# Binary Index Tree & Segment Tree Summary C++ Solution

• Count of Smaller Numbers After Self

``````class Solution {
public:
vector<int> countSmaller(vector<int>& nums) {
vector<int> t, res(nums.size());
for (int i = nums.size() - 1; i >= 0; i--) {
int d = distance(t.begin(), lower_bound(t.begin(), t.end(), nums[i]));
res[i] = d;
t.insert(t.begin() + d, nums[i]);
}
return res;
}
};
``````

Count of Smaller Numbers Before Self

``````class Solution {
public:
vector<int> countOfSmallerNumberII(vector<int>& A) {
vector<int> t, res(A.size());
for (int i = 0; i <= static_cast<int>(A.size()) - 1; i++) {
int d = distance(t.begin(), lower_bound(t.begin(), t.end(), A[i]));
res[i] = d;
t.insert(t.begin() + d, A[i]);
}
return res;
}
};
``````

Build Segment Tree 1 & 2

``````class Solution {
public:
/**
*@param start, end: Denote an segment / interval
*@return: The root of Segment Tree
*/
SegmentTreeNode * build(int start, int end) {
if (start > end)    return NULL;
SegmentTreeNode* root = new SegmentTreeNode(start, end);
if (start == end)  return root;
int mid=(start+end)/2;
root->left = build(start, mid);
root->right = build(mid+1, end);
return root;
}
};
``````

Support record the max value of the corresponding interval max value :

Segment tree build 2

``````class Solution {
public:
/**
*@param A: a list of integer
*@return: The root of Segment Tree
*/
SegmentTreeNode * build(vector<int>& A) {
return buildRecu(A, 0, A.size() - 1);
}

SegmentTreeNode *buildRecu(const vector<int>& A,
const int start, const int end) {
if (start > end) {
return nullptr;
}
// The root's start and end is given by build method.
SegmentTreeNode *root = new SegmentTreeNode(start, end, INT_MAX);

// If start equals to end, there will be no children for this node.
if (start == end) {
root->max = A[start];
return root;
}

// Left child: start=A.left, end=(A.left + A.right) / 2.
root->left = buildRecu(A, start, (start + end) / 2);

// Right child: start=(A.left + A.right) / 2 + 1, end=A.right.
root->right = buildRecu(A, (start + end) / 2 + 1, end);

const int left_max = root->left != nullptr ? root->left->max : INT_MAX;
const int right_max = root->right != nullptr ? root->right->max : INT_MAX;

// Update max.
root->max = max(left_max, right_max);
return root;
}
};
``````

Segment Tree Query 1 & 2

Segment Tree Query 1

``````class Solution {
public:
/**
*@param root, start, end: The root of segment tree and
*                         an segment / interval
*@return: The maximum number in the interval [start, end]
*/
int query(SegmentTreeNode *root, int start, int end) {
// Out of range.
if (root == nullptr || root->start > end || root->end <  start) {
return INT_MIN;
}

// Current segment is totally within range [start, end]
if (root->start >= start && root->end <= end) {
return root->max;
}

int left = query(root->left, start, end);
int right = query(root->right, start, end);

// Find max in the children.
return max(left, right);
}
};
``````

Segment Tree Query 2

``````class Solution {
public:
/**
*@param root, start, end: The root of segment tree and
*                         an segment / interval
*@return: The count number in the interval [start, end]
*/
int query(SegmentTreeNode *root, int start, int end) {
// Out of range.
if (root == nullptr || root->start > end || root->end <  start) {
return 0;
}

// Current segment is totally within range [start, end]
if (root->start >= start && root->end <= end) {
return root->count;
}

int left = query(root->left, start, end);
int right = query(root->right, start, end);

// Find max in the children.
return left + right;
}
};
``````

