Given an array arr[] of size N. There are two types of operations:
- Update(l, r, x) : Increment the a[i] (l <= i <= r) with value x.
- Query(l, r) : Find the maximum value in the array in a range l to r (both are included).
Examples:
Input: arr[] = {1, 2, 3, 4, 5}
Update(0, 3, 4)
Query(1, 4)
Output: 8
After applying the update operation
in the given range with given value array becomes {5, 6, 7, 8, 5}.
Then the maximum value in the range 1 to 4 is 8.
Input: arr[] = {1, 2, 3, 4, 5}
Update(0, 0, 10)
Query(0, 4)
Output: 11
Approach: A detailed explanation about the lazy propagation in the segment tree is explained previously. The only thing that needed to change in the question is to return a maximum value between two child nodes when the parent node query is called. See the code for better understanding.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;#define MAX 1000// Ideally, we should not use global variables and large// constant-sized arrays, we have done it here for simplicity// To store segment treeint tree[MAX] = { 0 };// To store pending updatesint lazy[MAX] = { 0 };// si -> index of current node in segment tree// ss and se -> Starting and ending indexes of// elements for which current nodes stores sum// us and ue -> starting and ending indexes of update query// diff -> which we need to add in the range us to uevoid updateRangeUtil(int si, int ss, int se, int us, int ue, int diff){ // If lazy value is non-zero for current node of segment // tree, then there are some pending updates. So we need // to make sure that the pending updates are done before // making new updates. Because this value may be used by // parent after recursive calls (See last line of this // function) if (lazy[si] != 0) { // Make pending updates using value stored in lazy // nodes tree[si] += lazy[si]; // Checking if it is not leaf node because if // it is leaf node then we cannot go further if (ss != se) { // We can postpone updating children we don't // need their new values now. // Since we are not yet updating children of si, // we need to set lazy flags for the children lazy[si * 2 + 1] += lazy[si]; lazy[si * 2 + 2] += lazy[si]; } // Set the lazy value for current node as 0 as it // has been updated lazy[si] = 0; } // Out of range if (ss > se || ss > ue || se < us) return; // Current segment is fully in range if (ss >= us && se <= ue) { // Add the difference to current node tree[si] += diff; // Same logic for checking leaf node or not if (ss != se) { // This is where we store values in lazy nodes, // rather than updating the segment tree itself // Since we don't need these updated values now // we postpone updates by storing values in lazy[] lazy[si * 2 + 1] += diff; lazy[si * 2 + 2] += diff; } return; } // If not completely in range, but overlaps // recur for children int mid = (ss + se) / 2; updateRangeUtil(si * 2 + 1, ss, mid, us, ue, diff); updateRangeUtil(si * 2 + 2, mid + 1, se, us, ue, diff); // And use the result of children calls // to update this node tree[si] = max(tree[si * 2 + 1], tree[si * 2 + 2]);}// Function to update a range of values in segment// tree// us and eu -> starting and ending indexes of update query// ue -> ending index of update query// diff -> which we need to add in the range us to uevoid updateRange(int n, int us, int ue, int diff){ updateRangeUtil(0, 0, n - 1, us, ue, diff);}// A recursive function to get the max of values in given// a range of the array. The following are the parameters// for this function// si --> Index of the current node in the segment tree// Initially, 0 is passed as root is always at index 0// ss & se --> Starting and ending indexes of the// segment represented by current node// i.e., tree[si]// qs & qe --> Starting and ending indexes of query// rangeint getMaxUtil(int ss, int se, int qs, int qe, int si){ // If lazy flag is set for current node of segment tree // then there are some pending updates. So we need to // make sure that the pending updates are done before // processing the sub sum query if (lazy[si] != 0) { // Make pending updates to this node. Note that this // node represents sum of elements in arr[ss..se] and // all these elements must be increased by lazy[si] tree[si] += lazy[si]; // Checking if it is not leaf node because if // it is leaf node then we cannot go further if (ss != se) { // Since we are not yet updating children os si, // we need to set lazy values for the children