aaa

src/codeforces/set1/set19/set198/set1980/d/solution.go

@@ -0,0 +1,139 @@
+package main
+
+import (
+	"bufio"
+	"bytes"
+	"fmt"
+	"os"
+	"sort"
+)
+
+func main() {
+	reader := bufio.NewReader(os.Stdin)
+
+	tc := readNum(reader)
+
+	var buf bytes.Buffer
+
+	for tc > 0 {
+		tc--
+		n := readNum(reader)
+		a := readNNums(reader, n)
+		res := solve(a)
+		if res {
+			buf.WriteString("YES\n")
+		} else {
+			buf.WriteString("NO\n")
+		}
+	}
+
+	fmt.Print(buf.String())
+}
+func readString(reader *bufio.Reader) string {
+	s, _ := reader.ReadString('\n')
+	for i := 0; i < len(s); i++ {
+		if s[i] == '\n' || s[i] == '\r' {
+			return s[:i]
+		}
+	}
+	return s
+}
+
+func readInt(bytes []byte, from int, val *int) int {
+	i := from
+	sign := 1
+	if bytes[i] == '-' {
+		sign = -1
+		i++
+	}
+	tmp := 0
+	for i < len(bytes) && bytes[i] >= '0' && bytes[i] <= '9' {
+		tmp = tmp*10 + int(bytes[i]-'0')
+		i++
+	}
+	*val = tmp * sign
+	return i
+}
+
+func readNum(reader *bufio.Reader) (a int) {
+	bs, _ := reader.ReadBytes('\n')
+	readInt(bs, 0, &a)
+	return
+}
+
+func readTwoNums(reader *bufio.Reader) (a int, b int) {
+	res := readNNums(reader, 2)
+	a, b = res[0], res[1]
+	return
+}
+
+func readThreeNums(reader *bufio.Reader) (a int, b int, c int) {
+	res := readNNums(reader, 3)
+	a, b, c = res[0], res[1], res[2]
+	return
+}
+
+func readNNums(reader *bufio.Reader, n int) []int {
+	res := make([]int, n)
+	x := 0
+	bs, _ := reader.ReadBytes('\n')
+	for i := 0; i < n; i++ {
+		for x < len(bs) && (bs[x] < '0' || bs[x] > '9') && bs[x] != '-' {
+			x++
+		}
+		x = readInt(bs, x, &res[i])
+	}
+	return res
+}
+
+const inf = 1 << 30
+
+func solve(a []int) bool {
+	// 如果已经是升序的，答案是肯定的
+	// else 假设删除a[i]后，可以满足条件
+	// 删除前, b[i-1] = gcd(a[i-1], a[i]), b[i] = gcd(a[i], a[i+1]), b[i+1] = gcd(a[i+1], a[i+2])
+	// 可以看到, a[i]影响的只有 b[i-1]和 b[i],
+	// 删除后, b[i-1] = gcd(a[i-1], a[i+1]), b[i] = b[i+1] = gcd(a[i+1], a[i+2])
+	// b[i-1] 有可能变大，也可能变小，b[i+1]保持不变
+	// 但是 b[i-2] <= b[i-1] <= b[i+1] <= b[i+2]
+	// 所以，在i-2和i+1的关系不能变，且新的b[i-1] 要处在中间
+	// 头尾单独处理
+	n := len(a)
+	b := make([]int, n)
+	for i := 0; i+1 < n; i++ {
+		b[i] = gcd(a[i], a[i+1])
+	}
+	if n <= 3 || sort.IntsAreSorted(b) {
+		return true
+	}
+	b[n-1] = inf
+	// suf[i] = 从b[i]开始，是否升序
+	suf := make([]bool, n)
+	suf[n-1] = true
+	for i := n - 2; i >= 0; i-- {
+		suf[i] = suf[i+1] && b[i] <= b[i+1]
+	}
+	if suf[1] {
+		// 删掉a[0]后，直接就可以了， 这个好像没啥意义， b[0] = gcd(a[0], a[1])
+		return true
+	}
+	pref := make([]bool, n)
+	pref[0] = true
+	for i := 1; i < n-1; i++ {
+		// 删除a[i]
+		cur := gcd(a[i-1], a[i+1])
+		if (i == 1 || b[i-2] <= cur && pref[i-2]) && cur <= b[i+1] && suf[i+1] {
+			return true
+		}
+		pref[i] = pref[i-1] && b[i-1] <= b[i]
+	}
+
+	return pref[n-3]
+}
+
+func gcd(a, b int) int {
+	for b > 0 {
+		a, b = b, a%b
+	}
+	return a
+}

src/codeforces/set1/set19/set198/set1980/d/solution_test.go

@@ -0,0 +1,53 @@
+package main
+
+import "testing"
+
+func runSample(t *testing.T, a []int, expect bool) {
+	res := solve(a)
+
+	if res != expect {
+		t.Fatalf("Sample expect %t, but got %t", expect, res)
+	}
+}
+
+func TestSample1(t *testing.T) {
+	a := []int{20, 6, 12, 3, 48, 36}
+	expect := true
+	runSample(t, a, expect)
+}
+
+func TestSample2(t *testing.T) {
+	a := []int{12, 6, 3, 4}
+	expect := false
+	runSample(t, a, expect)
+}
+
+func TestSample3(t *testing.T) {
+	a := []int{10, 12, 3}
+	expect := true
+	runSample(t, a, expect)
+}
+
+func TestSample4(t *testing.T) {
+	a := []int{32, 16, 8, 4, 2}
+	expect := false
+	runSample(t, a, expect)
+}
+
+func TestSample5(t *testing.T) {
+	a := []int{100, 50, 2, 10, 20}
+	expect := true
+	runSample(t, a, expect)
+}
+
+func TestSample6(t *testing.T) {
+	a := []int{1, 6, 11, 12, 6, 12, 3, 6}
+	expect := true
+	runSample(t, a, expect)
+}
+
+func TestSample7(t *testing.T) {
+	a := []int{2, 4, 8, 1}
+	expect := true
+	runSample(t, a, expect)
+}