キャントストップ1発登頂チャンス cant stop oneshot probabilities

cantstop.rs

#![allow(dead_code)]

struct DiceRoll {
    st: Vec<Vec<usize>>,
    dices: usize,
}

fn dice_roll(dices: usize) -> DiceRoll {
    return DiceRoll {
        st: vec![vec![]],
        dices: dices,
    };
}

impl Iterator for DiceRoll {
    type Item = Vec<usize>;
    fn next(&mut self) -> Option<Vec<usize>> {
        while let Some(t) = self.st.pop() {
            if t.len() < self.dices {
                for i in 1..7 {
                    let mut old = t.clone();
                    old.push(i);
                    self.st.push(old)
                }
            } else {
                return Some(t);
            }
        }
        return None;
    }
}

struct AllTargets {
    st: Vec<Vec<usize>>,
    size: usize,
}

fn all_targets(size: usize) -> AllTargets {
    return AllTargets {
        st: vec![vec![1]],
        size: size,
    };
}

impl Iterator for AllTargets {
    type Item = Vec<usize>;
    fn next(&mut self) -> Option<Vec<usize>> {
        while let Some(t) = self.st.pop() {
            if t.len() - 1 < self.size {
                for i in (t[t.len() - 1] + 1)..13 {
                    let mut old = t.clone();
                    old.push(i);
                    self.st.push(old)
                }
            } else {
                return Some(t[1..self.size + 1].to_vec());
            }
        }
        return None;
    }
}

fn all_hips(dices: Vec<usize>) -> Vec<(usize, usize)> {
    let sum = dices.iter().fold(0, |s, a| s + a);
    let a = vec![
        dices[0] + dices[1],
        dices[1] + dices[2],
        dices[2] + dices[0],
    ];
    return a.iter().map(|&s| (s, sum - s)).collect();
}

fn succ_comb(dices: &Vec<usize>, targets: &Vec<usize>) -> bool {
    for (x, y) in all_hips(dices.clone()) {
        if targets.iter().any(|&i| i == x || i == y) {
            return true;
        }
    }
    return false;
}

fn fail_rate(dices: usize, targets: &Vec<usize>) -> f64 {
    let mut sum = 0;
    let mut failed = 0;
    for t in dice_roll(dices) {
        sum += 1;
        if !succ_comb(&t, &targets) {
            failed += 1;
        }
    }
    return failed as f64 / (sum as f64);
}

fn all_fail_rate(dices: usize, targets: usize) -> Vec<(Vec<usize>, f64)> {
    let mut res = vec![];
    for t in all_targets(targets) {
        let f = fail_rate(dices, &t);
        res.push((t, f));
    }
    return res;
}

fn comp_succ(dices: usize, targets: &Vec<usize>, remains: &Vec<usize>) -> f64 {
    // DP[0][1][2] -> rate
    let mut dp = vec![vec! {vec!{0.0; remains[2]+1}; remains[1]+1}; remains[0] + 1];
    dp[0][0][0] = 1.0;
    for t0 in 0..remains[0] + 1 {
        for t1 in 0..remains[1] + 1 {
            for t2 in 0..remains[2] + 1 {
                if t0 == 0 && t1 == 0 && t2 == 0 {
                    continue;
                }
                let mut cur = targets.clone();
                if t0 == 0 {
                    cur[0] = 0
                }
                if t1 == 0 {
                    cur[1] = 0
                }
                if t2 == 0 {
                    cur[2] = 0
                }
                let mut sum = 0;
                let mut nv = 0.0f64;
                for d in dice_roll(dices) {
                    let mut rate = 0.0f64;
                    for (x, y) in all_hips(d.clone()) {
                        let ix = cur.iter().position(|&i| i == x);
                        let iy = cur.iter().position(|&i| i == y);
                        let c = |k| match k {
                            None => vec![0, 0, 0],
                            Some(0) => vec![1, 0, 0],
                            Some(1) => vec![0, 1, 0],
                            Some(2) => vec![0, 0, 1],
                            Some(_) => unreachable!(),
                        };
                        let cx = c(ix);
                        let cy = c(iy);
                        let c = vec![cx[0] + cy[0], cx[1] + cy[1], cx[2] + cy[2]];
                        let s = |a, b| ((a as i64 - b) as i64).max(0) as usize;
                        let r = dp[s(t0, c[0])][s(t1, c[1])][s(t2, c[2])];
                        rate = rate.max(r);
                    }
                    nv += rate;
                    sum += 1;
                }
                dp[t0][t1][t2] = nv as f64 / sum as f64;
            }
        }
    }

