68 lines
1.6 KiB
Go
68 lines
1.6 KiB
Go
// Package q1622 implements a solution for https://leetcode.com/problems/fancy-sequence/
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// ref: https://en.wikipedia.org/wiki/Fermat%27s_little_theorem
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package q1622
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const MOD int = 1e9 + 7
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type Fancy struct {
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numbers []int
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states []fancyState // this can be optimized out
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add, mul, inv int
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}
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type fancyState struct{ add, inv int }
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func Constructor() Fancy {
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return Fancy{
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numbers: make([]int, 0, 128),
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states: make([]fancyState, 0, 128),
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mul: 1,
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inv: 1,
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}
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}
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// findInv calculates num^(MOD-2), which is the inverse of num under mod MOD
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// when MOD is a prime number. `inv(num) * num % MOD == 1`.
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func findInv(num int) int {
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pow := MOD - 2
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ret := 1
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cur := num % MOD
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for i := 1; 1<<(i-1) <= pow; i++ {
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if (pow>>(i-1))&1 == 1 {
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ret = (ret * cur) % MOD
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}
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cur = cur * cur % MOD
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}
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return ret
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}
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func (f *Fancy) Append(val int) {
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f.numbers = append(f.numbers, val)
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f.states = append(f.states, fancyState{add: f.add, inv: f.inv})
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}
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func (f *Fancy) AddAll(inc int) { f.add = (f.add + inc) % MOD }
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func (f *Fancy) MultAll(m int) {
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f.mul = f.mul * m % MOD
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f.add = f.add * m % MOD
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f.inv = findInv(f.mul)
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}
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func (f *Fancy) GetIndex(idx int) int {
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if idx >= len(f.numbers) {
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return -1
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}
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num := f.numbers[idx] * f.mul % MOD * f.states[idx].inv % MOD
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savedAdd := f.states[idx].add * f.mul % MOD * f.states[idx].inv % MOD
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return (num + MOD + f.add - savedAdd) % MOD
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}
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/**
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* Your Fancy object will be instantiated and called as such:
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* obj := Constructor();
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* obj.Append(val);
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* obj.AddAll(inc);
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* obj.MultAll(m);
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* param_4 := obj.GetIndex(idx);
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*/
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