lazy[si * 2 + 1] += lazy[si]; lazy[si * 2 + 2] += lazy[si]; } // Unset the lazy value for current node as it has // been updated lazy[si] = 0; } // Out of range if (ss > se || ss > qe || se < qs) return 0; // At this point, we are sure that pending lazy updates // are done for current node. So we can return value // (same as it was for a query in our previous post) // If this segment lies in range if (ss >= qs && se <= qe) return tree[si]; // If a part of this segment overlaps with the given // range int mid = (ss + se) / 2; return max(getMaxUtil(ss, mid, qs, qe, 2 * si + 1), getMaxUtil(mid + 1, se, qs, qe, 2 * si + 2));}// Return max of elements in range from index qs (query// start) to qe (query end). It mainly uses getSumUtil()int getMax(int n, int qs, int qe){ // Check for erroneous input values if (qs < 0 || qe > n - 1 || qs > qe) { printf("Invalid Input"); return -1; } return getMaxUtil(0, n - 1, qs, qe, 0);}// A recursive function that constructs Segment Tree for// array[ss..se]. si is index of current node in segment// tree st.void constructSTUtil(int arr[], int ss, int se, int si){ // out of range as ss can never be greater than se if (ss > se) return; // If there is one element in array, store it in // current node of segment tree and return if (ss == se) { tree[si] = arr[ss]; return; } // If there are more than one elements, then recur // for left and right subtrees and store the sum // of values in this node int mid = (ss + se) / 2; constructSTUtil(arr, ss, mid, si * 2 + 1); constructSTUtil(arr, mid + 1, se, si * 2 + 2); tree[si] = max(tree[si * 2 + 1], tree[si * 2 + 2]);}// Function to construct a segment tree from a given array// This function allocates memory for segment tree and// calls constructSTUtil() to fill the allocated memoryvoid constructST(int arr[], int n){ // Fill the allocated memory st constructSTUtil(arr, 0, n - 1, 0);}// Driver codeint main(){ int arr[] = { 1, 2, 3, 4, 5 }; int n = sizeof(arr) / sizeof(arr[0]); // Build segment tree from given array constructST(arr, n); // Add 4 to all nodes in index range [0, 3] updateRange(n, 0, 3, 4); // Print maximum element in index range [1, 4] cout << getMax(n, 1, 4); return 0;} |
Java
// Java implementation of the approachclass GFG { static int MAX =1000;// Ideally, we should not use global variables and large// constant-sized arrays, we have done it here for simplicity// To store segment treestatic int tree[] = new int[MAX];// To store pending updatesstatic int lazy[] = new int[MAX];// si -> index of current node in segment tree// ss and se -> Starting and ending indexes of// elements for which current nodes stores sum// us and ue -> starting and ending indexes of update query// diff -> which we need to add in the range us to uestatic void updateRangeUtil(int si, int ss, int se, int us, int ue, int diff){ // If lazy value is non-zero for current node of segment // tree, then there are some pending updates. So we need // to make sure that the pending updates are done before // making new updates. Because this value may be used by // parent after recursive calls (See last line of this // function) if (lazy[si] != 0) { // Make pending updates using value stored in lazy // nodes tree[si] += lazy[si]; // Checking if it is not leaf node because if // it is leaf node then we cannot go further if (ss != se) { // We can postpone updating children we don't // need their new values now. // Since we are not yet updating children of si, // we need to set lazy flags for the children lazy[si * 2 + 1] += lazy[si]; lazy[si * 2 + 2] += lazy[si]; } // Set the lazy value for current node as 0 as it // has been updated lazy[si] = 0; } // Out of range if (ss > se || ss > ue || se < us) return; // Current segment is fully in range if (ss >= us && se <= ue) { // Add the difference to current node tree[si] += diff; // Same logic for checking leaf node or not if (ss != se) { // This is where we store values in lazy nodes, // rather than updating the segment tree itself // Since we don't need these updated values now // we postpone updates by storing values in lazy[] lazy[si * 2 + 1] += diff; lazy[si * 2 + 2] += diff; } return; } // If not completely in range, but overlaps // recur for children int mid = (ss + se) / 2; updateRangeUtil(si * 2 + 1, ss, mid, us, ue, diff); updateRangeUtil(si * 2 + 2, mid + 1, se, us, ue, diff); // And use the result of children calls // to update this node