    return dp[remains[0]][remains[1]][remains[2]];
}

fn all_succ() {
    let ms = vec![0, 0, 3, 5, 7, 9, 11, 13, 11, 9, 7, 5, 3];
    for ts in all_targets(3) {
        let m: Vec<usize> = ts.iter().map(|&s| ms[s]).collect();
        let r = comp_succ(4, &ts, &m);
        println!("{:?} {:?} => {}", ts, m, r)
    }
}

fn playout(tries: usize, targets: &Vec<usize>, remains: &Vec<usize>) -> f64 {
    let mut sum = 0;
    let mut succ = 0;
    for _ in 0..tries {
        if playonce(targets, remains) {
            succ += 1;
        }
        sum += 1;
    }
    return succ as f64 / sum as f64;
}
fn playonce(targets: &Vec<usize>, remains: &Vec<usize>) -> bool {
    use rand::seq::SliceRandom;
    use rand::Rng;
    let mut rng = rand::thread_rng();
    let mut remains: Vec<i64> = remains.iter().map(|&n| n as i64).collect();
    loop {
        let d = vec![
            rng.gen_range(1, 7),
            rng.gen_range(1, 7),
            rng.gen_range(1, 7),
            rng.gen_range(1, 7),
        ];
        let mut ok = false;
        let mut cur = targets.clone();
        if remains[0] <= 0 {
            cur[0] = 0
        }
        if remains[1] <= 0 {
            cur[1] = 0
        }
        if remains[2] <= 0 {
            cur[2] = 0
        }
        for (x, y) in all_hips(d.clone()) {
            let ix = cur.iter().position(|&i| i == x);
            let iy = cur.iter().position(|&i| i == y);
            if ix == None && iy == None {
                continue;
            }
            if let Some(ix) = ix {
                remains[ix] -= 1
            }
            if let Some(iy) = iy {
                remains[iy] -= 1
            }
            ok = true;
            break;
        }
        if !ok {
            return false;
        }
        if remains.iter().all(|&i| i <= 0) {
            return true;
        }
    }
}
fn main() {
    //println!("{:?}", dice_move(4, &vec!{2, 3, 5}));
    all_succ();
    //println!("{:?}", comp_succ(4, &vec! {6,7,8}, &vec! {2,2,2}));
    //println!("{:?}", playout(100000, &vec! {6,7,8}, &vec! {2,2,2}));
    //fail_rate(4, &vec!{6,7,8});
    //let mut rates = all_fail_rate(4, 3);
    //rates.sort_by(|c, d| c.1.partial_cmp(&d.1).unwrap());
    //println!("{:?}", rates);
}

