// Program to show segment tree to demonstrate lazy
// propagation
#include <stdio.h>
#include <math.h>
#define MAX 1000
// Ideally, we should not use global variables and large
// constant-sized arrays, we have done it here for simplicity.
int tree[MAX] = {0}; // To store segment tree
int lazy[MAX] = {0}; // To store pending updates
/* 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 */
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] += (se-ss+1)*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] += (se-ss+1)*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 rang, 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] = 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 */
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
range of the array. The following are parameters for
this function.
si --> Index of 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 */
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] += (se-ss+1)*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 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 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()
int getSum(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 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.
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] = tree[si*2 + 1] + tree[si*2 + 2];
}
/* Function to construct segment tree from given array.
This function allocates memory for segment tree and
calls constructSTUtil() to fill the allocated memory */
void constructST(int arr[], int n)
{
// Fill the allocated memory st
constructSTUtil(arr, 0, n-1, 0);
}
// Driver program to test above functions
int main()
{
int arr[] = {1, 3, 5, 7, 9, 11};
int n = sizeof(arr)/sizeof(arr[0]);
// Build segment tree from given array
constructST(arr, n);
// Print sum of values in array from index 1 to 3
printf("Sum of values in given range = %d\n",
getSum(n, 1, 3));
// Add 10 to all nodes at indexes from 1 to 5.
updateRange(n, 1, 5, 10);
// Find sum after the value is updated
printf("Updated sum of values in given range = %d\n",
getSum( n, 1, 3));
return 0;
}