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;

constexpr int INF = (1 << 29);

class Node {
  public:
    int val;
    Node* lch;
    Node* rch;
    int pri, cnt, sum, min;

    Node(int v, int p) : val{v}, pri{p}, cnt{1}, sum{v}, min{val} {
        lch = rch = nullptr;
    }
};

class Treap {
  private:
    Node* root;

    int count(Node* t)
    {
        return t == nullptr ? 0 : t->cnt;
    }

    int sum(Node* t)
    {
        return t == nullptr ? 0 : t->sum;
    }

    int rmin(Node* t)
    {
        return t != nullptr ? t->min : INF;
    }
    
    Node* update(Node* t)
    {
        t->cnt = count(t->lch) + count(t->rch) + 1;
        t->sum = sum(t->lch) + sum(t->rch) + t->val;
        t->min = min(min(rmin(t->lch), rmin(t->rch)), t->val);
        return t;
    }

    Node* merge(Node* l, Node* r)
    {
        if (l == nullptr || r == nullptr) {
            return (l == nullptr ? 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 == nullptr) {
            return {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};
        }
    }

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

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

    int range_min(Node* t, int l, int r)
    {
        l = max(l, 0); r = min(r, count(t));
        if (l >= r) return INF;
        if (l == 0 && r == count(t)) {
            return t->min;
        }

        int sl = count(t->lch);
        int res = min(range_min(t->lch, l, r),
                      range_min(t->rch, l - sl - 1, r - sl - 1));

        if (l <= sl && sl < r) {
            res = min(res, t->val);
        }
        
        return res;            
    }
    
  public:
    Treap() : root{nullptr} {}

    int size()
    {
        return count(root);
    }
    
    void insert(int k, int val)
    {
        root = insert(root, k, val, rand());
    }
        
    void erase(int k)
    {
        root = erase(root, k);
    }

    void update(int k, int val)
    {
        erase(k);
        insert(k, val);
    }

    void shift(int l, int r)
    {
        auto s1 = split(root, r);
        auto s2 = split(s1.first, r - 1);
        auto s3 = split(s2.first, l);
        root = merge(s3.first, s2.second);
        root = merge(root, s3.second);
        root = merge(root, s1.second);
    }   
    
    int range_min(int l, int r)
    {
        return range_min(root, l, r + 1);
    }
};

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    int N, Q;
    cin >> N >> Q;
    
    Treap t;
    for (int i = 0; i < N; i++) {
        int a;
        cin >> a;
        t.insert(i, a);
    }

    while (Q--) {
        int x, y, z;
        cin >> x >> y >> z;

        switch (x) {
            case 0:
                t.shift(y, z + 1);
                break;
                
            case 1:
                cout << t.range_min(y, z) << endl;
                break;
                
            case 2:
                t.update(y, z);
                break;
        }
    }    
    return 0;
}