確率表 probabilities

[2, 3, 4]    [3, 5, 7]    => 0.000025564439917238523
[2, 3, 5]    [3, 5, 9]    => 0.00005927363292716724
[2, 3, 6]    [3, 5, 11]   => 0.0003492213715781228
[2, 3, 7]    [3, 5, 13]   => 0.0012078961974730021
[2, 3, 8]    [3, 5, 11]   => 0.0011801101801356038
[2, 3, 9]    [3, 5, 9]    => 0.0005555811764881801
[2, 3, 10]   [3, 5, 7]    => 0.00019540987013117172
[2, 3, 11]   [3, 5, 5]    => 0.00004896451206860815
[2, 3, 12]   [3, 5, 3]    => 0.000023890874680418654
[2, 4, 5]    [3, 7, 9]    => 0.00020491958831998764
[2, 4, 6]    [3, 7, 11]   => 0.0014330734745359168
[2, 4, 7]    [3, 7, 13]   => 0.00368435603769096
[2, 4, 8]    [3, 7, 11]   => 0.0037016067910537395
[2, 4, 9]    [3, 7, 9]    => 0.0012210239234110823
[2, 4, 10]   [3, 7, 7]    => 0.0009434451208343333
[2, 4, 11]   [3, 7, 5]    => 0.00020972437016999315
[2, 4, 12]   [3, 7, 3]    => 0.00008801206947410924
[2, 5, 6]    [3, 9, 11]   => 0.0016962562883425507
[2, 5, 7]    [3, 9, 13]   => 0.003904996096209413
[2, 5, 8]    [3, 9, 11]   => 0.005045008379149678
[2, 5, 9]    [3, 9, 9]    => 0.0012841475752787043
[2, 5, 10]   [3, 9, 7]    => 0.0012310077072657751
[2, 5, 11]   [3, 9, 5]    => 0.0005993471314746929
[2, 5, 12]   [3, 9, 3]    => 0.00022515038009823107
[2, 6, 7]    [3, 11, 13]  => 0.013344623702580582
[2, 6, 8]    [3, 11, 11]  => 0.01595893560653182
[2, 6, 9]    [3, 11, 9]   => 0.0054833151535683385
[2, 6, 10]   [3, 11, 7]   => 0.003595726950184641
[2, 6, 11]   [3, 11, 5]   => 0.0013013575405945283
[2, 6, 12]   [3, 11, 3]   => 0.001053846095238263
[2, 7, 8]    [3, 13, 11]  => 0.02073492531747651
[2, 7, 9]    [3, 13, 9]   => 0.006220546534082804
[2, 7, 10]   [3, 13, 7]   => 0.00581978912998253
[2, 7, 11]   [3, 13, 5]   => 0.0020239523510390926
[2, 7, 12]   [3, 13, 3]   => 0.0021481134531276575
[2, 8, 9]    [3, 11, 9]   => 0.004153327241436465
[2, 8, 10]   [3, 11, 7]   => 0.003663851585755454
[2, 8, 11]   [3, 11, 5]   => 0.0009040918952828436
[2, 8, 12]   [3, 11, 3]   => 0.0010538460952382717
[2, 9, 10]   [3, 9, 7]    => 0.0005284985092256307
[2, 9, 11]   [3, 9, 5]    => 0.00016431921767766944
[2, 9, 12]   [3, 9, 3]    => 0.00022515038009823292
[2, 10, 11]  [3, 7, 5]    => 0.0000805487092437797
[2, 10, 12]  [3, 7, 3]    => 0.0000880120694741112
[2, 11, 12]  [3, 5, 3]    => 0.000023890874680418735
[3, 4, 5]    [5, 7, 9]    => 0.00016562394472824683
[3, 4, 6]    [5, 7, 11]   => 0.0008773157426008451
[3, 4, 7]    [5, 7, 13]   => 0.0024628283625393117
[3, 4, 8]    [5, 7, 11]   => 0.0025458986869387884
[3, 4, 9]    [5, 7, 9]    => 0.0015923944959876943
[3, 4, 10]   [5, 7, 7]    => 0.0010510706522522612
[3, 4, 11]   [5, 7, 5]    => 0.00021750782989781977
[3, 4, 12]   [5, 7, 3]    => 0.00008054870924377988
[3, 5, 6]    [5, 9, 11]   => 0.0013856375087786684