tree[si] = Math.max(tree[si * 2 + 1], tree[si * 2 + 2]);}// Function to update a range of values in segment// tree// us and eu -> starting and ending indexes of update query// ue -> ending index of update query// diff -> which we need to add in the range us to uestatic void updateRange(int n, int us, int ue, int diff){ updateRangeUtil(0, 0, n - 1, us, ue, diff);}// A recursive function to get the sum of values in given// a range of the array. The following are the parameters// for this function// si --> Index of the current node in the segment tree// Initially, 0 is passed as root is always at index 0// ss & se --> Starting and ending indexes of the// segment represented by current node// i.e., tree[si]// qs & qe --> Starting and ending indexes of query// rangestatic int getSumUtil(int ss, int se, int qs, int qe, int si){ // If lazy flag is set for current node of segment tree // then there are some pending updates. So we need to // make sure that the pending updates are done before // processing the sub sum query if (lazy[si] != 0) { // Make pending updates to this node. Note that this // node represents sum of elements in arr[ss..se] and // all these elements must be increased by lazy[si] tree[si] += lazy[si]; // Checking if it is not leaf node because if // it is leaf node then we cannot go further if (ss != se) { // Since we are not yet updating children os si, // we need to set lazy values for the children lazy[si * 2 + 1] += lazy[si]; lazy[si * 2 + 2] += lazy[si]; } // Unset the lazy value for current node as it has // been updated lazy[si] = 0; } // Out of range if (ss > se || ss > qe || se < qs) return 0; // At this point, we are sure that pending lazy updates // are done for current node. So we can return value // (same as it was for a query in our previous post) // If this segment lies in range if (ss >= qs && se <= qe) return tree[si]; // If a part of this segment overlaps with the given // range int mid = (ss + se) / 2; return Math.max(getSumUtil(ss, mid, qs, qe, 2 * si + 1), getSumUtil(mid + 1, se, qs, qe, 2 * si + 2));}// Return sum of elements in range from index qs (query// start) to qe (query end). It mainly uses getSumUtil()static int getSum(int n, int qs, int qe){ // Check for erroneous input values if (qs < 0 || qe > n - 1 || qs > qe) { System.out.print("Invalid Input"); return -1; } return getSumUtil(0, n - 1, qs, qe, 0);}// A recursive function that constructs Segment Tree for// array[ss..se]. si is index of current node in segment// tree st.static void constructSTUtil(int arr[], int ss, int se, int si){ // out of range as ss can never be greater than se if (ss > se) return; // If there is one element in array, store it in // current node of segment tree and return if (ss == se) { tree[si] = arr[ss]; return; } // If there are more than one elements, then recur // for left and right subtrees and store the sum // of values in this node int mid = (ss + se) / 2; constructSTUtil(arr, ss, mid, si * 2 + 1); constructSTUtil(arr, mid + 1, se, si * 2 + 2); tree[si] = Math.max(tree[si * 2 + 1], tree[si * 2 + 2]);}// Function to construct a segment tree from a given array// This function allocates memory for segment tree and// calls constructSTUtil() to fill the allocated memorystatic void constructST(int arr[], int n){ // Fill the allocated memory st constructSTUtil(arr, 0, n - 1, 0);}// Driver codepublic static void main(String[] args) { int arr[] = { 1, 2, 3, 4, 5 }; int n = arr.length; // Build segment tree from given array constructST(arr, n); // Add 4 to all nodes in index range [0, 3] updateRange(n, 0, 3, 4); // Print maximum element in index range [1, 4] System.out.println(getSum(n, 1, 4));}}/* This code contributed by PrinciRaj1992 */ |
Python3
# Python3 implementation of the approach MAX = 1000# Ideally, we should not use global variables# and large constant-sized arrays, # we have done it here for simplicity # To store segment tree tree = [0] * MAX; # To store pending updates lazy = [0] * MAX; # si -> index of current node in segment tree # ss and se -> Starting and ending indexes of # elements for which current nodes stores sum # us and ue -> starting and ending indexes of update query # diff -> which we need to add in the range us to ue def updateRangeUtil(si, ss, se, us, ue, diff) : # If lazy value is non-zero for current node # of segment tree, then there are some # pending updates. So we need to make sure that # the pending