Call take arrays once per repartitioned input batch (#22159)

## Which issue does this PR close?

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- Does not close an issue.
- This is targeted toward high fanout repartitions we see in shuffles in
distributed-datafusion
(datafusion-contrib/datafusion-distributed#385,
datafusion-contrib/datafusion-distributed#353).
- Related ongoing effort to improve metrics and repartition performance:
#21148, #22155.

## Rationale for this change

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Why are you proposing this change? If this is already explained clearly
in the issue then this section is not needed.
Explaining clearly why changes are proposed helps reviewers understand
your changes and offer better suggestions for fixes.
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Hash repartition currently builds one output batch per non-empty target
partition by calling `take_arrays` separately for each partition. At
high fanout this means an input batch can issue many take kernels, which
shows in repartition-heavy queries.

This changes hash repartition to concatenate the per-partition row
indices, call `take_arrays` once for the input batch, and then slice the
reordered batch back into per-partition output batches.

This is complementary to #22010: that PR reduces channel/gate traffic
from many small batches, while this PR reduces the Arrow take-kernel
work required to create the repartitioned batches.

## What changes are included in this PR?

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There is no need to duplicate the description in the issue here but it
is sometimes worth providing a summary of the individual changes in this
PR.
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- Replaces per-partition hash repartition `take_arrays` calls with one
grouped `take_arrays` call per input batch.
- Tracks partition ranges into the grouped reordered batch and returns
zero-copy `RecordBatch::slice` outputs for each non-empty partition.

How the grouped take works:

```text
input rows:        0   1   2   3   4   5   6

partition 0:      [2, 5]
partition 1:      []
partition 2:      [0, 3, 4]
partition 3:      [1, 6]

grouped indices:  [2, 5, 0, 3, 4, 1, 6]
partition ranges: [(0, start=0, len=2),
                   (2, start=2, len=3),
                   (3, start=5, len=2)]

take once:        rows [2, 5, 0, 3, 4, 1, 6]
slice outputs:    partition 0 = slice(0, 2)
                  partition 2 = slice(2, 3)
                  partition 3 = slice(5, 2)
```

## Are these changes tested?

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- `cargo test -p datafusion-physical-plan repartition --lib`

**Benchmarks:**

Default TPCH SF10 summary, with no `--batch-size` override:

| Partitions | main total ms | grouped total ms | change | wins | losses
| biggest win | biggest loss
|---:|---:|---:|---:|---:|---:|---:|---:|
| 8 | 6234.28 | 6149.98 | -1.35% | 10 | 12 | Q3 -22.12% | Q21 5.47% |
| 16 | 5602.63 | 5427.40 | -3.13% | 18 | 4 | Q21 -10.67% | Q10 4.47% |
| 32 | 6097.10 | 5738.12 | -5.89% | 20 | 2 | Q8 -10.45% | Q6 0.47% |
| 64 | 7194.70 | 6693.30 | -6.97% | 15 | 7 | Q21 -15.92% | Q1 5.02% |
| 300 | 26276.60 | 23701.32 | -9.80% | 19 | 3 | Q21 -24.24% | Q1 9.45% |


<details>
<summary>TPCH SF10 default batch size, 8 partitions, all
queries</summary>

