Segment Tree is used for interval search(sum, minimum or maximum) with log(n) time complexity, my implementation is as follows(including 3 types),
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class SegmentNode {
public:
int val;
int start;
int end;
SegmentNode* left;
SegmentNode* right;
SegmentNode(int start, int end) {
this->start = start;
this->end = end;
this->left = this->right = nullptr;
}
};
class SegmentTree {
public:
int treeType;
SegmentNode* head;
// 0 -> sum tree
// 1 -> min tree
// 2 -> max tree
SegmentTree(vector<int>& input, int treeType = 0) {
this->treeType = treeType;
head = buildTree(input, 0, input.size() - 1);
}
SegmentNode* buildTree(vector<int>& input, int start, int end) {
SegmentNode* newNode = new SegmentNode(start, end);
if (start == end) {
newNode->val = input[start];
return newNode;
}
int mid = start + (end - start >> 1);
newNode->left = buildTree(input, start, mid);
newNode->right = buildTree(input, mid + 1, end);
switch (treeType)
{
case 0:
newNode->val = newNode->left->val + newNode->right->val;
break;
case 1:
newNode->val = min(newNode->left->val, newNode->right->val);
break;
case 2:
newNode->val = max(newNode->left->val, newNode->right->val);
break;
}
return newNode;
}
int search(SegmentNode* cur, int start, int end) {
int result;
switch (treeType)
{
case 0:
result = 0;
if (start == cur->start && end == cur->end)
return cur->val;
if (start <= cur->left->end)
result += search(cur->left, start, min(end, cur->left->end));
if (end >= cur->right->start)
result += search(cur->right, max(start, cur->right->start), end);
break;
case 1:
result = INT_MIN;
if (start == cur->start && end == cur->end)
return cur->val;
if (start <= cur->left->end)
result = max(result, search(cur->left, start, min(end, cur->left->end)));
if (end >= cur->right->start)
result = max(result, search(cur->right, max(start, cur->right->start), end));
break;
case 2:
result = INT_MAX;
if (start == cur->start && end == cur->end)
return cur->val;
if (start <= cur->left->end)
result = min(result, search(cur->left, start, min(end, cur->left->end)));
if (end >= cur->right->start)
result = min(result, search(cur->right, max(start, cur->right->start), end));
break;
}
return result;
}
void update(SegmentNode* cur, int index, int value) {
if (cur->start == cur->end) {
cur->val = value;
return;
}
int mid = cur->start + (cur->end - cur->start >> 1);
switch (treeType)
{
case 0:
if (index <= mid) {
cur->val = cur->right->val;
update(cur->left, index, value);
cur->val += cur->left->val;
}
else {
cur->val = cur->left->val;
update(cur->right, index, value);
cur->val += cur->right->val;
}
break;
case 1:
if (index <= mid) {
cur->val = cur->right->val;
update(cur->left, index, value);
cur->val = min(cur->val, cur->left->val);
}
else {
cur->val = cur->left->val;
update(cur->right, index, value);
cur->val = min(cur->val, cur->right->val);
}
break;
case 2:
if (index <= mid) {
cur->val = cur->right->val;
update(cur->left, index, value);
cur->val = max(cur->val, cur->left->val);
}
else {
cur->val = cur->left->val;
update(cur->right, index, value);
cur->val = max(cur->val, cur->right->val);
}
break;
}
}
};
2D Segment Tree
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class SegmentNode2D {
public:
int val;
int startx;
int endx;
int starty;
int endy;
SegmentNode2D* leftxlefty;
SegmentNode2D* leftxrighty;
SegmentNode2D* rightxlefty;
SegmentNode2D* rightxrighty;
SegmentNode2D(int startx, int endx, int starty, int endy) {
this->startx = startx;
this->endx = endx;
this->starty = starty;
this->endy = endy;
this->leftxlefty = this->leftxrighty = this->rightxlefty = this->rightxrighty = nullptr;
}
};
class SegmentTree2D {
public:
int treeType;
SegmentNode2D* head;
// 0 -> sum tree
// 1 -> max tree
// 2 -> min tree
SegmentTree2D(vector<vector<int>>& input, int treeType = 0) {
this->treeType = treeType;
