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>
using namespace std;
using ll = long long;
#define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i))
#define all(x) (x).begin(),(x).end()
#define pb push_back
#define fi first
#define se second
#define dbg(x) cout<<#x" = "<<((x))<<endl
template<class T,class U> ostream& operator<<(ostream& o, const pair<T,U> &p){o<<"("<<p.fi<<","<<p.se<<")";return o;}
template<class T> ostream& operator<<(ostream& o, const vector<T> &v){o<<"[";for(T t:v){o<<t<<",";}o<<"]";return o;}

template<class T>
struct treap{
    struct node_t{
        T val; // 値
        node_t *lch, *rch;
        int pri; // 優先度
        int cnt; // 部分木のサイズ
        T sum; // 部分木の値の和
        T mn; // 部分木の最小値

        node_t(T v, int p):val(v), pri(p), cnt(1), sum(v), mn(v){
            lch = rch = NULL;
        }
    };

    const T INF = 19191919; // TODO:initialize
    mt19937 mt;
    node_t *root;
    treap():root(NULL){
        const int seed = 364364;
        mt = mt19937(seed);
    }

    int count(node_t *t){ return t ? t->cnt : 0; }
    T sum(node_t *t){ return t ? t->sum : 0; }
    T min(node_t *t){ return t ? t->mn : INF; }

    node_t *update(node_t *t){
        t->cnt = count(t->lch) + count(t->rch) + 1;
        t->sum = sum(t->lch) + sum(t->rch) + t->val;
        t->mn = std::min({min(t->lch), min(t->rch), t->val});
        return t;
    }

    node_t *merge(node_t *l, node_t *r){
        if(!l || !r) return l?l:r;

        if(l->pri > r->pri){ // 左の部分木の根のほうが優先度が高い
            l->rch = merge(l->rch, r);
            return update(l);
        }
        else{
            r->lch = merge(l, r->lch);
            return update(r);
        }
    }

    pair<node_t*, node_t*> split(node_t *t, int k){ // [0,k), [k,n)
        if(!t) return {NULL,NULL};
        if(k <= count(t->lch)){
            auto s = split(t->lch,k);
            t->lch = s.second;
            return {s.first, update(t)};
        }
        else{
            auto s = split(t->rch, k-count(t->lch)-1);
            t->rch = s.first;
            return {update(t), s.second};
        }
    }

    node_t *insert(node_t *t, int k, T val, int pri){
        auto s = split(t,k);
        t = merge(s.first, new node_t(val,pri));
        t = merge(t, s.second);
        return update(t);
    }

    node_t *erase(node_t *t, int k){
        auto s2 = split(t,k+1);
        auto s1 = split(s2.first, k);
        t = merge(s1.first, s2.second);
        return update(t);
    }

    node_t *find(node_t *t, int k){
        int c = count(t->lch);
        if(k < c) return find(t->lch,k);
        if(k == c) return t;
        return find(t->rch, k-c-1);
    }

    void insert(int k, T val){ root = insert(root, k, val, mt()); }
    void erase(int k){ root = erase(root, k); }
    node_t *find(int k){ return find(root,k); }

    void shift(int l, int r){
        if(r-l==1) return;
        assert(l<r);
        auto sr = split(root, r);
        auto sl = split(sr.first, l);
        auto lr = split(sl.second, r-l-1);
        root = merge(merge(sl.first, merge(lr.second, lr.first)), sr.second);
    }

    // [l,r)
    T min(int l, int r){
        assert(l<r);
        auto sr = split(root, r);
        auto sl = split(sr.first, l);
        auto lr = sl.second;
        T ret = min(lr);
        // 元に戻す
        root = merge(merge(sl.first, lr), sr.second);
        return ret;
    }
};

int main(){
    treap<int> t;

    int n,q;
    cin >>n >>q;
    rep(i,n){
        int a;
        cin >>a;
        t.insert(i,a);
    }

    while(q--){
        int x,y,z;
        cin >>x >>y >>z;
        if(x==0){
            t.shift(y,z+1);
        }
        else if(x==1){
            cout << t.min(y,z+1) << endl;
        }
        else{
            t.erase(y);
            t.insert(y,z);
        }
    }

    return 0;
}