Segment Tree Modify

``````class Solution {
public:
/**
*@param root, index, value: The root of segment tree and
*@ change the node's value with [index, index] to the new given value
*@return: void
*/
void modify(SegmentTreeNode *root, int index, int value) {
// Out of range.
if (root == nullptr || root->start > index || root->end < index) {
return;
}

// Change the node's value with [index, index] to the new given value.
if (root->start == index && root->end == index) {
root->max = value;
return;
}

modify(root->left, index, value);
modify(root->right, index, value);

int left_max = root->left != nullptr? root->left->max : INT_MIN;
int right_max = root->right != nullptr? root->right->max : INT_MIN;

// Update max.
root->max = max(left_max, right_max);
}
};

``````

Interval Sum--1

Given an integer array (index from 0 to n-1, where n is the size of this array), and an query list. Each query has two integers [start, end]. For each query, calculate the sum number between index start and end in the given array, return the result list.

``````/**
* Definition of Interval:
* classs Interval {
*     int start, end;
*     Interval(int start, int end) {
*         this->start = start;
*         this->end = end;
*     }
*/
class SegmentTreeSumNode {
public:
int start, end;
long long sum;
SegmentTreeSumNode *left, *right;
SegmentTreeSumNode(int start, int end, long long sum) {
this->start = start;
this->end = end;
this->sum = sum;
this->left = this->right = NULL;
}
};

class Solution {
public:
/**
*@param A, queries: Given an integer array and an query list
*@return: The result list
*/
vector<long long> intervalSum(vector<int> &A, vector<Interval> &queries) {
vector<long long> res;

// Build segment tree.
SegmentTreeSumNode *root = build(A, 0, A.size() - 1);

// Do each query.
for (const auto& q : queries) {
res.emplace_back(query(root, q.start, q.end));
}

return res;
}

// Build segment tree.
SegmentTreeSumNode *build(vector<int> &A, int start, int end) {
if (start > end) {
return nullptr;
}

// The root's start and end is given by build method.
SegmentTreeSumNode *root = new SegmentTreeSumNode(start, end, 0);

// If start equals to end, there will be no children for this node.
if (start == end) {
root->sum = A[start];
return root;
}

// Left child: start=A.left, end=(A.left + A.right) / 2.
root->left = build(A, start, (start + end) / 2);

// Right child: start=(A.left + A.right) / 2 + 1, end=A.right.
root->right = build(A, (start + end) / 2 + 1, end);

long long left_sum = root->left != nullptr? root->left->sum : 0;
long long right_sum = root->right != nullptr? root->right->sum : 0;

// Update sum.
root->sum = left_sum + right_sum;
return root;
}

// Query sum in given range.
long long query(SegmentTreeSumNode *root, int start, int end) {
// Out of range.
if (root == nullptr || root->start > end || root->end <  start) {
return 0;
}

// Current segment is totally within range [start, end]
if (root->start >= start && root->end <= end) {
return root->sum;
}

long long left = query(root->left, start, end);
long long right = query(root->right, start, end);

// Find sum in the children.
return left + right;
}
};
``````