[3, 5, 7]    [5, 9, 13]   => 0.002178769424250058
[3, 5, 8]    [5, 9, 11]   => 0.003290067932883377
[3, 5, 9]    [5, 9, 9]    => 0.0015366847973816544
[3, 5, 10]   [5, 9, 7]    => 0.0011270203007502679
[3, 5, 11]   [5, 9, 5]    => 0.0004770496936408061
[3, 5, 12]   [5, 9, 3]    => 0.00016431921767766974
[3, 6, 7]    [5, 11, 13]  => 0.013083416029259857
[3, 6, 8]    [5, 11, 11]  => 0.009951723299418534
[3, 6, 9]    [5, 11, 9]   => 0.0050569479516541374
[3, 6, 10]   [5, 11, 7]   => 0.004299882462624441
[3, 6, 11]   [5, 11, 5]   => 0.0012754341757669808
[3, 6, 12]   [5, 11, 3]   => 0.0009040918952828353
[3, 7, 8]    [5, 13, 11]  => 0.023089935370854187
[3, 7, 9]    [5, 13, 9]   => 0.007512966609244167
[3, 7, 10]   [5, 13, 7]   => 0.006384508034410984
[3, 7, 11]   [5, 13, 5]   => 0.0019493193697614753
[3, 7, 12]   [5, 13, 3]   => 0.0020239523510390987
[3, 8, 9]    [5, 11, 9]   => 0.005802882626755753
[3, 8, 10]   [5, 11, 7]   => 0.0052977308866770725
[3, 8, 11]   [5, 11, 5]   => 0.0012754341757669986
[3, 8, 12]   [5, 11, 3]   => 0.0013013575405945407
[3, 9, 10]   [5, 9, 7]    => 0.0016027081654223525
[3, 9, 11]   [5, 9, 5]    => 0.00047704969364080116
[3, 9, 12]   [5, 9, 3]    => 0.0005993471314746975
[3, 10, 11]  [5, 7, 5]    => 0.00021750782989781608
[3, 10, 12]  [5, 7, 3]    => 0.00020972437016999242
[3, 11, 12]  [5, 5, 3]    => 0.00004896451206860658
[4, 5, 6]    [7, 9, 11]   => 0.002572182187115604
[4, 5, 7]    [7, 9, 13]   => 0.008419152469681558
[4, 5, 8]    [7, 9, 11]   => 0.007808721932728033
[4, 5, 9]    [7, 9, 9]    => 0.0026128589801566494
[4, 5, 10]   [7, 9, 7]    => 0.0038982399044457015
[4, 5, 11]   [7, 9, 5]    => 0.001602708165422363
[4, 5, 12]   [7, 9, 3]    => 0.0005284985092256341
[4, 6, 7]    [7, 11, 13]  => 0.02376029812820459
[4, 6, 8]    [7, 11, 11]  => 0.03482147108433543
[4, 6, 9]    [7, 11, 9]   => 0.011957962995389624
[4, 6, 10]   [7, 11, 7]   => 0.01549556825974864
[4, 6, 11]   [7, 11, 5]   => 0.00529773088667707
[4, 6, 12]   [7, 11, 3]   => 0.003663851585755429
[4, 7, 8]    [7, 13, 11]  => 0.03418466641667157
[4, 7, 9]    [7, 13, 9]   => 0.022045325734773642
[4, 7, 10]   [7, 13, 7]   => 0.0158805379200486
[4, 7, 11]   [7, 13, 5]   => 0.006384508034410957
[4, 7, 12]   [7, 13, 3]   => 0.005819789129982582
[4, 8, 9]    [7, 11, 9]   => 0.011089383300200801
[4, 8, 10]   [7, 11, 7]   => 0.015495568259748523
[4, 8, 11]   [7, 11, 5]   => 0.00429988246262429
[4, 8, 12]   [7, 11, 3]   => 0.0035957269501848102
[4, 9, 10]   [7, 9, 7]    => 0.0038982399044456754
[4, 9, 11]   [7, 9, 5]    => 0.0011270203007502312
[4, 9, 12]   [7, 9, 3]    => 0.0012310077072657298
[4, 10, 11]  [7, 7, 5]    => 0.0010510706522522538
[4, 10, 12]  [7, 7, 3]    => 0.000943445120834327
[4, 11, 12]  [7, 5, 3]    => 0.00019540987013117277
[5, 6, 7]    [9, 11, 13]  => 0.02316894550327935