head = buildTree(input, 0, input.size() - 1, 0, input[0].size() - 1);
}
SegmentNode2D* buildTree(vector<vector<int>>& input, int startx, int endx, int starty, int endy) {
SegmentNode2D* newNode = new SegmentNode2D(startx, endx, starty, endy);
if (startx == endx && starty == endy) {
newNode->val = input[startx][starty];
return newNode;
}
int midx = startx + (endx - startx >> 1);
int midy = starty + (endy - starty >> 1);
newNode->leftxlefty = buildTree(input, startx, midx, starty, midy);
if (starty < endy)
newNode->leftxrighty = buildTree(input, startx, midx, midy + 1, endy);
if (startx < endx)
newNode->rightxlefty = buildTree(input, midx + 1, endx, starty, midy);
if (startx < endx && starty < endy)
newNode->rightxrighty = buildTree(input, midx + 1, endx, midy + 1, endy);
switch (treeType)
{
case 0:
newNode->val = newNode->leftxlefty->val;
if (starty < endy)
newNode->val += newNode->leftxrighty->val;
if (startx < endx)
newNode->val += newNode->rightxlefty->val;
if (startx < endx && starty < endy)
newNode->val += newNode->rightxrighty->val;
break;
case 1:
newNode->val = newNode->leftxlefty->val;
if (starty < endy)
newNode->val = max(newNode->val, newNode->leftxrighty->val);
if (startx < endx)
newNode->val = max(newNode->val, newNode->rightxlefty->val);
if (startx < endx && starty < endy)
newNode->val = max(newNode->val, newNode->rightxrighty->val);
break;
case 2:
newNode->val = newNode->leftxlefty->val;
if (starty < endy)
newNode->val = min(newNode->val, newNode->leftxrighty->val);
if (startx < endx)
newNode->val = min(newNode->val, newNode->rightxlefty->val);
if (startx < endx && starty < endy)
newNode->val = min(newNode->val, newNode->rightxrighty->val);
break;
}
return newNode;
}
int search(SegmentNode2D* cur, int startx, int endx, int starty, int endy) {
int result;
switch (treeType)
{
case 0:
result = 0;
if (startx == cur->startx && starty == cur->starty && endx == cur->endx && endy == cur->endy)
return cur->val;
if (cur->leftxlefty && startx <= cur->leftxlefty->endx && starty <= cur->leftxlefty->endy)
result += search(cur->leftxlefty, startx, min(endx, cur->leftxlefty->endx), starty, min(endy, cur->leftxlefty->endy));
if (cur->leftxrighty && startx <= cur->leftxrighty->endx && endy >= cur->leftxrighty->starty)
result += search(cur->leftxrighty, startx, min(endx, cur->leftxrighty->endx), max(starty, cur->leftxrighty->starty), endy);
if (cur->rightxlefty && endx >= cur->rightxlefty->startx && starty <= cur->rightxlefty->endy)
result += search(cur->rightxlefty, max(startx, cur->rightxlefty->startx), endx, starty, min(endy, cur->rightxlefty->endy));
if (cur->rightxrighty && endx >= cur->rightxrighty->startx && endy >= cur->rightxrighty->starty)
result += search(cur->rightxrighty, max(startx, cur->rightxrighty->startx), endx, max(starty, cur->rightxrighty->starty), endy);
break;
case 1:
result = INT_MIN;
if (startx == cur->startx && starty == cur->starty && endx == cur->endx && endy == cur->endy)
return cur->val;
if (cur->leftxlefty && startx <= cur->leftxlefty->endx && starty <= cur->leftxlefty->endy)
result = max(result, search(cur->leftxlefty, startx, min(endx, cur->leftxlefty->endx), starty, min(endy, cur->leftxlefty->endy)));
if (cur->leftxrighty && startx <= cur->leftxrighty->endx && endy >= cur->leftxrighty->starty)
result = max(result, search(cur->leftxrighty, startx, min(endx, cur->leftxrighty->endx), max(starty, cur->leftxrighty->starty), endy));
if (cur->rightxlefty && endx >= cur->rightxlefty->startx && starty <= cur->rightxlefty->endy)
result = max(result, search(cur->rightxlefty, max(startx, cur->rightxlefty->startx), endx, starty, min(endy, cur->rightxlefty->endy)));
if (cur->rightxrighty && endx >= cur->rightxrighty->startx && endy >= cur->rightxrighty->starty)
result = max(result, search(cur->rightxrighty, max(startx, cur->rightxrighty->startx), endx, max(starty, cur->rightxrighty->starty), endy));
