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| 1 | +/* |
| 2 | +307. Range Sum Query - Mutable |
| 3 | +https://leetcode.com/problems/range-sum-query-mutable/ |
| 4 | + |
| 5 | +Given an integer array nums, find the sum of the elements between indices i and j (i ≤ j), inclusive. |
| 6 | + |
| 7 | +The update(i, val) function modifies nums by updating the element at index i to val. |
| 8 | + |
| 9 | +Note: |
| 10 | +The array is only modifiable by the update function. |
| 11 | +You may assume the number of calls to update and sumRange function is distributed evenly. |
| 12 | +*/ |
| 13 | +// time: 2019年01月29日 |
| 14 | +// 线段树时间复杂度为:O(log n) |
| 15 | + |
| 16 | +package rsqm |
| 17 | + |
| 18 | +// NumArray 线段树 |
| 19 | +type NumArray struct { |
| 20 | + segmentTree []int |
| 21 | + data []int |
| 22 | +} |
| 23 | + |
| 24 | +// Constructor 线段树生成函数 |
| 25 | +func Constructor(nums []int) NumArray { |
| 26 | + na := NumArray{segmentTree: make([]int, len(nums)*4), data: nums[:]} |
| 27 | + na.buildSegmentTree(0, 0, len(na.data)-1) |
| 28 | + return na |
| 29 | +} |
| 30 | + |
| 31 | +func (na *NumArray) buildSegmentTree(treeIndex, left, right int) { |
| 32 | + // 线段树处理的数据不能为空。 |
| 33 | + //if right < left { |
| 34 | + // return |
| 35 | + //} |
| 36 | + if left == right { |
| 37 | + na.segmentTree[treeIndex] = na.data[left] |
| 38 | + return |
| 39 | + } |
| 40 | + mid := left + (right-left)>>1 |
| 41 | + leftTreeIndex := 2*treeIndex + 1 |
| 42 | + rightTreeIndex := 2*treeIndex + 2 |
| 43 | + na.buildSegmentTree(leftTreeIndex, left, mid) |
| 44 | + na.buildSegmentTree(rightTreeIndex, mid+1, right) |
| 45 | + na.segmentTree[treeIndex] = na.segmentTree[leftTreeIndex] + na.segmentTree[rightTreeIndex] |
| 46 | +} |
| 47 | + |
| 48 | +// Update 线段树更新操作。 |
| 49 | +func (na *NumArray) Update(i int, val int) { |
| 50 | + na.setter(0, 0, len(na.data)-1, i, val) |
| 51 | +} |
| 52 | + |
| 53 | +func (na *NumArray) setter(treeIndex, left, right, index, val int) { |
| 54 | + if left == right { |
| 55 | + na.segmentTree[treeIndex] = val |
| 56 | + return |
| 57 | + } |
| 58 | + mid := left + (right-left)>>1 |
| 59 | + leftTreeIndex := 2*treeIndex + 1 |
| 60 | + rightTreeIndex := 2*treeIndex + 2 |
| 61 | + if index >= mid+1 { |
| 62 | + na.setter(rightTreeIndex, mid+1, right, index, val) |
| 63 | + } else { |
| 64 | + na.setter(leftTreeIndex, left, mid, index, val) |
| 65 | + } |
| 66 | + na.segmentTree[treeIndex] = na.segmentTree[leftTreeIndex] + na.segmentTree[rightTreeIndex] |
| 67 | +} |
| 68 | + |
| 69 | +// SumRange 线段树查询 |
| 70 | +func (na *NumArray) SumRange(i int, j int) int { |
| 71 | + return na.query(0, 0, len(na.data)-1, i, j) |
| 72 | +} |
| 73 | + |
| 74 | +func (na *NumArray) query(treeIndex, left, right, queryL, queryR int) int { |
| 75 | + if left == queryL && right == queryR { |
| 76 | + return na.segmentTree[treeIndex] |
| 77 | + } |
| 78 | + mid := left + (right-left)>>1 |
| 79 | + leftTreeIndex := 2*treeIndex + 1 |
| 80 | + rightTreeIndex := 2*treeIndex + 2 |
| 81 | + if queryL >= mid+1 { |
| 82 | + return na.query(rightTreeIndex, mid+1, right, queryL, queryR) |
| 83 | + } else if queryR <= mid { |
| 84 | + return na.query(leftTreeIndex, left, mid, queryL, queryR) |
| 85 | + } else { |
| 86 | + return na.query(leftTreeIndex, left, mid, queryL, mid) + na.query(rightTreeIndex, mid+1, right, mid+1, queryR) |
| 87 | + } |
| 88 | +} |
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