[5, 6, 8]    [9, 11, 11]  => 0.02724093465836428
[5, 6, 9]    [9, 11, 9]   => 0.012242392243214485
[5, 6, 10]   [9, 11, 7]   => 0.01108938330020087
[5, 6, 11]   [9, 11, 5]   => 0.005802882626755763
[5, 6, 12]   [9, 11, 3]   => 0.00415332724143643
[5, 7, 8]    [9, 13, 11]  => 0.04481735379193718
[5, 7, 9]    [9, 13, 9]   => 0.009863523031459806
[5, 7, 10]   [9, 13, 7]   => 0.022045325734773847
[5, 7, 11]   [9, 13, 5]   => 0.007512966609244104
[5, 7, 12]   [9, 13, 3]   => 0.006220546534082767
[5, 8, 9]    [9, 11, 9]   => 0.012242392243214406
[5, 8, 10]   [9, 11, 7]   => 0.011957962995389586
[5, 8, 11]   [9, 11, 5]   => 0.005056947951653804
[5, 8, 12]   [9, 11, 3]   => 0.005483315153568336
[5, 9, 10]   [9, 9, 7]    => 0.00261285898015666
[5, 9, 11]   [9, 9, 5]    => 0.0015366847973816604
[5, 9, 12]   [9, 9, 3]    => 0.0012841475752786665
[5, 10, 11]  [9, 7, 5]    => 0.0015923944959876717
[5, 10, 12]  [9, 7, 3]    => 0.0012210239234110832
[5, 11, 12]  [9, 5, 3]    => 0.0005555811764881666
[6, 7, 8]    [11, 13, 11] => 0.057548888319900036
[6, 7, 9]    [11, 13, 9]  => 0.044817353791937325
[6, 7, 10]   [11, 13, 7]  => 0.03418466641667139
[6, 7, 11]   [11, 13, 5]  => 0.02308993537085435
[6, 7, 12]   [11, 13, 3]  => 0.020734925317476702
[6, 8, 9]    [11, 11, 9]  => 0.027240934658364517
[6, 8, 10]   [11, 11, 7]  => 0.03482147108433481
[6, 8, 11]   [11, 11, 5]  => 0.009951723299418562
[6, 8, 12]   [11, 11, 3]  => 0.015958935606531915
[6, 9, 10]   [11, 9, 7]   => 0.0078087219327280305
[6, 9, 11]   [11, 9, 5]   => 0.003290067932883336
[6, 9, 12]   [11, 9, 3]   => 0.005045008379149739
[6, 10, 11]  [11, 7, 5]   => 0.002545898686938808
[6, 10, 12]  [11, 7, 3]   => 0.003701606791053711
[6, 11, 12]  [11, 5, 3]   => 0.001180110180135599
[7, 8, 9]    [13, 11, 9]  => 0.023168945503279262
[7, 8, 10]   [13, 11, 7]  => 0.023760298128204432
[7, 8, 11]   [13, 11, 5]  => 0.013083416029259588
[7, 8, 12]   [13, 11, 3]  => 0.013344623702580615
[7, 9, 10]   [13, 9, 7]   => 0.008419152469681534
[7, 9, 11]   [13, 9, 5]   => 0.0021787694242500107
[7, 9, 12]   [13, 9, 3]   => 0.003904996096209468
[7, 10, 11]  [13, 7, 5]   => 0.0024628283625393547
[7, 10, 12]  [13, 7, 3]   => 0.003684356037691129
[7, 11, 12]  [13, 5, 3]   => 0.0012078961974729672
[8, 9, 10]   [11, 9, 7]   => 0.0025721821871155385
[8, 9, 11]   [11, 9, 5]   => 0.0013856375087786834
[8, 9, 12]   [11, 9, 3]   => 0.0016962562883425644
[8, 10, 11]  [11, 7, 5]   => 0.0008773157426008375
[8, 10, 12]  [11, 7, 3]   => 0.0014330734745359405
[8, 11, 12]  [11, 5, 3]   => 0.00034922137157813223
[9, 10, 11]  [9, 7, 5]    => 0.00016562394472824425
[9, 10, 12]  [9, 7, 3]    => 0.00020491958831998867
[9, 11, 12]  [9, 5, 3]    => 0.00005927363292716705
[10, 11, 12] [7, 5, 3]    => 0.000025564439917238984