| Query | main ms | grouped ms | change | speedup |
|---:|---:|---:|---:|---:|
| Q1 | 411.40 | 356.46 | -13.35% | 1.154x |
| Q2 | 117.97 | 95.68 | -18.89% | 1.233x |
| Q3 | 278.88 | 217.20 | -22.12% | 1.284x |
| Q4 | 104.92 | 98.47 | -6.15% | 1.065x |
| Q5 | 311.36 | 302.12 | -2.97% | 1.031x |
| Q6 | 133.82 | 135.13 | 0.98% | 0.990x |
| Q7 | 366.32 | 360.50 | -1.59% | 1.016x |
| Q8 | 408.86 | 391.14 | -4.33% | 1.045x |
| Q9 | 509.62 | 515.74 | 1.20% | 0.988x |
| Q10 | 278.97 | 273.80 | -1.85% | 1.019x |
| Q11 | 76.55 | 75.34 | -1.58% | 1.016x |
| Q12 | 175.56 | 180.87 | 3.03% | 0.971x |
| Q13 | 211.03 | 221.03 | 4.74% | 0.955x |
| Q14 | 183.05 | 189.95 | 3.77% | 0.964x |
| Q15 | 318.46 | 328.85 | 3.26% | 0.968x |
| Q16 | 57.66 | 57.70 | 0.08% | 0.999x |
| Q17 | 505.05 | 503.77 | -0.25% | 1.003x |
| Q18 | 596.49 | 602.77 | 1.05% | 0.990x |
| Q19 | 273.60 | 283.41 | 3.58% | 0.965x |
| Q20 | 255.73 | 267.30 | 4.52% | 0.957x |
| Q21 | 592.44 | 624.83 | 5.47% | 0.948x |
| Q22 | 66.54 | 67.91 | 2.05% | 0.980x |

</details>

<details>
<summary>TPCH SF10 default batch size, 16 partitions, all
queries</summary>

| Query | main ms | grouped ms | change | speedup |
|---:|---:|---:|---:|---:|
| Q1 | 278.95 | 276.85 | -0.76% | 1.008x |
| Q2 | 95.84 | 94.86 | -1.02% | 1.010x |
| Q3 | 205.24 | 195.05 | -4.97% | 1.052x |
| Q4 | 93.60 | 90.58 | -3.23% | 1.033x |
| Q5 | 292.34 | 289.93 | -0.82% | 1.008x |
| Q6 | 103.59 | 106.02 | 2.35% | 0.977x |
| Q7 | 370.86 | 365.40 | -1.47% | 1.015x |
| Q8 | 392.01 | 364.63 | -6.98% | 1.075x |
| Q9 | 512.66 | 483.45 | -5.70% | 1.060x |
| Q10 | 246.01 | 257.01 | 4.47% | 0.957x |
| Q11 | 73.33 | 70.21 | -4.26% | 1.045x |
| Q12 | 143.58 | 143.53 | -0.04% | 1.000x |
| Q13 | 193.30 | 193.57 | 0.14% | 0.999x |
| Q14 | 157.01 | 146.14 | -6.92% | 1.074x |
| Q15 | 255.58 | 258.73 | 1.23% | 0.988x |
| Q16 | 58.90 | 57.14 | -2.97% | 1.031x |
| Q17 | 515.22 | 491.16 | -4.67% | 1.049x |
| Q18 | 518.50 | 516.90 | -0.31% | 1.003x |
| Q19 | 212.28 | 211.63 | -0.30% | 1.003x |
| Q20 | 229.34 | 224.54 | -2.09% | 1.021x |
| Q21 | 594.29 | 530.87 | -10.67% | 1.119x |
| Q22 | 60.20 | 59.18 | -1.70% | 1.017x |

</details>

<details>
<summary>TPCH SF10 default batch size, 32 partitions, all
queries</summary>

| Query | main ms | grouped ms | change | speedup |
|---:|---:|---:|---:|---:|
| Q1 | 294.06 | 286.80 | -2.47% | 1.025x |
| Q2 | 110.59 | 103.55 | -6.37% | 1.068x |
| Q3 | 227.86 | 215.08 | -5.61% | 1.059x |
| Q4 | 110.99 | 102.77 | -7.41% | 1.080x |
| Q5 | 347.34 | 319.49 | -8.02% | 1.087x |
| Q6 | 109.39 | 109.91 | 0.47% | 0.995x |
| Q7 | 423.98 | 385.42 | -9.09% | 1.100x |
| Q8 | 428.83 | 384.00 | -10.45% | 1.117x |
| Q9 | 559.81 | 510.72 | -8.77% | 1.096x |
| Q10 | 269.17 | 265.02 | -1.54% | 1.016x |
| Q11 | 85.99 | 80.21 | -6.72% | 1.072x |
| Q12 | 153.67 | 150.36 | -2.15% | 1.022x |
| Q13 | 197.90 | 188.72 | -4.64% | 1.049x |
| Q14 | 161.28 | 153.93 | -4.55% | 1.048x |
| Q15 | 259.92 | 261.01 | 0.42% | 0.996x |
| Q16 | 64.90 | 63.70 | -1.85% | 1.019x |
| Q17 | 574.18 | 531.76 | -7.39% | 1.080x |
| Q18 | 572.23 | 538.68 | -5.86% | 1.062x |
| Q19 | 227.95 | 220.19 | -3.41% | 1.035x |
| Q20 | 232.25 | 225.80 | -2.78% | 1.029x |
| Q21 | 622.54 | 579.94 | -6.84% | 1.073x |
| Q22 | 62.29 | 61.06 | -1.98% | 1.020x |

