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266 lines
9.7 KiB
Go
266 lines
9.7 KiB
Go
package template
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// SegmentTree define
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type SegmentTree struct {
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data, tree, lazy []int
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left, right int
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merge func(i, j int) int
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}
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// Init define
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func (st *SegmentTree) Init(nums []int, oper func(i, j int) int) {
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st.merge = oper
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data, tree, lazy := make([]int, len(nums)), make([]int, 4*len(nums)), make([]int, 4*len(nums))
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for i := 0; i < len(nums); i++ {
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data[i] = nums[i]
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}
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st.data, st.tree, st.lazy = data, tree, lazy
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if len(nums) > 0 {
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st.buildSegmentTree(0, 0, len(nums)-1)
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}
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}
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// 在 treeIndex 的位置创建 [left....right] 区间的线段树
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func (st *SegmentTree) buildSegmentTree(treeIndex, left, right int) {
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if left == right {
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st.tree[treeIndex] = st.data[left]
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return
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}
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midTreeIndex, leftTreeIndex, rightTreeIndex := left+(right-left)>>1, st.leftChild(treeIndex), st.rightChild(treeIndex)
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st.buildSegmentTree(leftTreeIndex, left, midTreeIndex)
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st.buildSegmentTree(rightTreeIndex, midTreeIndex+1, right)
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st.tree[treeIndex] = st.merge(st.tree[leftTreeIndex], st.tree[rightTreeIndex])
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}
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func (st *SegmentTree) leftChild(index int) int {
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return 2*index + 1
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}
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func (st *SegmentTree) rightChild(index int) int {
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return 2*index + 2
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}
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// 查询 [left....right] 区间内的值
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// Query define
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func (st *SegmentTree) Query(left, right int) int {
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if len(st.data) > 0 {
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return st.queryInTree(0, 0, len(st.data)-1, left, right)
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}
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return 0
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}
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// 在以 treeIndex 为根的线段树中 [left...right] 的范围里，搜索区间 [queryLeft...queryRight] 的值
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func (st *SegmentTree) queryInTree(treeIndex, left, right, queryLeft, queryRight int) int {
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if left == queryLeft && right == queryRight {
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return st.tree[treeIndex]
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}
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midTreeIndex, leftTreeIndex, rightTreeIndex := left+(right-left)>>1, st.leftChild(treeIndex), st.rightChild(treeIndex)
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if queryLeft > midTreeIndex {
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return st.queryInTree(rightTreeIndex, midTreeIndex+1, right, queryLeft, queryRight)
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} else if queryRight <= midTreeIndex {
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return st.queryInTree(leftTreeIndex, left, midTreeIndex, queryLeft, queryRight)
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}
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return st.merge(st.queryInTree(leftTreeIndex, left, midTreeIndex, queryLeft, midTreeIndex),
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st.queryInTree(rightTreeIndex, midTreeIndex+1, right, midTreeIndex+1, queryRight))
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}
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// 查询 [left....right] 区间内的值
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// QueryLazy define
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func (st *SegmentTree) QueryLazy(left, right int) int {
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if len(st.data) > 0 {
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return st.queryLazyInTree(0, 0, len(st.data)-1, left, right)
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}
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return 0
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}
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func (st *SegmentTree) queryLazyInTree(treeIndex, left, right, queryLeft, queryRight int) int {
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midTreeIndex, leftTreeIndex, rightTreeIndex := left+(right-left)>>1, st.leftChild(treeIndex), st.rightChild(treeIndex)
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if left > queryRight || right < queryLeft { // segment completely outside range
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return 0 // represents a null node
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}
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if st.lazy[treeIndex] != 0 { // this node is lazy
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for i := 0; i < right-left+1; i++ {
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st.tree[treeIndex] = st.merge(st.tree[treeIndex], st.lazy[treeIndex])
