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 <cstdlib>
#include <cassert>
#include <utility>
#include <tuple>
#include <ctime>
#include <cstdio>
#include <vector>
#include <algorithm>
#define loop(i,a,b) for(int i=(a);i<int(b);i++)
#define rep(i,n) loop(i,0,n)

using namespace std;

int const inf = 1e9;
#define np nullptr

unsigned int xor128(){
    static unsigned int x = 123456789, y = 362436069, z = 521288629, w = time(0);
    unsigned long t = x^(x<<11);
    x = y; y = z; z = w;
    return w=(w^(w>>19))^(t^(t>>8));
}
unsigned int xor128r(int n){
    return xor128()%n;
}
double xor128d(){
    return xor128() * 0.00000000023283064365386962890625;
}

struct Node {
    int val;
    Node * ch[2];
    int pri, cnt, sum_;
    int min_;
    Node(int v, int p) : val(v), pri(p), cnt(1), sum_(v), min_(v) {
        ch[0] = ch[1] = np;
    }
    // ~Node(){
    //     if(ch[0]) delete ch[0];
    //     if(ch[1]) delete ch[1];
    // }
    void * operator new(size_t sz){
        static int pos = 0;
        static char mem[400020*sizeof(Node)];
        Node * res = (Node*)(mem+pos);
        pos += sizeof(Node);
        return res;
    }

    static int count(Node * t){
        return t == np ? 0 : t->cnt;
    }
    static int sum(Node * t){
        return t == np ? 0 : t->sum_;
    }
    static int min(Node * t){
        return t == np ? inf : t->min_;
    }

    void show(int ofs=0){
        if(ch[0]) ch[0]->show(ofs+1);
        rep(i,ofs*2) putchar(' ');
        printf("v:%d m:%d (%p)\n", val, min_, this);
        if(ch[1]) ch[1]->show(ofs+1);
    }

    void update(){
        cnt = count(ch[0]) + count(ch[1]) + 1;
        sum_ = sum(ch[0]) + sum(ch[1]) + val;
        min_ = std::min({ min(ch[0]), min(ch[1]), val });
    }

    static Node * merge(Node * l, Node * r){
        if(l == np || r == np) return l == np ? r : l;
        if(l->pri > r->pri){
            l->ch[1] = merge(l->ch[1],r);
            l->update();
            return l;
        } else {
            r->ch[0] = merge(l,r->ch[0]);
            r->update();
            return r;
        }
    }

    pair<Node*,Node*> split(int k){
        if(k <= count(ch[0])){
            auto s = ch[0] ? ch[0]->split(k) : make_pair(np,np);
            ch[0] = s.second;
            update();
            return make_pair(s.first, this);
        } else {
            k -= count(ch[0]) + 1;
            auto s = ch[1] ? ch[1]->split(k) : make_pair(np,np);
            ch[1] = s.first;
            update();
            return make_pair(this,s.second);
        }
    }

    static Node * erase(Node * t, int k){
        Node *l,*m,*r;
        tie(l,m) = t->split(k);
        tie(m,r) = m->split(1);
        //delete m;
        return merge(l,r);
    }

    static Node * at(Node * t, int k){
        int lc = count(t->ch[0]);
        if(k < lc) return at(t->ch[0],k);
        else if(k == lc) return t;
        else return at(t->ch[1], k-lc-1);
    }

    static void set(Node * t, int k, int x){
        int lc = count(t->ch[0]);
        if(k < lc) set(t->ch[0], k, x);
        else if(k == lc) t->val = x;
        else if(k > lc) set(t->ch[1], k-lc-1, x);
        t->update();
    }

    static Node * insert(Node * t, int k, int v){
        Node *l,*m = new Node(v,xor128()), *r;
        if(t == nullptr) return m;
        tie(l,r) = t->split(k);
        return merge(merge(l,m),r);
    }

    static int min(Node * t, int l, int r){
        if(r - l <= 0) return inf;
        if(r - l == count(t)) return min(t);
        int lc = count(t->ch[0]);
        if(l == lc && r - lc == 1) return t->val;
        int res = inf;
        if(l < lc) res = std::min(res, min(t->ch[0], l, std::min(lc,r)));
        if(l <= lc && lc < r) res = std::min(res, min(t, lc, lc+1));
        if(lc+1 < r) res = std::min(res, min(t->ch[1], max(0,l-lc-1), r-lc-1));
        return res;
    }
};

struct Treap {
    Node * root;
    int size;
    Treap() : root(nullptr) {}
    void shift(int l, int r){
        int tmp = Node::at(root,r)->val;
        root = Node::erase(root, r);
        root = Node::insert(root, l, tmp);
    }
    void set(int k, int x){
        Node::set(root, k, x);
    }
    int rangemin(int l, int r){
        return Node::min(root,l,r);
    }
    void push_back(int x){
        root = Node::insert(root,size++,x);
    }
};

int get(){
    int x;
    scanf("%d",&x);
    return x;
}

void put(int x){
    //printf("ans : %d\n",x);
    printf("%d\n",x);
}

int main(){
#ifdef DEBUG
    freopen("in","r",stdin);
#endif
    int n = get(), q = get();
    Treap t;
    rep(i,n) t.push_back(get());

    rep(i,q){
        int op = get();
        if(false){
        } else if(op == 0){
            int l = get(), r = get();
            t.shift(l,r);
        } else if(op == 1){
            int l = get(), r = get();
            r++;
            put(t.rangemin(l,r));
        } else if(op == 2){
            int p = get(), v = get();
            t.set(p,v);
        }
    }
    //delete root;
}