# Problem

Implement FreqStack, a class which simulates the operation of a stack-like data structure.

FreqStack has two functions:

• push(int x), which pushes an integer x onto the stack.
• pop(), which removes and returns the most frequent element in the stack.
• If there is a tie for most frequent element, the element closest to the top of the stack is removed and returned.

Example 1:

Input:
["FreqStack","push","push","push","push","push","push","pop","pop","pop","pop"],
[[],,,,,,,[],[],[],[]]
Output: [null,null,null,null,null,null,null,5,7,5,4]
Explanation:
After making six .push operations, the stack is [5,7,5,7,4,5] from bottom to top.  Then:

pop() -> returns 5, as 5 is the most frequent.
The stack becomes [5,7,5,7,4].

pop() -> returns 7, as 5 and 7 is the most frequent, but 7 is closest to the top.
The stack becomes [5,7,5,4].

pop() -> returns 5.
The stack becomes [5,7,4].

pop() -> returns 4.
The stack becomes [5,7].


Note:

• Calls to FreqStack.push(int x) will be such that 0 <= x <= 10^9.
• It is guaranteed that FreqStack.pop() won’t be called if the stack has zero elements.
• The total number of FreqStack.push calls will not exceed 10000 in a single test case.
• The total number of FreqStack.pop calls will not exceed 10000 in a single test case.
• The total number of FreqStack.push and FreqStack.pop calls will not exceed 150000 across all test cases.

# Solution 1: Buckets

We have n  stacks. The i-th stack has the of elements with freq i when pushed.

We keep tracking the freq of each element.

push(x): stacks[++freq(x)].push(x)  # inc x’s freq and push it onto freq-th stack

pop(): x = stacks[max_freq].pop(), –freq(x); # pop element x from the max_freq stack and dec it’s freq.

Time complexity: O(1) push / pop

Space complexity: O(n)

# Solution2: Priority Queue

Use a max heap with key: (freq, seq), the max freq and closest to the top of stack element will be extracted first.

Time complexity: O(logn)

Space complexity: O(n)

# Problem

Given a function rand7 which generates a uniform random integer in the range 1 to 7, write a function rand10 which generates a uniform random integer in the range 1 to 10.

Do NOT use system’s Math.random().

Example 1:

Input: 1
Output: 


Example 2:

Input: 2
Output: [8,4]


Example 3:

Input: 3
Output: [8,1,10]


Note:

1. rand7 is predefined.
2. Each testcase has one argument: n, the number of times that rand10 is called.

# Solution: Math

Time complexity: O(49/40) = O(1)

Time complexity: O(7/6 + 7 / 5) = O(1)

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