Go: package main

// packed from [splaytree.go main.rmq.go splaytree_debug.go] with goone.

import (
	"bufio"
	"fmt"
	"io"
	"os"
	"strconv"
	"strings"
)

type SplayTreeNode struct {
	parent, left, right *SplayTreeNode

	size    int
	value   int
	minimum int
}

func newSplayTreeNode(v int) *SplayTreeNode {
	return &SplayTreeNode{value: v}
}

func (node *SplayTreeNode) rotate() {
	var pp, p, c *SplayTreeNode
	p = node.parent
	pp = p.parent
	if pp != nil && pp.left == p {
		pp.left = node
	}
	if pp != nil && pp.right == p {
		pp.right = node
	}
	node.parent = pp
	if p.left == node {
		c = node.right
		node.right = p
		p.left = c
	} else {
		c = node.left
		node.left = p
		p.right = c
	}
	p.parent = node
	if c != nil {
		c.parent = p
	}
	p.update()
	node.update()
}

func (node *SplayTreeNode) state() int {
	if node.parent == nil {
		return 0
	}
	if node.parent.left == node {
		return -1
	} else if node.parent.right == node {
		return 1
	}
	return 0
}

func (node *SplayTreeNode) splay() {
	for node.state() != 0 {
		if node.parent.state() == 0 {
			node.rotate()
			return
		}
		if node.state() == node.parent.state() {
			node.parent.rotate()
			node.rotate()
		} else {
			node.rotate()
			node.rotate()
		}
	}
}

func (node *SplayTreeNode) update() {
	node.size = 1
	node.minimum = node.value
	if node.left != nil {
		node.size += node.left.size
		node.minimum = min(node.minimum, node.left.minimum)
	}
	if node.right != nil {
		node.size += node.right.size
		node.minimum = min(node.minimum, node.right.minimum)
	}
}
func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func (node *SplayTreeNode) Get(idx int) *SplayTreeNode {
	cur := node
	for true {
		lSize := 0
		if cur.left != nil {
			lSize = cur.left.size
		}
		if idx < lSize {
			cur = cur.left
		}
		if lSize == idx {
			cur.splay()
			return cur
		}
		if idx > lSize {
			cur = cur.right
			idx = idx - lSize - 1
		}
	}
	return nil
}

func mergeSplayNode(l, r *SplayTreeNode) (root *SplayTreeNode) {
	if l == nil {
		return r
	}
	if r == nil {
		return l
	}
	root = l.Get(l.size - 1)
	root.right = r
	r.parent = root
	root.update()
	return root
}

func (node *SplayTreeNode) Split(leftCount int) (left *SplayTreeNode, right *SplayTreeNode) {
	root := node.Get(leftCount)
	lRoot, rRoot := root.left, root

	rRoot.left = nil
	if lRoot != nil {
		lRoot.parent = nil
	}
	rRoot.update()
	return lRoot, rRoot
}

func splayTreeInsert(t *SplayTreeNode, idx int, node *SplayTreeNode) (root *SplayTreeNode) {
	l, r := t.Split(idx)
	return mergeSplayNode(
		mergeSplayNode(l, node),
		r,
	)
}

func removeSplayTree(t *SplayTreeNode, idx int) (root *SplayTreeNode, removed *SplayTreeNode) {
	target := t.Get(idx)
	l, r := target.left, target.right
	if l != nil {
		l.parent = nil
	}
	if r != nil {
		r.parent = nil
	}
	target.left = nil
	target.right = nil
	target.update()
	return mergeSplayNode(l, r), target
}

const (
	initialBufSize = 100000
	maxBufSize     = 1000000
)

var sc *bufio.Scanner

func initScanner(r io.Reader) *bufio.Scanner {
	buf := make([]byte, initialBufSize)

	sc := bufio.NewScanner(r)
	sc.Buffer(buf, maxBufSize)
	sc.Split(bufio.ScanWords)
	return sc
}