updates are done before making # new updates. Because this value may be used by # parent after recursive calls (See last line of this # function) if (lazy[si] != 0) : # Make pending updates using value # stored in lazy nodes tree[si] += lazy[si]; # Checking if it is not leaf node because if # it is leaf node then we cannot go further if (ss != se) : # We can postpone updating children # we don't need their new values now. # Since we are not yet updating children of si, # we need to set lazy flags for the children lazy[si * 2 + 1] += lazy[si]; lazy[si * 2 + 2] += lazy[si]; # Set the lazy value for current node # as 0 as it has been updated lazy[si] = 0; # Out of range if (ss > se or ss > ue or se < us) : return; # Current segment is fully in range if (ss >= us and se <= ue) : # Add the difference to current node tree[si] += diff; # Same logic for checking leaf node or not if (ss != se) : # This is where we store values in lazy nodes, # rather than updating the segment tree itself # Since we don't need these updated values now # we postpone updates by storing values in lazy[] lazy[si * 2 + 1] += diff; lazy[si * 2 + 2] += diff; return; # If not completely in range, but overlaps # recur for children mid = (ss + se) // 2; updateRangeUtil(si * 2 + 1, ss, mid, us, ue, diff); updateRangeUtil(si * 2 + 2, mid + 1, se, us, ue, diff); # And use the result of children calls # to update this node tree[si] = max(tree[si * 2 + 1], tree[si * 2 + 2]); # Function to update a range of values # in segment tree # us and eu -> starting and ending # indexes of update query # ue -> ending index of update query # diff -> which we need to add in the range us to ue def updateRange(n, us, ue, diff) : updateRangeUtil(0, 0, n - 1, us, ue, diff); # A recursive function to get the sum of values # in a given range of the array. The following # are the parameters for this function # si --> Index of the current node in the segment tree # Initially, 0 is passed as root is always at index 0 # ss & se --> Starting and ending indexes of the # segment represented by current node # i.e., tree[si] # qs & qe --> Starting and ending indexes of query # range def getSumUtil(ss, se, qs, qe, si) : # If lazy flag is set for current node # of segment tree then there are some # pending updates. So we need to make sure # that the pending updates are done before # processing the sub sum query if (lazy[si] != 0) : # Make pending updates to this node. # Note that this node represents sum of # elements in arr[ss..se] and all these # elements must be increased by lazy[si] tree[si] += lazy[si]; # Checking if it is not leaf node because if # it is leaf node then we cannot go further if (ss != se) : # Since we are not yet updating children os si, # we need to set lazy values for the children lazy[si * 2 + 1] += lazy[si]; lazy[si * 2 + 2] += lazy[si]; # Unset the lazy value for current node # as it has been updated lazy[si] = 0; # Out of range if (ss > se or ss > qe or se < qs) : return 0; # At this point, we are sure that pending lazy updates # are done for current node. So we can return value # (same as it was for a query in our previous post) # If this segment lies in range if (ss >= qs and se <= qe) : return tree[si]; # If a part of this segment overlaps # with the given range mid = (ss + se) // 2; return max(getSumUtil(ss, mid, qs, qe, 2 * si + 1), getSumUtil(mid + 1, se, qs, qe, 2 * si + 2)); # Return sum of elements in range from index qs (query # start) to qe (query end). It mainly uses getSumUtil() def getSum(n, qs, qe) : # Check for erroneous input values if (qs < 0 or qe > n - 1 or qs > qe) : print("Invalid Input", end = ""); return -1; return getSumUtil(0, n - 1, qs, qe, 0); # A recursive function that constructs # Segment Tree for array[ss..se]. # si is index of current node in segment # tree st. def constructSTUtil(arr, ss, se, si) : # out of range as ss can never be # greater than se if (ss > se) : return; # If there is one element in array, # store it in current node of segment # tree and return if (ss == se) : tree[si] = arr[ss]; return; # If there are more than one elements, # then recur for left and right subtrees # and store the sum of values in this node mid = (ss + se) // 2; constructSTUtil(arr, ss, mid, si * 2 + 1); constructSTUtil(arr, mid + 1, se, si * 2 + 2); tree[si] = max(tree[si * 2 + 1], tree[si * 2 + 2]); # Function to construct a segment tree # from a given array. This function allocates # memory for segment tree and calls# constructSTUtil() to fill the allocated memory def constructST(arr, n) : # Fill the allocated memory st constructSTUtil(arr, 0, n - 1, 0); # Driver code if __name__ == "__main__" : arr = [ 1, 2, 3, 4, 5 ]; n = len(arr) ; # Build segment tree from given array constructST(arr, n); # Add 4 to all nodes in index range [0, 3] updateRange(n, 0, 3, 4); # Print maximum element in index range [1, 4] print(getSum(n, 1, 4)); # This code is contributed by AnkitRai01 |
C#
