結果
問題 | No.738 平らな農地 |
ユーザー | 草苺奶昔 |
提出日時 | 2024-04-25 13:42:41 |
言語 | Go (1.22.1) |
結果 |
AC
|
実行時間 | 248 ms / 2,000 ms |
コード長 | 10,483 bytes |
コンパイル時間 | 11,550 ms |
コンパイル使用メモリ | 220,840 KB |
実行使用メモリ | 10,156 KB |
最終ジャッジ日時 | 2024-11-08 00:42:33 |
合計ジャッジ時間 | 23,187 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge1 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 1 ms
6,820 KB |
testcase_01 | AC | 1 ms
5,248 KB |
testcase_02 | AC | 1 ms
5,248 KB |
testcase_03 | AC | 2 ms
5,248 KB |
testcase_04 | AC | 2 ms
5,248 KB |
testcase_05 | AC | 4 ms
5,248 KB |
testcase_06 | AC | 4 ms
5,248 KB |
testcase_07 | AC | 10 ms
6,528 KB |
testcase_08 | AC | 4 ms
5,248 KB |
testcase_09 | AC | 2 ms
5,248 KB |
testcase_10 | AC | 1 ms
5,248 KB |
testcase_11 | AC | 5 ms
5,248 KB |
testcase_12 | AC | 3 ms
5,248 KB |
testcase_13 | AC | 5 ms
5,248 KB |
testcase_14 | AC | 2 ms
5,248 KB |
testcase_15 | AC | 189 ms
7,552 KB |
testcase_16 | AC | 175 ms
7,508 KB |
testcase_17 | AC | 175 ms
7,424 KB |
testcase_18 | AC | 186 ms
7,508 KB |
testcase_19 | AC | 175 ms
6,784 KB |
testcase_20 | AC | 195 ms
7,552 KB |
testcase_21 | AC | 222 ms
7,496 KB |
testcase_22 | AC | 196 ms
7,680 KB |
testcase_23 | AC | 185 ms
7,040 KB |
testcase_24 | AC | 227 ms
7,416 KB |
testcase_25 | AC | 4 ms
5,248 KB |
testcase_26 | AC | 4 ms
5,248 KB |
testcase_27 | AC | 4 ms
5,248 KB |
testcase_28 | AC | 5 ms
5,248 KB |
testcase_29 | AC | 4 ms
5,248 KB |
testcase_30 | AC | 4 ms
5,248 KB |
testcase_31 | AC | 4 ms
5,248 KB |
testcase_32 | AC | 4 ms
5,248 KB |
testcase_33 | AC | 3 ms
5,248 KB |
testcase_34 | AC | 4 ms
5,248 KB |
testcase_35 | AC | 4 ms
5,248 KB |
testcase_36 | AC | 4 ms
5,248 KB |
testcase_37 | AC | 4 ms
5,248 KB |
testcase_38 | AC | 4 ms
5,248 KB |
testcase_39 | AC | 5 ms
5,248 KB |
testcase_40 | AC | 4 ms
5,248 KB |
testcase_41 | AC | 3 ms
5,248 KB |
testcase_42 | AC | 4 ms
5,248 KB |
testcase_43 | AC | 4 ms
5,248 KB |
testcase_44 | AC | 3 ms
5,248 KB |
testcase_45 | AC | 206 ms
8,576 KB |
testcase_46 | AC | 172 ms
7,552 KB |
testcase_47 | AC | 205 ms
8,572 KB |
testcase_48 | AC | 160 ms
8,576 KB |
testcase_49 | AC | 168 ms
8,576 KB |
testcase_50 | AC | 166 ms
9,144 KB |
testcase_51 | AC | 208 ms
8,008 KB |
testcase_52 | AC | 204 ms
8,052 KB |
testcase_53 | AC | 205 ms
8,064 KB |
testcase_54 | AC | 206 ms
8,056 KB |
testcase_55 | AC | 207 ms
8,060 KB |
testcase_56 | AC | 169 ms
8,040 KB |
testcase_57 | AC | 173 ms
8,028 KB |
testcase_58 | AC | 202 ms
8,108 KB |
testcase_59 | AC | 168 ms
9,280 KB |
testcase_60 | AC | 178 ms
9,300 KB |
testcase_61 | AC | 178 ms
9,140 KB |
testcase_62 | AC | 175 ms
8,148 KB |
testcase_63 | AC | 220 ms
8,140 KB |
testcase_64 | AC | 195 ms
8,604 KB |
testcase_65 | AC | 68 ms
5,632 KB |
testcase_66 | AC | 69 ms
5,632 KB |
testcase_67 | AC | 86 ms
5,888 KB |
testcase_68 | AC | 75 ms
5,888 KB |
testcase_69 | AC | 248 ms
6,656 KB |
testcase_70 | AC | 236 ms
9,208 KB |
testcase_71 | AC | 44 ms
5,248 KB |
testcase_72 | AC | 64 ms
5,248 KB |
testcase_73 | AC | 63 ms
5,376 KB |
testcase_74 | AC | 73 ms
5,376 KB |
testcase_75 | AC | 157 ms
7,336 KB |
testcase_76 | AC | 145 ms
8,908 KB |
testcase_77 | AC | 151 ms
6,768 KB |
testcase_78 | AC | 211 ms
7,240 KB |
testcase_79 | AC | 203 ms
6,784 KB |
testcase_80 | AC | 181 ms
7,888 KB |
testcase_81 | AC | 173 ms
