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segtrees.py
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from collections import defaultdict as dt
from math import ceil,log2
import sys
import os
class SegmentTree:
def __init__(self, arr, nodes):
self.arr = arr
self.nodes=nodes
def constructTree_sum(self,st,end,cur):
if st==end:
self.segment[cur]=self.arr[st]
return self.segment[cur]
middle=st+(end-st)//2
self.segment[cur]= self.constructTree_sum(st,middle,2*cur+1)+self.constructTree_sum(middle+1,end,2*cur+2)
return self.segment[cur]
def constructTree_min(self,st,end,cur):
if st==end:
self.segment[cur]=(self.arr[st],1)
return self.segment[cur]
middle=st+(end-st)//2
a,b=self.constructTree_min(st,middle,2*cur+1),self.constructTree_min(middle+1,end,2*cur+2)
if a[0]==b[0]:
self.segment[cur]= (a[0],a[1]+b[1])
elif a[0]<b[0]:
self.segment[cur]=a
else:
self.segment[cur]=b
return self.segment[cur]
def constructTree_max(self,st,end,cur):
if st==end:
self.segment[cur]=self.arr[st]
return self.segment[cur]
middle=st+(end-st)//2
self.segment[cur]= max(self.constructTree_max(st,middle,2*cur+1),self.constructTree_max(middle+1,end,2*cur+2))
return self.segment[cur]
def makeTree(self,type='sum'):
segmentLength=ceil(log2(self.nodes))
if type=='sum':
self.segment=[0]*(2*2**segmentLength-1)
self.constructTree_sum(0,self.nodes-1,0)
elif type=='min':
self.segment=[(0,0)]*(2*2**segmentLength-1)
self.constructTree_min(0,self.nodes-1,0)
elif type=='max':
self.segment=[0]*(2*2**segmentLength-1)
self.constructTree_max(0,self.nodes-1,0)
return self.segment
def update_util_sum(self,st,end,index,cur,diff):
if st<=index<=end:
self.segment[cur]+=diff
if st!=end:
middle=st+(end-st)//2
self.update_util_sum(st,middle,index,2*cur+1,diff)
self.update_util_sum(middle+1,end,index,2*cur+2,diff)
def update_util_min(self,st,end,index,cur,new):
if st<=index<=end:
if st==end:
self.segment[cur]=(new,1)
else:
middle=st+(end-st)//2
if st<=index<=middle:
self.update_util_min(st,middle,index,2*cur+1,new)
else:
self.update_util_min(middle+1,end,index,2*cur+2,new)
a,b=self.segment[2*cur+1],self.segment[2*cur+2]
if a[0]==b[0]:
self.segment[cur]=(a[0],a[1]+b[1])
elif a[0]<b[0]:
self.segment[cur]=a
else:
self.segment[cur]=b
def update_util_max(self,st,end,index,cur,new):
if st<=index<=end:
# self.segment[cur]=max(new,self.segment[cur])
if st==end:
self.segment[cur]=new
else:
middle=st+(end-st)//2
if st<=index<=middle:
self.update_util_max(st,middle,index,2*cur+1,new)
else:
self.update_util_max(middle+1,end,index,2*cur+2,new)
self.segment[cur]=max(self.segment[2*cur+1],self.segment[2*cur+2])
def update(self,index,new,type='sum'):
if -1<index<self.nodes:
if type=='sum':
diff=new-self.arr[index]
arr[index]=new
self.update_util(0,self.nodes-1,index,0,diff)
elif type=='min':
arr[index]=new
self.update_util_min(0,self.nodes-1,index,0,new)
elif type=='max':
arr[index]=new
self.update_util_max(0,self,nodes-1,index,0,new)
def sum_util(self,st,end,l,r,cur):
if l<=st and end<=r:
return self.segment[cur]
if l>end or r<st:
return 0
middle= st+(end-st)//2
return self.sum_util(st,middle,l,r,2*cur+1)+self.sum_util(middle+1,end,l,r,2*cur+2)
def min_util(self,st,end,l,r,cur):
if l<=st and end<=r:
return self.segment[cur]
if l>end or r<st:
return (sys.maxsize,0)
middle= st+(end-st)//2
a,b=self.min_util(st,middle,l,r,2*cur+1),self.min_util(middle+1,end,l,r,2*cur+2)
if a[0]==b[0]:
return (a[0],b[1]+a[1])
elif a[0]<b[0]:
return a
else:
return b
def max_util(self,st,end,l,r,cur):
if l<=st and end<=r:
return self.segment[cur]
if l>end or r<st:
return -1
middle= st+(end-st)//2
return max(self.max_util(st,middle,l,r,2*cur+1),self.max_util(middle+1,end,l,r,2*cur+2))
def range_query(self,l,r,type='sum'):
if l>-1 and r<self.nodes:
if type=='sum':
return self.sum_util(0,self.nodes-1,l,r,0)
elif type=='min':
return self.min_util(0,self.nodes-1,l,r,0)
elif type=='max':
return self.max_util(0,self.nodes-1,l,r,0)
if __name__ == '__main__':
# arr=[5]
# segment_tree=SegmentTree(arr,1)
# use the queries with type variable
# example make_Tree(type)
# example update(index,value,type)
# example range_query(l,r,type)
# print the tree segment_tree.segment
n,m=list(map(int,input().split()))
arr=list(map(int,input().split()))
segment_tree=SegmentTree(arr,n)
segment_tree.makeTree('min')
# print(segment_tree.segment)
for _ in range(m):
t,a,b=list(map(int,input().split()))
if t==1:
segment_tree.update(a,b,'min')
else:
ans=segment_tree.range_query(a,b-1,'min')
print(ans[0], ans[1])