// C# implementation of the approachusing System; class GFG { static int MAX =1000; // Ideally, we should not use global variables and large// constant-sized arrays, we have done it here for simplicity // To store segment treestatic int []tree = new int[MAX]; // To store pending updatesstatic int []lazy = new int[MAX]; // si -> index of current node in segment tree// ss and se -> Starting and ending indexes of// elements for which current nodes stores sum// us and ue -> starting and ending indexes of update query// diff -> which we need to add in the range us to uestatic void updateRangeUtil(int si, int ss, int se, int us, int ue, int diff){ // If lazy value is non-zero for current node of segment // tree, then there are some pending updates. So we need // to make sure that the pending updates are done before // making new updates. Because this value may be used by // parent after recursive calls (See last line of this // function) if (lazy[si] != 0) { // Make pending updates using value stored in lazy // nodes tree[si] += lazy[si]; // Checking if it is not leaf node because if // it is leaf node then we cannot go further if (ss != se) { // We can postpone updating children we don't // need their new values now. // Since we are not yet updating children of si, // we need to set lazy flags for the children lazy[si * 2 + 1] += lazy[si]; lazy[si * 2 + 2] += lazy[si]; } // Set the lazy value for current node as 0 as it // has been updated lazy[si] = 0; } // Out of range if (ss > se || ss > ue || se < us) return; // Current segment is fully in range if (ss >= us && se <= ue) { // Add the difference to current node tree[si] += diff; // Same logic for checking leaf node or not if (ss != se) { // This is where we store values in lazy nodes, // rather than updating the segment tree itself // Since we don't need these updated values now // we postpone updates by storing values in lazy[] lazy[si * 2 + 1] += diff; lazy[si * 2 + 2] += diff; } return; } // If not completely in range, but overlaps // recur for children int mid = (ss + se) / 2; updateRangeUtil(si * 2 + 1, ss, mid, us, ue, diff); updateRangeUtil(si * 2 + 2, mid + 1, se, us, ue, diff); // And use the result of children calls // to update this node tree[si] = Math.Max(tree[si * 2 + 1], tree[si * 2 + 2]);} // Function to update a range of values in segment// tree// us and eu -> starting and ending indexes of update query// ue -> ending index of update query// diff -> which we need to add in the range us to uestatic void updateRange(int n, int us, int ue, int diff){ updateRangeUtil(0, 0, n - 1, us, ue, diff);} // A recursive function to get the sum of values in given// a range of the array. The following are the parameters// for this function// si --> Index of the current node in the segment tree// Initially, 0 is passed as root is always at index 0// ss & se --> Starting and ending indexes of the// segment represented by current node// i.e., tree[si]// qs & qe --> Starting and ending indexes of query// rangestatic int getSumUtil(int ss, int se, int qs, int qe, int si){ // If lazy flag is set for current node of segment tree // then there are some pending updates. So we need to // make sure that the pending updates are done before // processing the sub sum query if (lazy[si] != 0) { // Make pending updates to this node. Note that this // node represents sum of elements in arr[ss..se] and // all these elements must be increased by lazy[si] tree[si] += lazy[si]; // Checking if it is not leaf node because if // it is leaf node then we cannot go further if (ss != se) { // Since we are not yet updating children os si, // we need to set lazy values for the children lazy[si * 2 + 1] += lazy[si]; lazy[si * 2 + 2] += lazy[si]; } // Unset the lazy value for current node as it has // been updated lazy[si] = 0; } // Out of range if (ss > se || ss > qe || se < qs) return 0; // At this point, we are sure