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 <climits>
#include <iostream>
#include <queue>
#include <cmath>
#define REP(i,n) for(int i=0; i<(int)(n); i++)

#include <set>
#include <cstdio>
inline int getInt(){ int s; scanf("%d", &s); return s; }

using namespace std;

int main(){
  const int n = getInt();
  const int q = getInt();

  const int c = min(2000000 / 500, (int)(n / floor(sqrt(n) + 1e-9)));
  const int m = n / c + (n % c == 0 ? 0 : 1);

  vector<deque<int> > v(m);
  vector<multiset<int> > s(m);

  REP(i,n){
    const int a = getInt();
    v[i / c].push_back(a);
    s[i / c].insert(a);
  }

  REP(qq, q){
    const int x = getInt();
    const int y = getInt();
    const int z = getInt();

    if(x == 1){
      const int lIdx = y / c;
      const int rIdx = z / c;

      int ans = INT_MAX;
      if(lIdx == rIdx){
        for(int i = y % c; i <= z % c; i++)
          ans = min(ans, v[lIdx][i]);
      }else{
        for(int i = y % c; i < c; i++)
          ans = min(ans, v[lIdx][i]);

        for(int i = 0; i <= z % c; i++)
          ans = min(ans, v[rIdx][i]);

        for(int i = lIdx + 1; i < rIdx; i++)
          ans = min(ans, *s[i].begin());
      }

      printf("%d\n", ans);
    }else if(x == 0){
      const int lIdx = y / c;
      const int rIdx = z / c;

      const int rmemo = v[rIdx][z % c];

      v[rIdx].erase(v[rIdx].begin() + z % c);
      s[rIdx].erase(s[rIdx].find(rmemo));

      for(int i = rIdx; i > lIdx; i--){
        v[i].push_front(v[i - 1][c - 1]);
        s[i].insert(v[i - 1][c - 1]);

        s[i - 1].erase(s[i - 1].find(v[i - 1][c - 1]));
        v[i - 1].pop_back();
      }

      v[lIdx].insert(v[lIdx].begin() + y % c, rmemo);
      s[lIdx].insert(rmemo);

      // REP(i,n) printf("%d ", v[i / c][i % c]); puts("");
    }else{
      const int original = v[y / c][y % c];
      v[y / c][y % c] = z;
      s[y / c].erase(s[y / c].find(original));
      s[y / c].insert(z);
    }
  }

  return 0;
}