  `// Function to find the count ` `// of set bits in all the ` `// integers from 0 to n ` `static` `void` `findSetBits(``int` `n) ` `{ ` ` `  `    ``// dp[i] will store the count ` `    ``// of set bits in i ` `    ``int` `[]dp = ``new` `int``[n + 1]; ` ` `  `    ``// Count of set bits in 0 is 0 ` `    ``Console.Write(dp + ``" "``); ` ` `  `    ``// For every number starting from 1 ` `    ``for` `(``int` `i = 1; i <= n; i++)  ` `    ``{ ` ` `  `        ``// If current number is even ` `        ``if` `(i % 2 == 0)  ` `        ``{ ` ` `  `            ``// Count of set bits in i is equal to ` `            ``// the count of set bits in (i / 2) ` `            ``dp[i] = dp[i / 2]; ` `        ``} ` ` `  `        ``// If current element is odd ` `        ``else` `        ``{ ` ` `  `            ``// Count of set bits in i is equal to ` `            ``// the count of set bits in (i / 2) + 1 ` `            ``dp[i] = dp[i / 2] + 1; ` `        ``} ` ` `  `        ``// Print the count of set bits in i ` `        ``Console.Write(dp[i] + ``" "``); ` `    ``} ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String []args) ` `{ ` `    ``int` `n = 5; ` ` `  `    ``findSetBits(n); ` `} ` `} ` ` `  `// This code is contributed by 29AjayKumar `

Output:
```0 1 1 2 1 2
```

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