that pending lazy updates // are done for current node. So we can return value // (same as it was for a query in our previous post) // If this segment lies in range if (ss >= qs && se <= qe) return tree[si]; // If a part of this segment overlaps with the given // range int mid = (ss + se) / 2; return Math.Max(getSumUtil(ss, mid, qs, qe, 2 * si + 1), getSumUtil(mid + 1, se, qs, qe, 2 * si + 2));} // Return sum of elements in range from index qs (query// start) to qe (query end). It mainly uses getSumUtil()static int getSum(int n, int qs, int qe){ // Check for erroneous input values if (qs < 0 || qe > n - 1 || qs > qe) { Console.Write("Invalid Input"); return -1; } return getSumUtil(0, n - 1, qs, qe, 0);} // A recursive function that constructs Segment Tree for// array[ss..se]. si is index of current node in segment// tree st.static void constructSTUtil(int []arr, int ss, int se, int si){ // out of range as ss can never be greater than se if (ss > se) return; // If there is one element in array, store it in // current node of segment tree and return if (ss == se) { tree[si] = arr[ss]; return; } // If there are more than one elements, then recur // for left and right subtrees and store the sum // of values in this node int mid = (ss + se) / 2; constructSTUtil(arr, ss, mid, si * 2 + 1); constructSTUtil(arr, mid + 1, se, si * 2 + 2); tree[si] = Math.Max(tree[si * 2 + 1], tree[si * 2 + 2]);} // Function to construct a segment tree from a given array// This function allocates memory for segment tree and// calls constructSTUtil() to fill the allocated memorystatic void constructST(int []arr, int n){ // Fill the allocated memory st constructSTUtil(arr, 0, n - 1, 0);} // Driver codepublic static void Main(String[] args) { int []arr = { 1, 2, 3, 4, 5 }; int n = arr.Length; // Build segment tree from given array constructST(arr, n); // Add 4 to all nodes in index range [0, 3] updateRange(n, 0, 3, 4); // Print maximum element in index range [1, 4] Console.WriteLine(getSum(n, 1, 4));}}// This code has been contributed by 29AjayKumar |
Javascript
<script>// JavaScript implementation of the approachvar MAX = 1000;// Ideally, we should not use global variables and large// constant-sized arrays, we have done it here for simplicity// To store segment treevar tree = Array(MAX).fill(0);// To store pending updatesvar lazy = Array(MAX).fill(0);// si -> index of current node in segment tree// ss and se -> Starting and ending indexes of// elements for which current nodes stores sum// us and ue -> starting and ending indexes of update query// diff -> which we need to add in the range us to uefunction updateRangeUtil(si, ss, se, us, ue, diff){ // If lazy value is non-zero for current node of segment // tree, then there are some pending updates. So we need // to make sure that the pending updates are done before // making new updates. Because this value may be used by // parent after recursive calls (See last line of this // function) if (lazy[si] != 0) { // Make pending updates using value stored in lazy // nodes tree[si] += lazy[si]; // Checking if it is not leaf node because if // it is leaf node then we cannot go further if (ss != se) { // We can postpone updating children we don't // need their new values now. // Since we are not yet updating children of si, // we need to set lazy flags for the children lazy[si * 2 + 1] += lazy[si]; lazy[si * 2 + 2] += lazy[si]; } // Set the lazy value for current node as 0 as it // has been updated lazy[si] = 0; } // Out of range if (ss > se || ss > ue || se < us) return; // Current segment is fully in range if (ss >= us && se <= ue) { // Add the difference to current node tree[si] += diff; // Same logic for checking leaf node or not if (ss != se) { // This is where we store values in lazy nodes, // rather than updating the segment tree itself // Since we don't need these updated values now // we postpone updates by storing values in lazy[] lazy[si * 2 + 1] += diff; lazy[si * 2 + 2] += diff; } return; } // If not completely in range, but overlaps // recur for children var mid = parseInt((ss + se) / 2); updateRangeUtil(si * 2 + 1, ss, mid, us, ue, diff); updateRangeUtil(si * 2 + 2, mid + 1, se, us, ue, diff); // And use the result of children calls // to update this node tree[si] = Math.max(tree[si * 2 + 1], tree[si * 2 + 2]);}// Function to update a range of values in segment// tree// us and eu -> starting and ending indexes of