</details>

<details>
<summary>TPCH SF10 default batch size, 64 partitions, all
queries</summary>

| Query | main ms | grouped ms | change | speedup |
|---:|---:|---:|---:|---:|
| Q1 | 285.10 | 299.41 | 5.02% | 0.952x |
| Q2 | 161.42 | 153.51 | -4.90% | 1.052x |
| Q3 | 297.85 | 272.09 | -8.65% | 1.095x |
| Q4 | 147.28 | 140.69 | -4.47% | 1.047x |
| Q5 | 428.29 | 381.28 | -10.98% | 1.123x |
| Q6 | 106.27 | 108.41 | 2.02% | 0.980x |
| Q7 | 494.50 | 443.89 | -10.23% | 1.114x |
| Q8 | 507.01 | 446.69 | -11.90% | 1.135x |
| Q9 | 667.11 | 624.78 | -6.34% | 1.068x |
| Q10 | 294.91 | 299.05 | 1.40% | 0.986x |
| Q11 | 112.17 | 104.79 | -6.57% | 1.070x |
| Q12 | 168.23 | 166.87 | -0.81% | 1.008x |
| Q13 | 198.74 | 196.30 | -1.23% | 1.012x |
| Q14 | 175.31 | 177.74 | 1.39% | 0.986x |
| Q15 | 265.68 | 265.71 | 0.01% | 1.000x |
| Q16 | 85.69 | 82.93 | -3.22% | 1.033x |
| Q17 | 691.32 | 629.09 | -9.00% | 1.099x |
| Q18 | 697.85 | 617.88 | -11.46% | 1.129x |
| Q19 | 237.00 | 243.78 | 2.86% | 0.972x |
| Q20 | 272.55 | 278.57 | 2.21% | 0.978x |
| Q21 | 813.29 | 683.82 | -15.92% | 1.189x |
| Q22 | 87.14 | 76.04 | -12.73% | 1.146x |

</details>

<details>
<summary>TPCH SF10 default batch size, 300 partitions, all
queries</summary>

| Query | main ms | grouped ms | change | speedup |
|---:|---:|---:|---:|---:|
| Q1 | 277.84 | 304.08 | 9.45% | 0.914x |
| Q2 | 1303.10 | 1268.65 | -2.64% | 1.027x |
| Q3 | 1496.14 | 1393.15 | -6.88% | 1.074x |
| Q4 | 681.20 | 652.85 | -4.16% | 1.043x |
| Q5 | 1680.43 | 1469.91 | -12.53% | 1.143x |
| Q6 | 100.65 | 105.75 | 5.07% | 0.952x |
| Q7 | 1880.26 | 1652.83 | -12.10% | 1.138x |
| Q8 | 1956.81 | 1760.72 | -10.02% | 1.111x |
| Q9 | 1787.75 | 1454.84 | -18.62% | 1.229x |
| Q10 | 1334.62 | 1296.02 | -2.89% | 1.030x |
| Q11 | 1018.99 | 994.13 | -2.44% | 1.025x |
| Q12 | 768.97 | 780.88 | 1.55% | 0.985x |
| Q13 | 671.88 | 638.51 | -4.97% | 1.052x |
| Q14 | 603.10 | 586.19 | -2.80% | 1.029x |
| Q15 | 302.19 | 295.28 | -2.29% | 1.023x |
| Q16 | 597.64 | 585.39 | -2.05% | 1.021x |
| Q17 | 1963.57 | 1712.46 | -12.79% | 1.147x |
| Q18 | 1942.46 | 1634.96 | -15.83% | 1.188x |
| Q19 | 818.85 | 808.19 | -1.30% | 1.013x |
| Q20 | 1499.39 | 1468.55 | -2.06% | 1.021x |
| Q21 | 3006.35 | 2277.49 | -24.24% | 1.320x |
| Q22 | 584.39 | 560.47 | -4.09% | 1.043x |

