59 lines
1.5 KiB
Go
59 lines
1.5 KiB
Go
package top100liked
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import (
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"fmt"
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"strings"
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"testing"
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)
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// https://leetcode.cn/problems/n-queens/description/?envType=study-plan-v2&envId=top-100-liked
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func solveNQueens(n int) [][]string {
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res := [][]string{}
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path := []string{}
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// 同列/同对角线共享一个不变量，用三个独立数组各标记一条线是否被占。
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// 列：col；主对角线（↘）：row-col 为常数，+n-1 偏移成非负下标；
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// 副对角线（↙）：row+col 为常数，本身非负。行约束不需要（每行只放一个）。
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cols := make([]bool, n) // cols[col]：第 col 列是否被占
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diag1 := make([]bool, 2*n-1) // diag1[row-col+n-1]：↘ 对角线是否被占
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diag2 := make([]bool, 2*n-1) // diag2[row+col]：↙ 对角线是否被占
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var helper func()
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helper = func() {
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row := len(path)
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if row == n {
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cp := make([]string, len(path))
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copy(cp, path)
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res = append(res, cp)
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return
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}
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for col := range n {
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d1 := row - col + n - 1 // ↘ 对角线下标
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d2 := row + col // ↙ 对角线下标
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if !cols[col] && !diag1[d1] && !diag2[d2] {
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path = append(path, strings.Repeat(".", col)+"Q"+strings.Repeat(".", n-col-1))
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cols[col] = true
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diag1[d1] = true
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diag2[d2] = true
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helper()
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cols[col] = false
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diag1[d1] = false
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diag2[d2] = false
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path = path[:len(path)-1]
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}
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}
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}
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helper()
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return res
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}
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func Test(t *testing.T) {
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fmt.Printf("%+v\n", solveNQueens(4))
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}
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func Test2(t *testing.T) {
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fmt.Printf("%+v\n", solveNQueens(1))
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}
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