break;
case 2:
result = INT_MAX;
if (startx == cur->startx && starty == cur->starty && endx == cur->endx && endy == cur->endy)
return cur->val;
if (cur->leftxlefty && startx <= cur->leftxlefty->endx && starty <= cur->leftxlefty->endy)
result = min(result, search(cur->leftxlefty, startx, min(endx, cur->leftxlefty->endx), starty, min(endy, cur->leftxlefty->endy)));
if (cur->leftxrighty && startx <= cur->leftxrighty->endx && endy >= cur->leftxrighty->starty)
result = min(result, search(cur->leftxrighty, startx, min(endx, cur->leftxrighty->endx), max(starty, cur->leftxrighty->starty), endy));
if (cur->rightxlefty && endx >= cur->rightxlefty->startx && starty <= cur->rightxlefty->endy)
result = min(result, search(cur->rightxlefty, max(startx, cur->rightxlefty->startx), endx, starty, min(endy, cur->rightxlefty->endy)));
if (cur->rightxrighty && endx >= cur->rightxrighty->startx && endy >= cur->rightxrighty->starty)
result = min(result, search(cur->rightxrighty, max(startx, cur->rightxrighty->startx), endx, max(starty, cur->rightxrighty->starty), endy));
break;
}
return result;
}
void update(SegmentNode2D* cur, int indexx, int indexy, int value) {
if (cur->startx == cur->endx && cur->starty == cur->endy) {
cur->val = value;
return;
}
int midx = cur->startx + (cur->endx - cur->startx >> 1);
int midy = cur->starty + (cur->endy - cur->starty >> 1);
switch (treeType)
{
case 0:
if (indexx <= midx && indexy <= midy) {
cur->val -= cur->leftxlefty->val;
update(cur->leftxlefty, indexx, indexy, value);
cur->val += cur->leftxlefty->val;
}
else if (indexx > midx && indexy <= midy) {
cur->val -= cur->rightxlefty->val;
update(cur->rightxlefty, indexx, indexy, value);
cur->val += cur->rightxlefty->val;
}
else if (indexx <= midx && indexy > midy) {
cur->val -= cur->leftxrighty->val;
update(cur->leftxrighty, indexx, indexy, value);
cur->val += cur->leftxrighty->val;
}
else {
cur->val -= cur->rightxrighty->val;
update(cur->rightxrighty, indexx, indexy, value);
cur->val += cur->rightxrighty->val;
}
break;
case 1:
if (indexx <= midx && indexy <= midy) {
cur->val = max(max(cur->leftxrighty->val, cur->rightxlefty->val), cur->rightxrighty->val);
update(cur->leftxlefty, indexx, indexy, value);
cur->val = max(cur->val, cur->leftxlefty->val);
}
else if (indexx > midx && indexy <= midy) {
cur->val = max(max(cur->leftxlefty->val, cur->leftxrighty->val), cur->rightxrighty->val);
update(cur->rightxlefty, indexx, indexy, value);
cur->val = max(cur->val, cur->rightxlefty->val);
}
else if (indexx <= midx && indexy > midy) {
cur->val = max(max(cur->leftxlefty->val, cur->rightxlefty->val), cur->rightxrighty->val);
update(cur->leftxrighty, indexx, indexy, value);
cur->val = max(cur->val, cur->leftxrighty->val);
}
else {
cur->val = max(max(cur->leftxlefty->val, cur->leftxrighty->val), cur->rightxlefty->val);
update(cur->rightxrighty, indexx, indexy, value);
cur->val = max(cur->val, cur->rightxrighty->val);
}
break;
case 2:
if (indexx <= midx && indexy <= midy) {
cur->val = min(min(cur->leftxrighty->val, cur->rightxlefty->val), cur->rightxrighty->val);
update(cur->leftxlefty, indexx, indexy, value);
cur->val = min(cur->val, cur->leftxlefty->val);
}
else if (indexx > midx && indexy <= midy) {
cur->val = min(min(cur->leftxlefty->val, cur->leftxrighty->val), cur->rightxrighty->val);
update(cur->rightxlefty, indexx, indexy, value);
cur->val = min(cur->val, cur->rightxlefty->val);
}
else if (indexx <= midx && indexy > midy) {
cur->val = min(min(cur->leftxlefty->val, cur->rightxlefty->val), cur->rightxrighty->val);
update(cur->leftxrighty, indexx, indexy, value);
cur->val = min(cur->val, cur->leftxrighty->val);
}
else {
cur->val = min(min(cur->leftxlefty->val, cur->leftxrighty->val), cur->rightxlefty->val);
update(cur->rightxrighty, indexx, indexy, value);
cur->val = min(cur->val, cur->rightxrighty->val);
}
break;
}
}
};