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// st.tree[treeIndex] += (right - left + 1) * st.lazy[treeIndex] // normalize current node by removing lazinesss
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}
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if left != right { // update lazy[] for children nodes
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st.lazy[leftTreeIndex] = st.merge(st.lazy[leftTreeIndex], st.lazy[treeIndex])
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st.lazy[rightTreeIndex] = st.merge(st.lazy[rightTreeIndex], st.lazy[treeIndex])
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// st.lazy[leftTreeIndex] += st.lazy[treeIndex]
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// st.lazy[rightTreeIndex] += st.lazy[treeIndex]
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}
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st.lazy[treeIndex] = 0 // current node processed. No longer lazy
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}
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if queryLeft <= left && queryRight >= right { // segment completely inside range
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return st.tree[treeIndex]
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}
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if queryLeft > midTreeIndex {
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return st.queryLazyInTree(rightTreeIndex, midTreeIndex+1, right, queryLeft, queryRight)
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} else if queryRight <= midTreeIndex {
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return st.queryLazyInTree(leftTreeIndex, left, midTreeIndex, queryLeft, queryRight)
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}
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// merge query results
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return st.merge(st.queryLazyInTree(leftTreeIndex, left, midTreeIndex, queryLeft, midTreeIndex),
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st.queryLazyInTree(rightTreeIndex, midTreeIndex+1, right, midTreeIndex+1, queryRight))
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}
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// 更新 index 位置的值
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// Update define
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func (st *SegmentTree) Update(index, val int) {
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if len(st.data) > 0 {
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st.updateInTree(0, 0, len(st.data)-1, index, val)
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}
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}
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// 以 treeIndex 为根，更新 index 位置上的值为 val
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func (st *SegmentTree) updateInTree(treeIndex, left, right, index, val int) {
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if left == right {
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st.tree[treeIndex] = val
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return
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}
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midTreeIndex, leftTreeIndex, rightTreeIndex := left+(right-left)>>1, st.leftChild(treeIndex), st.rightChild(treeIndex)
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if index > midTreeIndex {
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st.updateInTree(rightTreeIndex, midTreeIndex+1, right, index, val)
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} else {
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st.updateInTree(leftTreeIndex, left, midTreeIndex, index, val)
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}
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st.tree[treeIndex] = st.merge(st.tree[leftTreeIndex], st.tree[rightTreeIndex])
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}
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// 更新 [updateLeft....updateRight] 位置的值
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// 注意这里的更新值是在原来值的基础上增加或者减少，而不是把这个区间内的值都赋值为 x，区间更新和单点更新不同
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// 这里的区间更新关注的是变化，单点更新关注的是定值
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// 当然区间更新也可以都更新成定值，如果只区间更新成定值，那么 lazy 更新策略需要变化，merge 策略也需要变化，这里暂不详细讨论
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// UpdateLazy define
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func (st *SegmentTree) UpdateLazy(updateLeft, updateRight, val int) {
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if len(st.data) > 0 {
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st.updateLazyInTree(0, 0, len(st.data)-1, updateLeft, updateRight, val)
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}
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}
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func (st *SegmentTree) updateLazyInTree(treeIndex, left, right, updateLeft, updateRight, val int) {
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midTreeIndex, leftTreeIndex, rightTreeIndex := left+(right-left)>>1, st.leftChild(treeIndex), st.rightChild(treeIndex)
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if st.lazy[treeIndex] != 0 { // this node is lazy
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for i := 0; i < right-left+1; i++ {
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st.tree[treeIndex] = st.merge(st.tree[treeIndex], st.lazy[treeIndex])
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//st.tree[treeIndex] += (right - left + 1) * st.lazy[treeIndex] // normalize current node by removing laziness
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}
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if left != right { // update lazy[] for children nodes
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st.lazy[leftTreeIndex] = st.merge(st.lazy[leftTreeIndex], st.lazy[treeIndex])
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st.lazy[rightTreeIndex] = st.merge(st.lazy[rightTreeIndex], st.lazy[treeIndex])
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// st.lazy[leftTreeIndex] += st.lazy[treeIndex]
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// st.lazy[rightTreeIndex] += st.lazy[treeIndex]
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}
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st.lazy[treeIndex] = 0 // current node processed. No longer lazy
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}
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if left > right || left > updateRight || right < updateLeft {
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return // out of range. escape.