</details>

**Stress cases:** 
- These runs use `--batch-size 1024` to stress the repartition path.
They are included to show the mechanism under smaller input batches and
higher output fanout, not as the primary end-to-end performance claim.

<details>
<summary>TPCH SF10, 8 partitions, all queries</summary>

| Query | main ms | grouped ms | change | speedup |
|---:|---:|---:|---:|---:|
| Q1 | 640.78 | 451.82 | -29.49% | 1.420x |
| Q2 | 315.81 | 150.07 | -52.48% | 2.100x |
| Q3 | 899.21 | 375.88 | -58.20% | 2.390x |
| Q4 | 469.31 | 217.07 | -53.75% | 2.160x |
| Q5 | 1131.37 | 446.36 | -60.55% | 2.530x |
| Q6 | 376.40 | 163.66 | -56.52% | 2.300x |
| Q7 | 1388.40 | 484.36 | -65.11% | 2.870x |
| Q8 | 1369.67 | 571.62 | -58.27% | 2.400x |
| Q9 | 1834.81 | 739.88 | -59.68% | 2.480x |
| Q10 | 813.73 | 361.94 | -55.52% | 2.250x |
| Q11 | 267.06 | 114.84 | -57.00% | 2.330x |
| Q12 | 526.41 | 250.39 | -52.43% | 2.100x |
| Q13 | 760.54 | 324.78 | -57.30% | 2.340x |
| Q14 | 446.91 | 221.04 | -50.54% | 2.020x |
| Q15 | 764.64 | 375.67 | -50.87% | 2.040x |
| Q16 | 167.74 | 80.36 | -52.09% | 2.090x |
| Q17 | 1801.72 | 763.58 | -57.62% | 2.360x |
| Q18 | 3303.89 | 1649.87 | -50.06% | 2.000x |
| Q19 | 694.16 | 354.97 | -48.86% | 1.960x |
| Q20 | 693.91 | 323.17 | -53.43% | 2.150x |
| Q21 | 3112.83 | 1065.36 | -65.78% | 2.920x |
| Q22 | 205.88 | 95.97 | -53.38% | 2.150x |

</details>

<details>
<summary>TPCH SF10, 16 partitions, all queries</summary>

| Query | main ms | grouped ms | change | speedup |
|---:|---:|---:|---:|---:|
| Q1 | 518.84 | 328.66 | -36.66% | 1.580x |
| Q2 | 350.47 | 148.64 | -57.59% | 2.360x |
| Q3 | 1003.55 | 371.04 | -63.03% | 2.700x |
| Q4 | 589.70 | 258.05 | -56.24% | 2.290x |
| Q5 | 1343.64 | 506.01 | -62.34% | 2.660x |
| Q6 | 322.21 | 130.93 | -59.37% | 2.460x |
| Q7 | 1527.85 | 550.88 | -63.94% | 2.770x |
| Q8 | 1476.46 | 578.77 | -60.80% | 2.550x |
| Q9 | 2091.16 | 785.54 | -62.44% | 2.660x |
| Q10 | 817.98 | 331.02 | -59.53% | 2.470x |
| Q11 | 341.46 | 123.31 | -63.89% | 2.770x |
| Q12 | 493.51 | 221.61 | -55.10% | 2.230x |
| Q13 | 690.52 | 290.54 | -57.92% | 2.380x |
| Q14 | 410.54 | 171.45 | -58.24% | 2.390x |
| Q15 | 733.96 | 290.56 | -60.41% | 2.530x |
| Q16 | 197.35 | 86.09 | -56.37% | 2.290x |
| Q17 | 2089.12 | 828.96 | -60.32% | 2.520x |
| Q18 | 2712.00 | 1097.77 | -59.52% | 2.470x |
| Q19 | 602.77 | 260.74 | -56.74% | 2.310x |
| Q20 | 661.20 | 288.58 | -56.35% | 2.290x |
| Q21 | 5490.50 | 1151.50 | -79.03% | 4.770x |
| Q22 | 198.38 | 103.13 | -48.01% | 1.920x |