Interval Sum--2

Given an integer array in the construct method, implement two methods query(start, end) and modify(index, value):
For query(start, end), return the sum from index start to index end in the given array.
For modify(index, value), modify the number in the given index to value

``````class SegmentTreeSumNode {
public:
int start, end;
long long sum;
SegmentTreeSumNode *left, *right;
SegmentTreeSumNode(int start, int end, long long sum) {
this->start = start;
this->end = end;
this->sum = sum;
this->left = this->right = NULL;
}
};

class Solution {
public:
/* you may need to use some attributes here */
SegmentTreeSumNode *root_;

/**
* @param A: An integer vector
*/
Solution(vector<int> A) {
root_ = build(A, 0, A.size() - 1);
}

/**
* @param start, end: Indices
* @return: The sum from start to end
*/
long long query(int start, int end) {
queryTree(root_, start, end);
}

/**
* @param index, value: modify A[index] to value.
*/
void modify(int index, int value) {
modifyTree(root_, index, value);
}

// Query Sum in given range.
long long queryTree(SegmentTreeSumNode *root, int start, int end) {
// Out of range.
if (root == nullptr || root->start > end || root->end <  start) {
return 0;
}

// Current segment is totally within range [start, end]
if (root->start >= start && root->end <= end) {
return root->sum;
}

long long left = queryTree(root->left, start, end);
long long right = queryTree(root->right, start, end);

// Find sum in the children.
return left + right;
}

void modifyTree(SegmentTreeSumNode *root, int index, int value) {
// Out of range.
if (root == nullptr || root->start > index || root->end < index) {
return;
}

// Change the node's value with [index, index] to the new given value.
if (root->start == index && root->end == index) {
root->sum = value;
return;
}

modifyTree(root->left, index, value);
modifyTree(root->right, index, value);

int left_sum = root->left != nullptr? root->left->sum : 0;
int right_sum = root->right != nullptr? root->right->sum : 0;

// Update sum.
root->sum = left_sum + right_sum;
}

// Build segment tree.
SegmentTreeSumNode *build(vector<int> &A, int start, int end) {
if (start > end) {
return nullptr;
}

// The root's start and end is given by build method.
SegmentTreeSumNode *root = new SegmentTreeSumNode(start, end, 0);

// If start equals to end, there will be no children for this node.
if (start == end) {
root->sum = A[start];
return root;
}

// Left child: start=A.left, end=(A.left + A.right) / 2.
root->left = build(A, start, (start + end) / 2);
// Right child: start=(A.left + A.right) / 2 + 1, end=A.right.
root->right = build(A, (start + end) / 2 + 1, end);

long long left_sum = root->left != nullptr? root->left->sum : 0;
long long right_sum = root->right != nullptr? root->right->sum : 0;

// Update sum.
root->sum = left_sum + right_sum;
return root;
}
};

``````

Interval Minimum Number

Given an integer array (index from 0 to n-1, where n is the size of this array), and an query list. Each query has two integers [start, end]. For each query, calculate the minimum number between index start and end in the given array, return the result list.

``````class SegmentTreeMinNode {
public:
int start, end, min;
SegmentTreeMinNode *left, *right;
SegmentTreeMinNode(int start, int end, int min) {
this->start = start;
this->end = end;
this->min = min;
this->left = this->right = NULL;
}
};

class Solution {
public:
/**
*@param A, queries: Given an integer array and an query list
*@return: The result list
*/
vector<int> intervalMinNumber(vector<int> &A, vector<Interval> &queries) {
vector<int> res;

// Build segment tree.
SegmentTreeMinNode *root = build(A, 0, A.size() - 1);

// Do each query.
for (const auto& q : queries) {
res.emplace_back(query(root, q.start, q.end));
}

return res;
}

// Build segment tree.
SegmentTreeMinNode *build(vector<int> &A, int start, int end) {
if (start > end) {
return nullptr;
}

// The root's start and end is given by build method.
SegmentTreeMinNode *root = new SegmentTreeMinNode(start, end, INT_MAX);

// If start equals to end, there will be no children for this node.
if (start == end) {
root->min = A[start];
return root;
}

// Left child: start=A.left, end=(A.left + A.right) / 2.
root->left = build(A, start, (start + end) / 2);

// Right child: start=(A.left + A.right) / 2 + 1, end=A.right.
root->right = build(A, (start + end) / 2 + 1, end);

int left_min = root->left != nullptr ? root->left->min : INT_MAX;
int right_min = root->right != nullptr ? root->right->min : INT_MAX;

// Update min.
root->min = min(left_min, right_min);
return root;
}

// Query min in given range.
int query(SegmentTreeMinNode *root, int start, int end) {
// Out of range.
if (root == nullptr || root->start > end || root->end < start) {
return INT_MAX;
}

// Current segment is totally within range [start, end]
if (root->start >= start && root->end <= end) {
return root->min;
}

const int left = query(root->left, start, end);
const int right = query(root->right, start, end);

// Find min in the children.
return min(left, right);
}
};
``````

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