add new solutions

solutions/16/q1622/solution.go

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