</details>

<details>
<summary>TPCH SF10, 32 partitions, all queries</summary>

| Query | main ms | grouped ms | change | speedup |
|---:|---:|---:|---:|---:|
| Q1 | 533.86 | 338.54 | -36.59% | 1.580x |
| Q2 | 439.59 | 199.50 | -54.62% | 2.200x |
| Q3 | 1242.19 | 510.11 | -58.93% | 2.440x |
| Q4 | 743.92 | 363.33 | -51.16% | 2.050x |
| Q5 | 1711.97 | 666.50 | -61.07% | 2.570x |
| Q6 | 325.39 | 134.07 | -58.80% | 2.430x |
| Q7 | 1947.59 | 722.22 | -62.92% | 2.700x |
| Q8 | 1914.31 | 775.62 | -59.48% | 2.470x |
| Q9 | 2662.07 | 976.47 | -63.32% | 2.730x |
| Q10 | 902.80 | 362.71 | -59.82% | 2.490x |
| Q11 | 400.93 | 170.81 | -57.40% | 2.350x |
| Q12 | 572.19 | 265.06 | -53.68% | 2.160x |
| Q13 | 736.31 | 296.82 | -59.69% | 2.480x |
| Q14 | 430.11 | 180.93 | -57.93% | 2.380x |
| Q15 | 732.36 | 327.12 | -55.33% | 2.240x |
| Q16 | 245.97 | 116.24 | -52.74% | 2.120x |
| Q17 | 2711.18 | 1100.17 | -59.42% | 2.460x |
| Q18 | 2946.70 | 1176.02 | -60.09% | 2.510x |
| Q19 | 600.47 | 258.58 | -56.94% | 2.320x |
| Q20 | 765.20 | 337.01 | -55.96% | 2.270x |
| Q21 | 10062.70 | 1534.95 | -84.75% | 6.560x |
| Q22 | 250.50 | 128.27 | -48.79% | 1.950x |

</details>

<details>
<summary>TPCH SF10, 64 partitions, all queries</summary>

| Query | main ms | grouped ms | change | speedup |
|---:|---:|---:|---:|---:|
| Q1 | 595.70 | 324.74 | -45.49% | 1.830x |
| Q2 | 663.08 | 305.30 | -53.96% | 2.170x |
| Q3 | 1744.90 | 727.81 | -58.29% | 2.400x |
| Q4 | 1070.72 | 566.20 | -47.12% | 1.890x |
| Q5 | 2447.07 | 938.91 | -61.63% | 2.610x |
| Q6 | 315.47 | 132.73 | -57.93% | 2.380x |
| Q7 | 2807.33 | 1004.83 | -64.21% | 2.790x |
| Q8 | 2674.51 | 1069.64 | -60.01% | 2.500x |
| Q9 | 3777.94 | 1424.08 | -62.31% | 2.650x |
| Q10 | 1086.91 | 469.38 | -56.82% | 2.320x |
| Q11 | 575.59 | 264.02 | -54.13% | 2.180x |
| Q12 | 841.83 | 387.25 | -54.00% | 2.170x |
| Q13 | 867.57 | 379.90 | -56.21% | 2.280x |
| Q14 | 470.87 | 214.58 | -54.43% | 2.190x |
| Q15 | 762.07 | 340.55 | -55.31% | 2.240x |
| Q16 | 337.20 | 179.25 | -46.84% | 1.880x |
| Q17 | 3953.82 | 1701.46 | -56.97% | 2.320x |
| Q18 | 3763.51 | 1606.90 | -57.30% | 2.340x |
| Q19 | 644.43 | 314.27 | -51.23% | 2.050x |
| Q20 | 973.56 | 453.24 | -53.45% | 2.150x |
| Q21 | 19356.91 | 2396.96 | -87.62% | 8.080x |
| Q22 | 366.20 | 195.40 | -46.64% | 1.870x |