func main() {
	sc = initScanner(os.Stdin)
	resolve()
}

func resolve() {
	n := scanInt(sc)
	q := scanInt(sc)
	table := newDebugNodeSlice(200001)
	for i := 0; i < n; i++ {
		table.l[i].parent = &table.l[i+1]
		table.l[i+1].left = &table.l[i]
		table.l[i].update()
		table.l[i+1].update()
	}
	var root *SplayTreeNode = &table.l[n]
	for i := 0; i < n; i++ {
		table.l[i].value = scanInt(sc)
		table.l[i].update()
	}
	table.l[n].update()
	for i := 0; i < q; i++ {
		switch scanInt(sc) {
		case 0:
			root = shift(root, scanInt(sc), scanInt(sc))
		case 1:
			l := scanInt(sc)
			r := scanInt(sc)
			tmp, rRoot := root.Split(r + 1)
			lRoot, cRoot := tmp.Split(l)
			fmt.Println(cRoot.minimum)
			root = mergeSplayNode(mergeSplayNode(lRoot, cRoot), rRoot)
		case 2:
			root = root.Get(scanInt(sc))
			root.value = scanInt(sc)
			root.update()
		}
	}
}


C++: #include<bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;i--)
using namespace std;
typedef pair<int,int> pii;
typedef vector<pii> vp;
typedef vector<int> vi;

//Segment Tree for Range Minimum Query
class SegmentTree{
  int n;
  vp node;
public:
  SegmentTree(int n_){
    n=1;
    while(n<n_)n*=2;
    node = vp(2*n-1);
  }

  SegmentTree(vector<int> a){
    int n_ = a.size();
    n=1;
    while(n<n_)n*=2;
    node.resize(2*n-1, pii(1e9, 1e9));
    for(int i=0;i<n_;i++)node[n-1+i] = pii(a[i],i);
    for(int i=n-2;i>=0;i--)node[i] = min(node[2*i+1], node[2*i+2]);
  }
  
  void update(int k, int v){
    int cur = k + n-1;
    node[cur] = pii(v,k);
    while(cur>0){
      cur = (cur-1)/2;
      node[cur] = min(node[cur*2+1],node[cur*2+2]);
    }
  }

  //return minimum value in [a,b). ( [l,r) is interval in which k is.)
  pii RMQ(int a,int b,int k=0,int l=0,int r=0){
    if(l>=r)r = n;
    if(r<=a || b<=l)return pii(1e9,1e9);
    if(a<=l && r<=b)return node[k];
    pii vl = RMQ(a,b,2*k+1,l,(l+r)/2);
    pii vr = RMQ(a,b,2*k+2,(l+r)/2,r);
    return min(vl,vr);
  }
};

struct FenwickTree{
  int n;
  vector<int> bit;
  FenwickTree(int x = 0):n(x){bit = vector<int>(x+1,0);}

  inline void add(int i, int x){
    i++;
    while(i <= n){
      bit[i] += x;
      i += i & -i;
      assert(i>0);
    }
  }

  inline int sum(int i){
    i++;
    int res = 0;
    while(i > 0){
      res += bit[i];
      i -= i & -i;
    }
    return res;
  }
};

int main(){
  int n,q;
  scanf("%d%d",&n,&q);

  vi a(n),x(q),y(q),z(q);
  rep(i,n)scanf("%d",&a[i]);
  vi cnt(n,0);
  rep(i,q){
    scanf("%d%d%d",&x[i],&y[i],&z[i]);
    if(x[i]==0)cnt[y[i]]++;
  }
    
  vi id(n);
  int len = 0;
  rep(i,n){
    len += cnt[i];
    id[i] = len;
    len++;
  }

  FenwickTree bit(len+1);
  rep(i,q){
    if(x[i]==0){
      z[i] = id[z[i]] + bit.sum(id[z[i]]);
      bit.add(id[y[i]],-1);
      y[i] = id[y[i]] + bit.sum(id[y[i]]);
      bit.add(id[z[i]]+1,+1);
    }else if(x[i] == 1){
      y[i] = id[y[i]] + bit.sum(id[y[i]]);
      z[i] = id[z[i]] + bit.sum(id[z[i]]);
    }else{
      y[i] = id[y[i]] + bit.sum(id[y[i]]);
    }
  }      

  vi v(len,1e9);
  rep(i,n)v[id[i]] = a[i];
	
  SegmentTree st(v);
  rep(i,q){
    if(x[i] == 0){
      st.update(y[i],v[z[i]]);
      st.update(z[i],1e9);
      v[y[i]] = v[z[i]]; v[z[i]] = 1e9;
    }else if(x[i] == 1){
      printf("%d\n",st.RMQ(y[i],z[i]+1).first);
    }else{
      st.update(y[i],z[i]);
      v[y[i]] = z[i];
    }
  }
}