update query// ue -> ending index of update query// diff -> which we need to add in the range us to uefunction updateRange( n, us, ue, diff){ updateRangeUtil(0, 0, n - 1, us, ue, diff);}// A recursive function to get the max of values in given// a range of the array. The following are the parameters// for this function// si --> Index of the current node in the segment tree// Initially, 0 is passed as root is always at index 0// ss & se --> Starting and ending indexes of the// segment represented by current node// i.e., tree[si]// qs & qe --> Starting and ending indexes of query// rangefunction getSumUtil(ss, se, qs, qe, si){ // If lazy flag is set for current node of segment tree // then there are some pending updates. So we need to // make sure that the pending updates are done before // processing the sub sum query if (lazy[si] != 0) { // Make pending updates to this node. Note that this // node represents sum of elements in arr[ss..se] and // all these elements must be increased by lazy[si] tree[si] += lazy[si]; // Checking if it is not leaf node because if // it is leaf node then we cannot go further if (ss != se) { // Since we are not yet updating children os si, // we need to set lazy values for the children lazy[si * 2 + 1] += lazy[si]; lazy[si * 2 + 2] += lazy[si]; } // Unset the lazy value for current node as it has // been updated lazy[si] = 0; } // Out of range if (ss > se || ss > qe || se < qs) return 0; // At this point, we are sure that pending lazy updates // are done for current node. So we can return value // (same as it was for a query in our previous post) // If this segment lies in range if (ss >= qs && se <= qe) return tree[si]; // If a part of this segment overlaps with the given // range var mid = (ss + se) / 2; return Math.max(getSumUtil(ss, mid, qs, qe, 2 * si + 1), getSumUtil(mid + 1, se, qs, qe, 2 * si + 2));}// Return max of elements in range from index qs (query// start) to qe (query end). It mainly uses getSumUtil()function getSum(n, qs, qe){ // Check for erroneous input values if (qs < 0 || qe > n - 1 || qs > qe) { document.write("Invalid Input"); return -1; } return getSumUtil(0, n - 1, qs, qe, 0);}// A recursive function that constructs Segment Tree for// array[ss..se]. si is index of current node in segment// tree st.function constructSTUtil(arr, ss, se, si){ // out of range as ss can never be greater than se if (ss > se) return; // If there is one element in array, store it in // current node of segment tree and return if (ss == se) { tree[si] = arr[ss]; return; } // If there are more than one elements, then recur // for left and right subtrees and store the sum // of values in this node var mid = parseInt((ss + se) / 2); constructSTUtil(arr, ss, mid, si * 2 + 1); constructSTUtil(arr, mid + 1, se, si * 2 + 2); tree[si] = Math.max(tree[si * 2 + 1], tree[si * 2 + 2]);}// Function to construct a segment tree from a given array// This function allocates memory for segment tree and// calls constructSTUtil() to fill the allocated memoryfunction constructST(arr, n){ // Fill the allocated memory st constructSTUtil(arr, 0, n - 1, 0);}// Driver codevar arr = [1, 2, 3, 4, 5];var n = arr.length;// Build segment tree from given arrayconstructST(arr, n);// Add 4 to all nodes in index range [0, 3]updateRange(n, 0, 3, 4);// Print maximum element in index range [1, 4]document.write( getSum(n, 1, 4));</script> |
Output
8
Another Version : Above was implementation in which while performing range update queries we add difference to each node in segment tree,
Another approach could be to set all values in range with given value.
Below is the implementation of the approach :
C++
#include<bits/stdc++.h>#define int long longusing namespace std;class LazySegmentTreeWithSetUpdate{ int n=0; int MYSIZE=0; vector<long long> tree,lazy,stamp; vector<bool> pending; vector<long long> arr; int tm=0; public: void init(int n){ this->n=n; this->MYSIZE=4*n+10; tree.assign(MYSIZE,0LL); lazy.assign(MYSIZE,0LL); arr.assign(MYSIZE,0LL); stamp.assign(MYSIZE,0LL); pending.assign(MYSIZE,false); } void post_init(){ this->constructST(); } LazySegmentTreeWithSetUpdate(vector<int> & v){ int n=v.size(); init(n); for(int i=0;i<n;i++){ arr[i]=v[i]; } post_init(); } LazySegmentTreeWithSetUpdate(int v[],int n){ init(n); for(int i=0;i<n;i++){ arr[i]=v[i]; } post_init(); } LazySegmentTreeWithSetUpdate(int n){ init(n); post_init(); } void updateRangeUtil(int