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}
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if updateLeft <= left && right <= updateRight { // segment is fully within update range
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for i := 0; i < right-left+1; i++ {
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st.tree[treeIndex] = st.merge(st.tree[treeIndex], val)
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//st.tree[treeIndex] += (right - left + 1) * val // update segment
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}
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if left != right { // update lazy[] for children
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st.lazy[leftTreeIndex] = st.merge(st.lazy[leftTreeIndex], val)
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st.lazy[rightTreeIndex] = st.merge(st.lazy[rightTreeIndex], val)
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// st.lazy[leftTreeIndex] += val
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// st.lazy[rightTreeIndex] += val
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}
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return
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}
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st.updateLazyInTree(leftTreeIndex, left, midTreeIndex, updateLeft, updateRight, val)
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st.updateLazyInTree(rightTreeIndex, midTreeIndex+1, right, updateLeft, updateRight, val)
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// merge updates
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st.tree[treeIndex] = st.merge(st.tree[leftTreeIndex], st.tree[rightTreeIndex])
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}
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// SegmentCountTree define
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type SegmentCountTree struct {
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data, tree []int
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left, right int
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merge func(i, j int) int
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}
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// Init define
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func (st *SegmentCountTree) Init(nums []int, oper func(i, j int) int) {
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st.merge = oper
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data, tree := make([]int, len(nums)), make([]int, 4*len(nums))
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for i := 0; i < len(nums); i++ {
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data[i] = nums[i]
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}
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st.data, st.tree = data, tree
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}
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// 在 treeIndex 的位置创建 [left....right] 区间的线段树
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func (st *SegmentCountTree) buildSegmentTree(treeIndex, left, right int) {
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if left == right {
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st.tree[treeIndex] = st.data[left]
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return
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}
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midTreeIndex, leftTreeIndex, rightTreeIndex := left+(right-left)>>1, st.leftChild(treeIndex), st.rightChild(treeIndex)
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st.buildSegmentTree(leftTreeIndex, left, midTreeIndex)
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st.buildSegmentTree(rightTreeIndex, midTreeIndex+1, right)
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st.tree[treeIndex] = st.merge(st.tree[leftTreeIndex], st.tree[rightTreeIndex])
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}
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func (st *SegmentCountTree) leftChild(index int) int {
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return 2*index + 1
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}
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func (st *SegmentCountTree) rightChild(index int) int {
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return 2*index + 2
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}
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// 查询 [left....right] 区间内的值
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// Query define
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func (st *SegmentCountTree) Query(left, right int) int {
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if len(st.data) > 0 {
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return st.queryInTree(0, 0, len(st.data)-1, left, right)
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}
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return 0
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}
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// 在以 treeIndex 为根的线段树中 [left...right] 的范围里，搜索区间 [queryLeft...queryRight] 的值，值是计数值
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func (st *SegmentCountTree) queryInTree(treeIndex, left, right, queryLeft, queryRight int) int {
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if queryRight < st.data[left] || queryLeft > st.data[right] {
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return 0
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}
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if queryLeft <= st.data[left] && queryRight >= st.data[right] || left == right {
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return st.tree[treeIndex]
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}
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midTreeIndex, leftTreeIndex, rightTreeIndex := left+(right-left)>>1, st.leftChild(treeIndex), st.rightChild(treeIndex)
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return st.queryInTree(rightTreeIndex, midTreeIndex+1, right, queryLeft, queryRight) +
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st.queryInTree(leftTreeIndex, left, midTreeIndex, queryLeft, queryRight)
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}
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// 更新计数
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// UpdateCount define
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func (st *SegmentCountTree) UpdateCount(val int) {
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if len(st.data) > 0 {
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st.updateCountInTree(0, 0, len(st.data)-1, val)
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}
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}
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// 以 treeIndex 为根，更新 [left...right] 区间内的计数
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func (st *SegmentCountTree) updateCountInTree(treeIndex, left, right, val int) {
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if val >= st.data[left] && val <= st.data[right] {
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st.tree[treeIndex]++
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if left == right {
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return
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}
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midTreeIndex, leftTreeIndex, rightTreeIndex := left+(right-left)>>1, st.leftChild(treeIndex), st.rightChild(treeIndex)
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st.updateCountInTree(rightTreeIndex, midTreeIndex+1, right, val)
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st.updateCountInTree(leftTreeIndex, left, midTreeIndex, val)
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}
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}
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