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 <cstdio>
#include <iostream>
#include <algorithm>
#include <string>
#include <cstring>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <cmath>
#include <iomanip>
#include <cassert>
#include <bitset>
#include <ctime>
#include <random>
using namespace std;

typedef pair<int, int> P;
#define rep(i, n) for (int i=0; i<(n); i++)
#define all(c) (c).begin(), (c).end()
#define uniq(c) c.erase(unique(all(c)), (c).end())
#define index(xs, x) (int)(lower_bound(all(xs), x) - xs.begin())
#define _1 first
#define _2 second
#define pb push_back
#define INF 1145141919
#define MOD 1000000007

mt19937 mt_rand(time(NULL));
using Value = int;

struct Treap {
  Value v;
  int cnt;
  int p;
  int seg_min;
  Treap *ch[2];
  Treap(Value v) : v(v), p(mt_rand()) {
    cnt = 1;
    seg_min = v;
    ch[0] = ch[1] = NULL;
  };
};
inline int count(Treap *t) { return t ? t->cnt : 0; }
inline int seg_min(Treap *t) { return t ? t->seg_min : INF; }
Treap *update(Treap *t) {
  if (t == NULL) return t;
  t->cnt = count(t->ch[0]) + count(t->ch[1]) + 1;
  t->seg_min = min({ seg_min(t->ch[0]), seg_min(t->ch[1]), t->v });
  return t;
}
Treap *merge(Treap *l, Treap *r) {
  if (l == NULL) return r;
  if (r == NULL) return l;
  if (l->p > r->p) {
    l->ch[1] = merge(l->ch[1], r);
    return update(l);
  }
  else {
    r->ch[0] = merge(l, r->ch[0]);
    return update(r);
  }
}

// [0, k), [k, n)
pair<Treap *, Treap *> split(Treap *t, int k) {
  if (t == NULL) return {NULL, NULL};
  if (k <= count(t->ch[0])) {
    auto s = split(t->ch[0], k);
    t->ch[0] = s._2;
    return { s._1, update(t) };
  }
  else {
    auto s = split(t->ch[1], k - count(t->ch[0]) - 1);
    t->ch[1] = s._1;
    return { update(t), s._2 };
  }
}

Treap *insert(Treap *t, int k, Value v) {
  Treap *l, *r;
  tie(l, r) = split(t, k);
  Treap *u = new Treap(v);
  return merge(merge(l, u), r);
}

pair<Treap *, Treap *> erase(Treap *t, int k) {
  Treap *l, *r, *u;
  tie(l, r) = split(t, k+1);
  tie(l, u) = split(l, k);
  return { merge(l, r), u };
}

int count_less(Treap *t, int x) {
  if (t == NULL) return 0;
  if (t->v <= x) {
    return count(t->ch[0]) + 1 + count_less(t->ch[1], x);
  }
  else {
    return count_less(t->ch[0], x);
  }
}
Treap *get(Treap *t, int k) {
  int l = count(t->ch[0]);
  if (k < l) return get(t->ch[0], k);
  if (k > l) return get(t->ch[1], k-l-1);
  return t;
}
void update_ancestor(Treap *t, int n) {
  int l = count(t->ch[0]);
  if (n < l) update_ancestor(t->ch[0], n);
  if (n > l) update_ancestor(t->ch[1], n-l-1);
  update(t);
}
Treap *shift(Treap *t) {
  if (t == NULL) return NULL;
  Treap *u;
  tie(t, u) = split(t, count(t)-1);
  return merge(u, t);
}

int N, Q;
signed main() {
  ios::sync_with_stdio(false); cin.tie(0);
  cin >> N >> Q;

  Treap *treap = NULL;
  rep(i, N) {
    int a; cin >> a;
    treap = insert(treap, i, a);
  }

  rep(i, Q) {
    int t, a, b;
    cin >> t >> a >> b;
    if (t == 0) {
      // shift [a, b]
      Treap *l, *u, *r;
      tie(l, r) = split(treap, a);
      tie(u, r) = split(r, b+1);
      u = shift(u);
      treap = merge(merge(l, u), r);
    }
    else if (t == 1) {
      // min [a, b]
      Treap *l, *u, *r;
      tie(l, r) = split(treap, a);
      tie(u, r) = split(r, b+1);
      cout << seg_min(u) << "\n";
      treap = merge(merge(l, u), r);
    }
    else {
      // update(a, b)
      get(treap, a)->v = b;
      update_ancestor(treap, a);
    }
  }
  return 0;
}