si, int ss, int se, int us, int ue, int diff,int stamp_value) { if (pending[si]) { tree[si] = (se-ss+1)*lazy[si]; if (ss != se) { if(stamp[si*2+1]<=stamp[si]){ lazy[si*2 + 1] = lazy[si]; stamp[si*2 + 1] = stamp[si]; pending[si*2+1]=true; } if(stamp[si*2+2]<=stamp[si]){ lazy[si*2 + 2] = lazy[si]; stamp[si*2 + 2] = stamp[si]; pending[si*2+2]=true; } } pending[si]=false; } if (ss>se || ss>ue || se<us) return ; if (ss>=us && se<=ue) { tree[si] = (se-ss+1)*diff; if (ss != se) { if(stamp[si*2+1]<=stamp_value){ lazy[si*2 + 1] = diff; stamp[si*2 + 1] = stamp_value; pending[si*2+1]=true; } if(stamp[si*2+2]<=stamp_value){ lazy[si*2 + 2] = diff; stamp[si*2 + 2] = stamp_value; pending[si*2+2]=true; } } stamp[si]=stamp_value; return; } int mid = (ss+se)/2; updateRangeUtil(si*2+1, ss, mid, us, ue, diff,stamp_value); updateRangeUtil(si*2+2, mid+1, se, us, ue, diff,stamp_value); tree[si] = tree[si*2+1] + tree[si*2+2]; } void updateRange(int us, int ue, int diff) { ++tm; updateRangeUtil(0, 0, n-1, us, ue, diff,tm); } void update(int us,int ue,int diff){ updateRange(us,ue,diff); } int getSumUtil(int ss, int se, int qs, int qe, int si) { if (pending[si]) { tree[si] = (se-ss+1)*lazy[si]; if (ss != se) { if(stamp[si*2+1]<=stamp[si]){ lazy[si*2+1] = lazy[si]; stamp[si*2+1]=stamp[si]; pending[si*2+1]=true; } if(stamp[si*2+2]<=stamp[si]){ lazy[si*2+2] = lazy[si]; stamp[si*2+2]=stamp[si]; pending[si*2+2]=true; } } pending[si]=false; } if (ss>se || ss>qe || se<qs) return 0; if (ss>=qs && se<=qe) return tree[si]; int mid = (ss + se)/2; return getSumUtil(ss, mid, qs, qe, 2*si+1) + getSumUtil(mid+1, se, qs, qe, 2*si+2); } int getSum(int qs, int qe) { if (qs < 0 || qe > n-1 || qs > qe) { printf("Invalid Input"); return -1; } return getSumUtil(0, n-1, qs, qe, 0); } int query(int qs,int qe){ return getSum(qs,qe); } void constructSTUtil(int ss, int se, int si) { if (ss > se) return ; if (ss == se){ tree[si] = arr[ss]; return; } int mid = (ss + se)/2; if(ss<=mid) constructSTUtil(ss, mid, si*2+1); if(mid+1<=se) constructSTUtil(mid+1, se, si*2+2); tree[si] = tree[si*2 + 1] + tree[si*2 + 2]; } void constructST(){ constructSTUtil(0, n-1, 0); } static void how_to_use(){ vector<int> arr={1,2,3,4}; LazySegmentTreeWithSetUpdate *mylst=new LazySegmentTreeWithSetUpdate(arr); mylst->update(0,3,0); mylst->update(2,3,2); mylst->update(0,2,10); int ans=mylst->query(1,2); cout<<ans<<endl; }};signed main(){ vector<int> arr={1,2,3,4}; LazySegmentTreeWithSetUpdate *mylst=new LazySegmentTreeWithSetUpdate(arr); mylst->update(0,3,0); cout<<"updating range from "<<0<<" to "<<3<<" with value : "<<0<<endl; mylst->update(2,3,2); cout<<"updating range from "<<2<<" to "<<3<<" with value : "<<2<<endl; mylst->update(0,2,10); cout<<"updating range from "<<0<<" to "<<2<<" with value : "<<10<<endl; int ans=mylst->query(1,2); cout<<"sum in range : "<<1<<" to "<<2<<" : "<<ans<<endl; return 0;} |
The implementation class has following members :
- n: The size of the input array.
- MYSIZE: The size of the Segment Tree array.
- tree: The Segment Tree array used to store the sum of the values of the input array over a range of indices.
- lazy: The lazy array used to store the updates to be propagated to the Segment Tree.
- stamp: The stamp array is used to store the timestamp of the update.
- pending: A boolean array to keep track of pending updates in the Segment Tree.
- arr: The input array of integers.
The class has the following member functions:
- init(int n): Initializes the data members of the class with the input size n.
- post_init(): Constructs the Segment Tree using the input array.
- updateRangeUtil(int si, int ss, int se, int us, int ue, int diff,int stamp_value): A utility function that updates the Segment Tree using lazy propagation technique.
- updateRange(int us, int ue, int diff): A function that updates the input array over a range of indices.
- update(int us, int ue, int diff): A function that updates the input array over a range of indices.
- getSumUtil(int ss, int se, int qs, int qe, int si): A utility function that returns the sum of the values of the input array over a range of indices.
- getSum(int qs, int qe): A function that returns the sum of the values of the input array over a range of indices.
- query(int qs, int qe): A function that returns the sum of the values of the input array over a range of indices.
Related Topic: Segment Tree
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