6,912 KB |
testcase_82 | AC | 138 ms
6,912 KB |
testcase_83 | AC | 60 ms
5,248 KB |
testcase_84 | AC | 66 ms
6,528 KB |
testcase_85 | AC | 77 ms
5,760 KB |
testcase_86 | AC | 81 ms
5,760 KB |
testcase_87 | AC | 152 ms
10,156 KB |
testcase_88 | AC | 141 ms
9,584 KB |
testcase_89 | AC | 1 ms
5,248 KB |
testcase_90 | AC | 1 ms
5,248 KB |
testcase_91 | AC | 1 ms
5,248 KB |
ソースコード
// 动态中位数,用两个可删除堆(对顶堆)实现 // api: // 1. Insert(x T) // 2. Discard(x T) bool // 3. Median() (low, high T) // 4. DistToMedian() T // 5. Size() int32 package main import ( "bufio" "fmt" "math/bits" "os" "sort" ) func main() { yuki738() } // 9 2 // 1 4 1 4 2 1 3 5 6 const INF int = 1e18 // No.738 平らな農地 // https://yukicoder.me/problems/no/738 // !滑动窗口所有数到中位数的距离和 func yuki738() { in := bufio.NewReader(os.Stdin) out := bufio.NewWriter(os.Stdout) defer out.Flush() var n, k int32 fmt.Fscan(in, &n, &k) nums := make([]int, n) for i := int32(0); i < n; i++ { fmt.Fscan(in, &nums[i]) } M := NewDynamicMedian() res := INF for i := int32(0); i < n; i++ { M.Insert(nums[i]) if i >= k { M.Discard(nums[i-k]) } if i >= k-1 { res = min(res, M.DistToMedian()) } // fmt.Println(M.Median()) // fmt.Println(M.DistToMedian(), 987, M.Size()) } fmt.Fprintln(out, res) } // 1e5 -> 200, 2e5 -> 400 const _LOAD int = 200 type S = int type DynamicMedian struct { size int32 lower *_sl upper *_sl lowerSum S upperSum S } func NewDynamicMedian() *DynamicMedian { return &DynamicMedian{ lower: NewSortedList(func(a, b S) bool { return a < b }), upper: NewSortedList(func(a, b S) bool { return a < b }), } } func (d *DynamicMedian) Insert(value S) { if d.size&1 == 0 { d.upper.Add(value) d.upperSum += value } else { d.lower.Add(value) d.lowerSum += value } d.size++ d.balance() } func (d *DynamicMedian) Discard(value S) bool { if d.lower.Has(value) { d.lower.Discard(value) d.lowerSum -= value d.size-- d.balance() return true } else if d.upper.Has(value) { d.upper.Discard(value) d.upperSum -= value d.size-- d.balance() return true } else { return false } } // 返回中位数.如果元素个数为偶数,返回两个中位数. func (d *DynamicMedian) Median() (low, high S) { if d.size == 0 { return } if d.size&1 == 0 { low = d.lower.Max() high = d.upper.Min() } else { low = d.upper.Min() high = low } return } func (d *DynamicMedian) DistToMedian() S { if d.size == 0 { return 0 } low, _ := d.Median() sum1 := low*S(d.lower.Len()) - d.lowerSum sum2 := d.upperSum - low*S(d.upper.Len()) return sum1 + sum2 } func (d *DynamicMedian) Size() int32 { return d.size } func (d *DynamicMedian) balance() { // 偶数个数时,|lower heap| == |upper heap| // 奇数个数时,|lower heap| + 1 == |upper heap| for d.lower.Len()+1 < d.upper.Len() { upperMin := d.upper.Pop(0) d.lower._append(upperMin) d.lowerSum += upperMin d.upperSum -= upperMin } for d.lower.Len() > d.upper.Len() { lowerMin := d.lower.Pop(0) d.upper.Add(lowerMin) d.upperSum += lowerMin d.lowerSum -= lowerMin } if d.size&1 == 0 { if d.lower.size != d.upper.size { panic("size error") } } else { if d.lower.size+1 != d.upper.size { panic("size error") } } if d.lower.Len() == 0 || d.upper.Len() == 0 { return } if d.lower.Max() > d.upper.Min() { upperMin := d.upper.Pop(0) d.lower.Add(upperMin) d.lowerSum += upperMin d.upperSum -= upperMin lowerMax := d.lower.Pop(d.lower.Len() - 1) d.upper.Add(lowerMax) d.upperSum += lowerMax d.lowerSum -= lowerMax } } // 