</details>





<details>
<summary>TPCH SF10, 300 partitions, targeted high-fanout
queries</summary>

Yes this is a real use case for fanout in distributed-datafusion

| Query | main ms | grouped ms | change | speedup |
|---:|---:|---:|---:|---:|
| Q3 | 2543.94 | 2250.91 | -11.52% | 1.130x |
| Q9 | 6495.22 | 4755.78 | -26.78% | 1.370x |
| Q10 | 1869.05 | 1709.18 | -8.55% | 1.090x |
| Q13 | 1238.63 | 1157.47 | -6.55% | 1.070x |
| Q15 | 461.51 | 446.25 | -3.31% | 1.030x |
| Q21 | 37810.29 | 5594.01 | -85.21% | 6.760x |
| Q22 | 1084.95 | 1058.74 | -2.42% | 1.020x |

</details>

<details>
<summary>TPCH SF10, 300 partitions, peak RSS stress</summary>

Measured with `/usr/bin/time -l`, one iteration, `--batch-size 1024`,
`--partitions 300`, and no DataFusion memory limit. RSS is process peak
resident set size from the OS.

| Query | main ms | grouped ms | time change | main peak RSS | grouped
peak RSS | RSS change |
|---:|---:|---:|---:|---:|---:|---:|
| Q7 | 5171.45 | 4151.15 | -19.73% | 3.69 GiB | 3.75 GiB | 1.61% |
| Q9 | 6055.57 | 4758.10 | -21.43% | 4.01 GiB | 4.01 GiB | 0.04% |
| Q21 | 36300.80 | 5810.14 | -83.99% | 2.96 GiB | 2.05 GiB | -30.79% |

</details>

#### Memory concern and follow-up work

This PR changes output batches from materializing per-partition batches
to slices of one reordered batch. This means sibling slices can share
the same buffers.

Potential concern:

```text
one reordered batch allocation
  -> slice for partition 0
  -> slice for partition 1
  -> slice for partition 2
```

A slow output partition can keep the shared reordered batch buffers
alive until its slice is dropped. Also,
`RecordBatch::get_array_memory_size()` may count shared slice buffers
repeatedly when repartition reserves memory per output batch.

The peak RSS stress above did not show a process-memory regression in
the measured queries. Follow-up work should add buffer-aware accounting.

## Are there any user-facing changes?

<!--
If there are user-facing changes then we may require documentation to be
updated before approving the PR.
-->

No.

<!--
If there are any breaking changes to public APIs, please add the `api
change` label.
-->

Author: gene-bordegaray

datafusion/physical-plan/src/repartition/mod.rs

@@ -52,8 +52,7 @@ use datafusion_common::stats::Precision;
 use datafusion_common::tree_node::TreeNodeRecursion;
 use datafusion_common::utils::transpose;
 use datafusion_common::{
-    ColumnStatistics, DataFusionError, HashMap, assert_or_internal_err,
-    internal_datafusion_err, internal_err,
+    ColumnStatistics, DataFusionError, HashMap, assert_or_internal_err, internal_err,
 };
 use datafusion_common::{Result, not_impl_err};
 use datafusion_common_runtime::SpawnedTask;
@@ -681,46 +680,8 @@ impl BatchPartitioner {
                     // Finished building index-arrays for output partitions
                     timer.done();
 
