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;

mt19937 rnd;

template<typename T, typename Func_mv>
struct TreapArray{
    struct Node{
        T val, sum;
        int pri, cnt;
        Node *lch, *rch;
        Node(T v):val(v), sum(v), pri(rnd()), cnt(1){
            lch = rch = nullptr;
        }
    };

    Node* node;
    Func_mv merge_values;
    T te;

    TreapArray(Func_mv merge_values, T te, Node* n=nullptr):merge_values(merge_values), te(te){ node = n; }
    TreapArray(Func_mv merge_values, T te, T v):merge_values(merge_values), te(te){ node = new Node(v); }

    int count(Node* t){ return !t ? 0 : t->cnt; }
    T   sum  (Node* t){ return !t ? te : t->sum; }
    int size(){ return count(node); }

    Node* update(Node* t){
        t->cnt = count(t->lch) + count(t->rch) + 1;
        t->sum = merge_values(merge_values(sum(t->lch), t->val), sum(t->rch));
        return t;
    }

    Node* merge(Node* l, Node* r){
        if(!l || !r) return !l ? r : l;
        if(l->pri > r->pri){
            l->rch = merge(l->rch, r);
            return update(l);
        }else{
            r->lch = merge(l, r->lch);
            return update(r);
        }
    }

    pair<Node*, Node*> split(Node* t, int k){
        if(!t) return make_pair(nullptr, nullptr);
        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};
        }
    }
    pair<TreapArray*, TreapArray*> split(int k){
        auto p = split(node, k);
        node = p.first;
        auto t2 = new TreapArray(merge_values, te, p.second);
        return make_pair(this, t2);
    }

    void insert(int k, T v){
        auto s = split(node, k);
        auto n = new Node(v);
        node = merge(s.first, n);
        node = merge(node, s.second);
    }

    void erase(int k){
        auto s1 = split(node, k);
        auto s2 = split(s1.second, 1);
        node = merge(s1.first, s2.second);
    }

    T kth_element(Node* t, int k){
        int my_idx = count(t->lch);
        if(k == my_idx){
            return t->val;
        }else if(k < my_idx){
            return kth_element(t->lch, k);
        }else{
            return kth_element(t->rch, k-my_idx-1);
        }
    }
    T kth_element(int k){
        return kth_element(node, k);
    }

    void change_kth_element(Node* t, int k, T v){
        int my_idx = count(t->lch);
        if(k == my_idx){
            t->val = v;
        }else if(k < my_idx){
            change_kth_element(t->lch, k, v);
        }else{
            change_kth_element(t->rch, k-my_idx-1, v);
        }
        update(t);
    }
    void change_kth_element(int k, T v){ change_kth_element(node, k, v); }

    T get_between(Node* t, int l, int r){
        int last_idx = count(t)-1;
        if(r < 0 || l > last_idx) return te;
        if(l <= 0 && last_idx <= r) return sum(t);

        T res = get_between(t->lch, l, r);
        int my_idx = count(t->lch);
        if(l <= my_idx && my_idx <= r) res = merge_values(res, t->val);
        res = merge_values(res, get_between(t->rch, l-my_idx-1, r-my_idx-1));
        return res;
    }
    T get_between(int l, int r){ return get_between(node, l, r); }

    void dump(Node* t, vector<T>& ret){
        if(!t) return;
        dump(t->lch, ret);
        ret.push_back(t->val);
        dump(t->rch, ret);
    }
    vector<T> dump(){
        vector<T> ret;
        dump(node, ret);
        return ret;
    }
};

int main(){
    int N, Q;
    cin >> N >> Q;
    auto merge = [](int a, int b){ return min(a, b); };
    TreapArray<int, decltype(merge)> tr(merge, 1e9);
    for(int i=0; i<N; i++){
        int a;
        scanf("%d", &a);
        tr.insert(i, a);
    }
    while(Q--){
        int t, a, b;
        scanf("%d %d %d", &t, &a, &b);
        if(t == 0){
            int v = tr.kth_element(b);
            tr.erase(b);
            tr.insert(a, v);
        }else if(t == 1){
            int ans = tr.get_between(a, b);
            printf("%d\n", ans);
        }else{
            tr.change_kth_element(a, b);
        }
    }
    return 0;
}