使用分块+树状数组维护的有序序列. type _sl struct { less func(a, b S) bool size int blocks [][]S mins []S tree []int shouldRebuildTree bool } func NewSortedList(less func(a, b S) bool, elements ...S) *_sl { elements = append(elements[:0:0], elements...) res := &_sl{less: less} sort.Slice(elements, func(i, j int) bool { return less(elements[i], elements[j]) }) n := len(elements) blocks := [][]S{} for start := 0; start < n; start += _LOAD { end := min(start+_LOAD, n) blocks = append(blocks, elements[start:end:end]) // !各个块互不影响, max参数也需要指定为end } mins := make([]S, len(blocks)) for i, cur := range blocks { mins[i] = cur[0] } res.size = n res.blocks = blocks res.mins = mins res.shouldRebuildTree = true return res } func (sl *_sl) Add(value S) *_sl { sl.size++ if len(sl.blocks) == 0 { sl.blocks = append(sl.blocks, []S{value}) sl.mins = append(sl.mins, value) sl.shouldRebuildTree = true return sl } pos, index := sl._locRight(value) sl._updateTree(pos, 1) sl.blocks[pos] = append(sl.blocks[pos][:index], append([]S{value}, sl.blocks[pos][index:]...)...) sl.mins[pos] = sl.blocks[pos][0] // n -> load + (n - load) if n := len(sl.blocks[pos]); _LOAD+_LOAD < n { sl.blocks = append(sl.blocks[:pos+1], append([][]S{sl.blocks[pos][_LOAD:]}, sl.blocks[pos+1:]...)...) sl.mins = append(sl.mins[:pos+1], append([]S{sl.blocks[pos][_LOAD]}, sl.mins[pos+1:]...)...) sl.blocks[pos] = sl.blocks[pos][:_LOAD:_LOAD] // !注意max的设置(为了让左右互不影响) sl.shouldRebuildTree = true } return sl } func (sl *_sl) _append(value S) *_sl { sl.size++ if len(sl.blocks) == 0 { sl.blocks = append(sl.blocks, []S{value}) sl.mins = append(sl.mins, value) sl.shouldRebuildTree = true return sl } pos := len(sl.blocks) - 1 sl._updateTree(pos, 1) sl.blocks[pos] = append(sl.blocks[pos], value) // n -> load + (n - load) if n := len(sl.blocks[pos]); _LOAD+_LOAD < n { sl.blocks = append(sl.blocks[:pos+1], append([][]S{sl.blocks[pos][_LOAD:]}, sl.blocks[pos+1:]...)...) sl.mins = append(sl.mins[:pos+1], append([]S{sl.blocks[pos][_LOAD]}, sl.mins[pos+1:]...)...) sl.blocks[pos] = sl.blocks[pos][:_LOAD:_LOAD] // !注意max的设置(为了让左右互不影响) sl.shouldRebuildTree = true } return sl } func (sl *_sl) _appendLeft(value S) *_sl { sl.size++ if len(sl.blocks) == 0 { sl.blocks = append(sl.blocks, []S{value}) sl.mins = append(sl.mins, value) sl.shouldRebuildTree = true return sl } pos := 0 sl._updateTree(pos, 1) sl.blocks[pos] = append([]S{value}, sl.blocks[pos]...) sl.mins[pos] = sl.blocks[pos][0] // n -> load + (n - load) if n := len(sl.blocks[pos]); _LOAD+_LOAD < n { sl.blocks = append([][]S{sl.blocks[pos][:_LOAD:_LOAD]}, sl.blocks...) sl.mins = append([]S{sl.blocks[pos][_LOAD]}, sl.mins...) sl.blocks[pos+1] = sl.blocks[pos+1][_LOAD:] sl.shouldRebuildTree = true } return sl } func (sl *_sl) Has(value S) bool { if len(sl.blocks) == 0 { return false } pos, index := sl._locLeft(value) return index < len(sl.blocks[pos]) && sl.blocks[pos][index] == value } func (sl *_sl) Pop(index int) S { if index < 0 { index += sl.size } if index < 0 || index >= sl.size { panic("index out of range") } pos, startIndex := sl._findKth(index) value := sl.blocks[pos][startIndex] sl._delete(pos, startIndex) return value } func (sl *_sl) Discard(value S) bool { if len(sl.blocks) == 0 { return false } pos, index := sl._locRight(value) if index > 0 && sl.blocks[pos][index-1] == value { sl._delete(pos, index-1) return true } return false } func (sl *_sl) Min() S { if sl.size == 0 { panic("Min() called on empty SortedList") } return sl.mins[0] } func (sl *_sl) Max() S { if sl.size == 0 { panic("Max() called on empty SortedList") } lastBlock := sl.blocks[len(sl.blocks)-1] return lastBlock[len(lastBlock)-1] } func (sl *_sl) Len() int { return sl.size } func (sl *_sl) _delete(pos, index int) { // !delete element sl.size-- sl._updateTree(pos, -1) sl.blocks[pos] = append(sl.blocks[pos][:index], sl.blocks[pos][index+1:]...) if len(sl.blocks[pos]) > 0 { sl.mins[pos] = sl.blocks[pos][0] return } // !delete block sl.blocks = append(sl.blocks[:pos], sl.blocks[pos+1:]...) sl.mins = append(sl.mins[:pos], sl.mins[pos+1:]...) sl.shouldRebuildTree = true } func (sl *_sl) _locLeft(value S) (pos, index int) { if sl.size == 0 { return } // find pos left := -1 right := len(sl.blocks) - 1 for left+1 < right { mid := (left + right) >> 1 if !sl.less(sl.mins[mid], value) { right = mid } else { left = mid } } if right > 0 { block := sl.blocks[right-1] if !sl.less(block[len(block)-1], value) { right-- } } pos = right // find index cur := sl.blocks[pos] left = -1 right = len(cur) for left+1 < right { mid := (left + right) >> 1 if !sl.less(cur[mid], value) { right = mid } else { left = mid } } index = right return } func (sl *_sl) _locRight(value S) (pos, index int) { if sl.size == 0 { return } // find pos left := 0 right := len(sl.blocks) for left+1 < right { mid := (left + right) >> 1 if sl.less(value, sl.mins[mid]) { right = mid } else { left = mid } } pos = left // find index cur := sl.blocks[pos] left = -1 right = len(cur) for left+1 < right { mid := (left + right) >> 1 if sl.less(value, cur[mid]) { right = mid } else { left = mid } } index = right return } func (sl *_sl) _locBlock(value S) int { left, right := -1, len(sl.blocks)-1 for left+1 < right { mid := (left + right) >> 1 if !sl.less(sl.mins[mid], value) { right = mid } else { left = mid } } if right > 0 { block := sl.blocks[right-1] if !sl.less(block[len(block)-1], value) { right-- } } return right } func (sl *_sl) _buildTree() { sl.tree = make([]int, len(sl.blocks)) for i := 0; i < len(sl.blocks); i++ { sl.tree[i] = len(sl.blocks[i]) } tree := sl.tree for i := 0; i < len(tree); i++ { j := i | (i + 1) if j < len(tree) { tree[j] += tree[i] } } sl.shouldRebuildTree = false } func (sl *_sl) _updateTree(index, delta int) { if sl.shouldRebuildTree { return } tree := sl.tree for i := index; i < len(tree); i |= i + 1 { tree[i] += delta } } func (sl *_sl) _queryTree(end int) int { if sl.shouldRebuildTree { sl._buildTree() } tree := sl.tree sum := 0 for end > 0 { sum += tree[end-1] end &= end - 1 } return sum } func (sl *_sl) _findKth(k int) (pos, index int) { if k < len(sl.blocks[0]) { return 0, k } last := len(sl.blocks) - 1 lastLen := len(sl.blocks[last]) if k >= sl.size-lastLen { return last, k + lastLen - sl.size } if sl.shouldRebuildTree { sl._buildTree() } tree := sl.tree pos = -1 bitLength := bits.Len32(uint32(len(tree))) for d := bitLength - 1; d >= 0; d-- { next := pos + (1 << d) if next < len(tree) && k >= tree[next] { pos = next k -= tree[pos] } } return pos + 1, k } func min(a, b int) int { if a < b { return a } return b } func max(a, b int) int { if a > b { return a } return b }