-                    // Borrowing partitioner timer to prevent moving `self` to closure
-                    let partitioner_timer = &self.timer;
-
-                    let mut partitioned_batches = vec![];
-                    for (partition, p_indices) in indices.iter_mut().enumerate() {
-                        if !p_indices.is_empty() {
-                            let taken_indices = std::mem::take(p_indices);
-                            let indices_array: PrimitiveArray<UInt32Type> =
-                                taken_indices.into();
-
-                            // Tracking time required for repartitioned batches construction
-                            let _timer = partitioner_timer.timer();
-
-                            // Produce batches based on indices
-                            let columns =
-                                take_arrays(batch.columns(), &indices_array, None)?;
-
-                            let mut options = RecordBatchOptions::new();
-                            options = options.with_row_count(Some(indices_array.len()));
-                            let batch = RecordBatch::try_new_with_options(
-                                batch.schema(),
-                                columns,
-                                &options,
-                            )
-                            .unwrap();
-
-                            partitioned_batches.push(Ok((partition, batch)));
-
-                            // Return the taken vec
-                            let (_, buffer, _) = indices_array.into_parts();
-                            let mut vec =
-                                buffer.into_inner().into_vec::<u32>().map_err(|e| {
-                                    internal_datafusion_err!(
-                                        "Could not convert buffer to vec: {e:?}"
-                                    )
-                                })?;
-                            vec.clear();
-                            *p_indices = vec;
-                        }
-                    }
+                    let partitioned_batches =
+                        Self::partition_grouped_take(&batch, indices, &self.timer)?;
 
                     Box::new(partitioned_batches.into_iter())
                 }
@@ -736,6 +697,66 @@ impl BatchPartitioner {
             BatchPartitionerState::Hash { indices, .. } => indices.len(),
         }
     }
+
+    /// Build repartitioned hash output batches using one `take` per input batch.
+    ///
+    /// The hash router first fills one index vector per output partition. This method
+    /// concatenates those index vectors, performs one grouped `take_arrays`, and
+    /// then returns each output partition as a slice of the reordered batch.
+    ///
+    /// For example, given partition indices:
+    ///
+    /// ```text
+    /// partition 0: [2, 5]
+    /// partition 1: []
+    /// partition 2: [0, 3, 4]
+    /// ```
+    ///
+    /// this method takes rows in `[2, 5, 0, 3, 4]` order once, then returns
+    /// `partition 0 = slice(0, 2)` and `partition 2 = slice(2, 3)`.
+    fn partition_grouped_take(
+        batch: &RecordBatch,
+        indices: &mut [Vec<u32>],
+        timer: &metrics::Time,
+    ) -> Result<Vec<Result<(usize, RecordBatch)>>> {
+        let mut partition_ranges = Vec::with_capacity(indices.len());
+        let mut reordered_indices = Vec::with_capacity(batch.num_rows());
+
+        for (partition, p_indices) in indices.iter_mut().enumerate() {
+            if p_indices.is_empty() {
+                continue;
+            }
+
+            let start = reordered_indices.len();
+            reordered_indices.extend_from_slice(p_indices);
+            partition_ranges.push((partition, start, p_indices.len()));
+            p_indices.clear();
+        }
+
+        if reordered_indices.is_empty() {
+            return Ok(vec![]);
+        }
+
+        let batches = {
+            let _timer = timer.timer();
+            let indices_array: PrimitiveArray<UInt32Type> = reordered_indices.into();
+            let columns = take_arrays(batch.columns(), &indices_array, None)?;
+
+            let mut options = RecordBatchOptions::new();
+            options = options.with_row_count(Some(indices_array.len()));
+            let reordered_batch =
+                RecordBatch::try_new_with_options(batch.schema(), columns, &options)?;
+
+            partition_ranges
+                .into_iter()
+                .map(|(partition, start, len)| {
+                    Ok((partition, reordered_batch.slice(start, len)))
+                })
+                .collect()
+        };
+
+        Ok(batches)
+    }
 }
 
 /// Maps `N` input partitions to `M` output partitions based on a