diff --git a/leetcode/338. Counting Bits/README.md b/leetcode/338. Counting Bits/README.md
index 41c3a7c3..fddd43e8 100644
--- a/leetcode/338. Counting Bits/README.md
+++ b/leetcode/338. Counting Bits/README.md
@@ -1,26 +1,50 @@
-# [338. Counting Bits (Medium)](https://leetcode.com/problems/counting-bits/)
+# [338. Counting Bits (Easy)](https://leetcode.com/problems/counting-bits/)
-Given a non negative integer number num. For every numbers i in the range 0 ≤ i ≤ num calculate the number of 1's in their binary representation and return them as an array.
+Given an integer n, return an array ans of length n + 1 such that for each i (0 <= i <= n), ans[i] is the number of 1's in the binary representation of i.
+
Example 1:
-Input: 2
-Output: [0,1,1]
+Input: n = 2
+Output: [0,1,1]
+Explanation:
+0 --> 0
+1 --> 1
+2 --> 10
+
Example 2:
-Input: 5
-Output: [0,1,1,2,1,2]
+Input: n = 5
+Output: [0,1,1,2,1,2]
+Explanation:
+0 --> 0
+1 --> 1
+2 --> 10
+3 --> 11
+4 --> 100
+5 --> 101
-Follow up:
+
+Constraints:
+
+
+
+
+Follow up:
- - It is very easy to come up with a solution with run time O(n*sizeof(integer)). But can you do it in linear time O(n) /possibly in a single pass?
- - Space complexity should be O(n).
- - Can you do it like a boss? Do it without using any builtin function like __builtin_popcount in c++ or in any other language.
+ - It is very easy to come up with a solution with a runtime of
O(n log n). Can you do it in linear time O(n) and possibly in a single pass?
+ - Can you do it without using any built-in function (i.e., like
__builtin_popcount in C++)?
+
+**Companies**:
+[Amazon](https://leetcode.com/company/amazon), [Google](https://leetcode.com/company/google), [Apple](https://leetcode.com/company/apple)
+
**Related Topics**:
[Dynamic Programming](https://leetcode.com/tag/dynamic-programming/), [Bit Manipulation](https://leetcode.com/tag/bit-manipulation/)
@@ -42,14 +66,14 @@ And `1, 2, 3, ..., 2^k - 1` doesn't have bit overlap with `2^k`.
// Space: O(1)
class Solution {
public:
- vector countBits(int num) {
- vector ans(num + 1);
- for (int i = 1; i <= num; i *= 2) {
- ans[i] = 1;
- for (int j = 1; j < i && i + j <= num; ++j) ans[i + j] = ans[i] + ans[j];
+ vector countBits(int n) {
+ vector ans(n + 1);
+ for (int i = 1; i <= n; i *= 2) {
+ ans[i] = 1;
+ for (int j = 1; j < i && i + j <= n; ++j) ans[i + j] = ans[i] + ans[j];
+ }
+ return ans;
}
- return ans;
- }
};
```
@@ -68,9 +92,9 @@ dp[i] = 1 + dp[i - (i & -i)]
// Space: O(1)
class Solution {
public:
- vector countBits(int num) {
- vector ans(num + 1);
- for (int i = 1; i <= num; ++i) ans[i] = 1 + ans[i - (i & -i)];
+ vector countBits(int n) {
+ vector ans(n + 1);
+ for (int i = 1; i <= n; ++i) ans[i] = 1 + ans[i - (i & -i)];
return ans;
}
};
@@ -85,10 +109,32 @@ public:
// Space: O(1)
class Solution {
public:
- vector countBits(int num) {
- vector ans(num + 1, 0);
- for (int i = 1; i <= num; ++i) ans[i] = ans[i / 2] + (i % 2);
- return ans;
- }
+ vector countBits(int n) {
+ vector ans(n + 1);
+ for (int i = 1; i <= n; ++i) ans[i] = ans[i / 2] + (i % 2);
+ return ans;
+ }
+};
+```
+
+## Solution 4. DP
+
+DP based on highest bit
+
+```cpp
+// OJ: https://leetcode.com/problems/counting-bits/
+// Author: github.com/lzl124631x
+// Time: O(N)
+// Space: O(1)
+class Solution {
+public:
+ vector countBits(int n) {
+ vector ans(n + 1);
+ for (int i = 1, hb = 1; i <= n; ++i) {
+ if ((hb & i) == 0) hb <<= 1;
+ ans[i] = 1 + ans[i - hb];
+ }
+ return ans;
+ }
};
```
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diff --git a/leetcode/338. Counting Bits/s1.cpp b/leetcode/338. Counting Bits/s1.cpp
deleted file mode 100644
index 711a1142..00000000
--- a/leetcode/338. Counting Bits/s1.cpp
+++ /dev/null
@@ -1,15 +0,0 @@
-// OJ: https://leetcode.com/problems/counting-bits
-// Author: github.com/lzl124631x
-// Time: O(N)
-// Space: O(1)
-class Solution {
-public:
- vector countBits(int num) {
- vector ans(num + 1);
- for (int i = 1; i <= num; i *= 2) {
- ans[i] = 1;
- for (int j = 1; j < i && i + j <= num; ++j) ans[i + j] = ans[i] + ans[j];
- }
- return ans;
- }
-};
\ No newline at end of file
diff --git a/leetcode/338. Counting Bits/s2.cpp b/leetcode/338. Counting Bits/s2.cpp
deleted file mode 100644
index 7ca479bb..00000000
--- a/leetcode/338. Counting Bits/s2.cpp
+++ /dev/null
@@ -1,12 +0,0 @@
-// OJ: https://leetcode.com/problems/counting-bits/
-// Author: github.com/lzl124631x
-// Time: O(N)
-// Space: O(1)
-class Solution {
-public:
- vector countBits(int num) {
- vector ans(num + 1);
- for (int i = 1; i <= num; ++i) ans[i] = 1 + ans[i - (i & -i)];
- return ans;
- }
-};
\ No newline at end of file
diff --git a/leetcode/338. Counting Bits/s3.cpp b/leetcode/338. Counting Bits/s3.cpp
deleted file mode 100644
index 67c32165..00000000
--- a/leetcode/338. Counting Bits/s3.cpp
+++ /dev/null
@@ -1,12 +0,0 @@
-// OJ: https://leetcode.com/problems/counting-bits
-// Author: github.com/lzl124631x
-// Time: O(N)
-// Space: O(1)
-class Solution {
-public:
- vector countBits(int num) {
- vector ans(num + 1, 0);
- for (int i = 1; i <= num; ++i) ans[i] = ans[i / 2] + (i % 2);
- return ans;
- }
-};
\ No newline at end of file